Subgroups — C₅×#74225 #14322893

Order 1920.

1200 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#892	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×D₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#872	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#382	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4977	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4975	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4935	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4668	C₂	1	4	yes	maximal
9	C₅×#4647	C₂	1	4	yes	maximal, complemented
10	C₅×#2317	—	3	1	no	maximal, Hall
11	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
12	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
16	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
17	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
18	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
19	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
20	C₂×C₅×C₄⋊Dic₃	C₂²	1	4	yes	—
21	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
22	C₂×C₅×Dic₃⋊C₄	C₂²	1	4	yes	—
23	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
24	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
25	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
26	C₅×#892	—	2	4	no	—
27	C₅×D₃×C₄⋊C₄	—	2	4	no	—
28	C₅×#872	C₄	1	8	yes	complemented
29	C₃×C₅×#95	C₂²	1	4	yes	—
30	C₅×C₃⋊#95	C₂²	1	4	yes	—
31	#74225	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
32	C₂×C₅×#117	—	3	1	no	—
33	C₂×C₅×#117	—	3	1	no	—
34	C₂²×C₅×C₄⋊C₄	—	3	1	no	—
35	C₅×#389	—	3	4	no	—
36	C₅×#385	—	3	4	no	—
37	C₅×#384	—	3	1	no	—
38	C₅×#384	—	3	1	no	—
39	C₅×#382	—	3	1	no	—
40	C₅×#382	D₃	1	1	yes	characteristic, complemented
41	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
42	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
43	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
44	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
45	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
46	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
47	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
48	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
49	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
50	C₂×C₄×C₅×D₃	—	2	4	no	—
51	C₂×C₄×C₅×D₃	—	4	4	no	—
52	C₂×C₄×C₅×D₃	C₂×C₄	1	4	yes	—
53	C₂×C₄×C₅×D₃	D₄	1	4	yes	—
54	C₂×C₄×C₅×D₃	Q₈	1	4	yes	—
55	C₃×C₅×C₄⋊C₄	—	2	2	no	—
56	C₃×C₅×C₄⋊C₄	—	2	2	no	—
57	C₃×C₄²×C₅	C₂×C₄	1	4	yes	complemented
58	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
59	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	8	yes	—
60	C₅×C₄⋊Dic₃	—	2	2	no	—
61	C₅×C₄⋊Dic₃	—	2	2	no	—
62	C₅×C₄⋊Dic₃	—	4	4	no	—
63	C₅×Dic₃⋊C₄	—	2	4	no	—
64	C₅×Dic₃⋊C₄	—	4	4	no	—
65	C₅×Dic₃⋊C₄	C₂×C₄	1	8	yes	complemented
66	C₄×C₅×Dic₃	—	2	4	no	—
67	C₄×C₅×Dic₃	C₂×C₄	1	4	yes	complemented
68	C₂×#892	C₂×C₅	1	1	yes	characteristic
69	C₂×D₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
70	C₂×#872	C₂×C₅	1	1	yes	characteristic
71	C₃×#382	C₂×C₅	1	1	yes	characteristic, complemented
72	#4977	C₂×C₅	1	1	yes	characteristic, complemented
73	#4975	C₂×C₅	1	1	yes	characteristic, complemented
74	#4935	C₂×C₅	1	1	yes	characteristic, complemented
75	#4668	C₂×C₅	1	4	yes	—
76	#4647	C₂×C₅	1	4	yes	complemented
77	C₂³×C₄×C₅	—	3	1	no	—
78	C₂³×C₄×C₅	—	3	2	no	—
79	C₅×#117	—	3	8	no	—
80	C₅×#117	—	6	4	no	—
81	C₂×C₅×C₄⋊C₄	—	3	2	no	—
82	C₂×C₅×C₄⋊C₄	—	3	1	no	—
83	C₂×C₅×C₄⋊C₄	—	3	1	no	—
84	C₂×C₅×C₄⋊C₄	—	3	2	no	—
85	C₂×C₅×C₄⋊C₄	—	3	4	no	—
86	C₂×C₅×C₄⋊C₄	—	3	4	no	—
87	C₂×C₅×C₄⋊C₄	—	6	4	no	—
88	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
89	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
90	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
91	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
92	C₂×C₄²×C₅	—	3	1	no	—
93	C₂×C₄²×C₅	—	3	2	no	—
94	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
95	C₅×#95	—	3	4	no	—
96	C₅×#95	C₂×D₃	1	4	yes	—
97	#2317	—	3	1	no	Sylow
98	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
99	C₂²×C₅×D₃	—	2	2	no	—
100	C₂²×C₅×D₃	—	2	2	no	—
101	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
102	C₂²×C₅×D₃	C₂×D₄	1	2	yes	—
103	C₂²×C₅×D₃	C₂×Q₈	1	2	yes	—
104	C₂×C₃×C₄×C₅	—	2	2	no	—
105	C₂×C₃×C₄×C₅	—	2	2	no	—
106	C₂×C₃×C₄×C₅	—	2	2	no	—
107	C₂×C₃×C₄×C₅	—	2	2	no	—
108	C₂×C₃×C₄×C₅	—	2	4	no	—
109	C₂×C₃×C₄×C₅	—	2	4	no	—
110	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
111	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
112	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
113	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
114	C₂×C₅×Dic₃	—	2	2	no	—
115	C₂×C₅×Dic₃	—	2	2	no	—
116	C₂×C₅×Dic₃	—	2	2	no	—
117	C₂×C₅×Dic₃	—	2	2	no	—
118	C₂×C₅×Dic₃	—	2	4	no	—
119	C₂×C₅×Dic₃	—	2	4	no	—
120	C₂×C₅×Dic₃	C₂²×C₄	1	4	yes	—
121	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
122	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
123	C₂×C₅×Dic₃	C₂×Q₈	1	2	yes	—
124	C₄×C₅×D₃	—	4	8	no	—
125	C₄×C₅×D₃	C₄⋊C₄	1	16	yes	complemented
126	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
127	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
128	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
129	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
130	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
131	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
132	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
133	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
134	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
135	C₂×C₄⋊Dic₃	C₂²×C₅	1	4	yes	—
136	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
137	C₂×Dic₃⋊C₄	C₂²×C₅	1	4	yes	—
138	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
139	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
140	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
141	#892	—	2	4	no	—
142	D₃×C₄⋊C₄	—	2	4	no	—
143	#872	C₄×C₅	1	8	yes	complemented
144	C₃×#95	C₂²×C₅	1	4	yes	—
145	C₃⋊#95	C₂²×C₅	1	4	yes	—
146	C₂⁴×C₅	—	3	1	no	—
147	C₂²×C₄×C₅	—	3	1	no	—
148	C₂²×C₄×C₅	—	3	4	no	—
149	C₂²×C₄×C₅	—	3	4	no	—
150	C₂²×C₄×C₅	—	3	4	no	—
151	C₂²×C₄×C₅	—	3	2	no	—
152	C₂²×C₄×C₅	—	3	2	no	—
153	C₂²×C₄×C₅	—	3	2	no	—
154	C₂²×C₄×C₅	—	6	4	no	—
155	C₂²×C₄×C₅	—	12	4	no	—
156	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
157	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
158	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
159	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
160	C₅×C₄⋊C₄	—	2	2	no	—
161	C₅×C₄⋊C₄	—	2	2	no	—
162	C₅×C₄⋊C₄	—	3	8	no	—
163	C₅×C₄⋊C₄	—	6	4	no	—
164	C₅×C₄⋊C₄	—	6	2	no	—
165	C₅×C₄⋊C₄	—	6	2	no	—
166	C₅×C₄⋊C₄	—	12	4	no	—
167	C₅×C₄⋊C₄	—	12	4	no	—
168	C₅×C₂²⋊C₄	—	3	8	no	—
169	C₅×C₂²⋊C₄	—	6	4	no	—
170	C₄²×C₅	—	3	4	no	—
171	C₄²×C₅	—	6	4	no	—
172	C₄²×C₅	C₄×D₃	1	4	yes	complemented
173	C₂×#117	—	3	1	no	—
174	C₂×#117	—	3	1	no	—
175	C₂²×C₄⋊C₄	—	3	1	no	—
176	#389	—	3	4	no	—
177	#385	—	3	4	no	—
178	#384	—	3	1	no	—
179	#384	—	3	1	no	—
180	#382	—	3	1	no	—
181	#382	C₅×D₃	1	1	yes	characteristic, complemented
182	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
183	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
184	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
185	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
186	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
187	C₂×C₅×D₃	—	2	4	no	—
188	C₂×C₅×D₃	—	2	2	no	—
189	C₂×C₅×D₃	—	2	2	no	—
190	C₂×C₅×D₃	—	2	4	no	—
191	C₂×C₅×D₃	C₂×C₄⋊C₄	1	4	yes	—
192	C₃×C₄×C₅	—	2	4	no	—
193	C₃×C₄×C₅	—	4	2	no	—
194	C₃×C₄×C₅	—	4	2	no	—
195	C₃×C₄×C₅	C₂×C₄⋊C₄	1	4	yes	—
196	C₅×Dic₃	—	2	4	no	—
197	C₅×Dic₃	—	4	2	no	—
198	C₅×Dic₃	—	4	2	no	—
199	C₅×Dic₃	C₂×C₄⋊C₄	1	4	yes	—
200	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
201	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
202	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
203	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
204	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
205	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
206	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
207	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
208	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
209	C₂×C₄×D₃	—	2	4	no	—
210	C₂×C₄×D₃	—	4	4	no	—
211	C₂×C₄×D₃	C₂×C₄×C₅	1	4	yes	—
212	C₂×C₄×D₃	C₅×D₄	1	4	yes	—
213	C₂×C₄×D₃	C₅×Q₈	1	4	yes	—
214	C₃×C₄⋊C₄	—	2	2	no	—
215	C₃×C₄⋊C₄	—	2	2	no	—
216	C₃×C₄²	C₂×C₄×C₅	1	4	yes	complemented
217	(C₂×D₃)⋊C₄	—	2	4	no	—
218	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	8	yes	—
219	C₄⋊Dic₃	—	2	2	no	—
220	C₄⋊Dic₃	—	2	2	no	—
221	C₄⋊Dic₃	—	4	4	no	—
222	Dic₃⋊C₄	—	2	4	no	—
223	Dic₃⋊C₄	—	4	4	no	—
224	Dic₃⋊C₄	C₂×C₄×C₅	1	8	yes	complemented
225	C₄×Dic₃	—	2	4	no	—
226	C₄×Dic₃	C₂×C₄×C₅	1	4	yes	complemented
227	C₂³×C₅	—	3	2	no	—
228	C₂³×C₅	—	3	2	no	—
229	C₂³×C₅	—	3	2	no	—
230	C₂³×C₅	—	6	2	no	—
231	C₂³×C₅	—	6	2	no	—
232	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
233	C₂×C₄×C₅	—	2	2	no	—
234	C₂×C₄×C₅	—	2	2	no	—
235	C₂×C₄×C₅	—	2	2	no	—
236	C₂×C₄×C₅	—	2	2	no	—
237	C₂×C₄×C₅	—	2	4	no	—
238	C₂×C₄×C₅	—	2	4	no	—
239	C₂×C₄×C₅	—	3	2	no	—
240	C₂×C₄×C₅	—	3	2	no	—
241	C₂×C₄×C₅	—	3	2	no	—
242	C₂×C₄×C₅	—	3	16	no	—
243	C₂×C₄×C₅	—	3	4	no	—
244	C₂×C₄×C₅	—	6	2	no	—
245	C₂×C₄×C₅	—	6	2	no	—
246	C₂×C₄×C₅	—	6	2	no	—
247	C₂×C₄×C₅	—	6	2	no	—
248	C₂×C₄×C₅	—	6	4	no	—
249	C₂×C₄×C₅	—	6	4	no	—
250	C₂×C₄×C₅	—	12	8	no	—
251	C₂×C₄×C₅	C₂×C₄×D₃	1	4	yes	—
252	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
253	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
254	C₂×C₄×C₅	D₃×Q₈	1	2	yes	—
255	C₂³×C₄	—	3	1	no	—
256	C₂³×C₄	—	3	2	no	—
257	#117	—	3	8	no	—
258	#117	—	6	4	no	—
259	C₂×C₄⋊C₄	—	3	2	no	—
260	C₂×C₄⋊C₄	—	3	1	no	—
261	C₂×C₄⋊C₄	—	3	2	no	—
262	C₂×C₄⋊C₄	—	3	1	no	—
263	C₂×C₄⋊C₄	—	3	4	no	—
264	C₂×C₄⋊C₄	—	3	4	no	—
265	C₂×C₄⋊C₄	—	6	4	no	—
266	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
267	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
268	C₂×C₂²⋊C₄	—	3	2	no	—
269	C₂×C₂²⋊C₄	—	3	2	no	—
270	C₂×C₄²	—	3	1	no	—
271	C₂×C₄²	—	3	2	no	—
272	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
273	#95	—	3	4	no	—
274	#95	C₂×C₅×D₃	1	4	yes	—
275	C₂×C₃×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
276	C₂×C₃×C₅	#520	1	2	yes	—
277	C₂×C₃×C₅	#535	1	1	yes	characteristic
278	C₂×C₃×C₅	#536	1	1	yes	characteristic
279	C₂×C₃×C₅	#544	1	2	yes	—
280	C₅×D₃	—	2	4	no	—
281	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
282	C₂²×D₃	—	2	2	no	—
283	C₂²×D₃	—	2	2	no	—
284	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
285	C₂²×D₃	C₂×C₅×D₄	1	2	yes	—
286	C₂²×D₃	C₂×C₅×Q₈	1	2	yes	—
287	C₂×C₃×C₄	—	2	2	no	—
288	C₂×C₃×C₄	—	2	2	no	—
289	C₂×C₃×C₄	—	2	2	no	—
290	C₂×C₃×C₄	—	2	2	no	—
291	C₂×C₃×C₄	—	2	4	no	—
292	C₂×C₃×C₄	—	2	4	no	—
293	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
294	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
295	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
296	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
297	C₂×Dic₃	—	2	2	no	—
298	C₂×Dic₃	—	2	2	no	—
299	C₂×Dic₃	—	2	2	no	—
300	C₂×Dic₃	—	2	2	no	—
301	C₂×Dic₃	—	2	4	no	—
302	C₂×Dic₃	—	2	4	no	—
303	C₂×Dic₃	C₂²×C₄×C₅	1	4	yes	—
304	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
305	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
306	C₂×Dic₃	C₂×C₅×Q₈	1	2	yes	—
307	C₄×D₃	—	4	8	no	—
308	C₄×D₃	C₅×C₄⋊C₄	1	16	yes	complemented
309	C₂²×C₅	—	3	4	no	—
310	C₂²×C₅	—	6	2	no	—
311	C₂²×C₅	—	6	2	no	—
312	C₂²×C₅	—	6	4	no	—
313	C₂²×C₅	—	6	4	no	—
314	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
315	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
316	C₂²×C₅	C₂×D₃×Q₈	1	1	yes	characteristic
317	C₂²×C₅	#1009	1	2	yes	—
318	C₂²×C₅	#1010	1	2	yes	—
319	C₄×C₅	—	2	4	no	—
320	C₄×C₅	—	3	4	no	—
321	C₄×C₅	—	4	2	no	—
322	C₄×C₅	—	4	2	no	—
323	C₄×C₅	—	6	4	no	—
324	C₄×C₅	—	12	2	no	—
325	C₄×C₅	—	12	2	no	—
326	C₄×C₅	D₃×C₄⋊C₄	1	4	yes	—
327	C₂⁴	—	3	1	no	—
328	C₂²×C₄	—	3	1	no	—
329	C₂²×C₄	—	3	4	no	—
330	C₂²×C₄	—	3	4	no	—
331	C₂²×C₄	—	3	4	no	—
332	C₂²×C₄	—	3	2	no	—
333	C₂²×C₄	—	3	2	no	—
334	C₂²×C₄	—	3	2	no	—
335	C₂²×C₄	—	6	4	no	—
336	C₂²×C₄	—	12	4	no	—
337	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
338	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
339	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
340	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	3	8	no	—
344	C₄⋊C₄	—	6	4	no	—
345	C₄⋊C₄	—	6	2	no	—
346	C₄⋊C₄	—	6	2	no	—
347	C₄⋊C₄	—	12	4	no	—
348	C₄⋊C₄	—	12	4	no	—
349	C₂²⋊C₄	—	3	8	no	—
350	C₂²⋊C₄	—	6	4	no	—
351	C₄²	—	3	4	no	—
352	C₄²	—	6	4	no	—
353	C₄²	C₄×C₅×D₃	1	4	yes	complemented
354	C₃×C₅	#2317	1	1	yes	characteristic, complemented, Hall
355	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
356	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
357	C₂²×C₃	C₂²×C₅×Q₈	1	1	yes	characteristic
358	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
359	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
360	C₂×D₃	—	2	4	no	—
361	C₂×D₃	—	2	2	no	—
362	C₂×D₃	—	2	2	no	—
363	C₂×D₃	—	2	4	no	—
364	C₂×D₃	C₂×C₅×C₄⋊C₄	1	4	yes	—
365	C₃×C₄	—	2	4	no	—
366	C₃×C₄	—	4	2	no	—
367	C₃×C₄	—	4	2	no	—
368	C₃×C₄	C₂×C₅×C₄⋊C₄	1	4	yes	—
369	Dic₃	—	2	4	no	—
370	Dic₃	—	4	2	no	—
371	Dic₃	—	4	2	no	—
372	Dic₃	C₂×C₅×C₄⋊C₄	1	4	yes	—
373	C₂×C₅	—	6	4	no	—
374	C₂×C₅	C₂×D₃×C₄⋊C₄	1	1	yes	characteristic
375	C₂×C₅	#5523	1	2	yes	—
376	C₂×C₅	#5674	1	1	yes	characteristic
377	C₂×C₅	#5675	1	1	yes	characteristic
378	C₂×C₅	#5689	1	2	yes	—
379	C₂³	—	3	2	no	—
380	C₂³	—	3	2	no	—
381	C₂³	—	3	2	no	—
382	C₂³	—	6	2	no	—
383	C₂³	—	6	2	no	—
384	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	3	2	no	—
392	C₂×C₄	—	3	2	no	—
393	C₂×C₄	—	3	2	no	—
394	C₂×C₄	—	3	16	no	—
395	C₂×C₄	—	3	4	no	—
396	C₂×C₄	—	6	2	no	—
397	C₂×C₄	—	6	2	no	—
398	C₂×C₄	—	6	2	no	—
399	C₂×C₄	—	6	2	no	—
400	C₂×C₄	—	6	4	no	—
401	C₂×C₄	—	6	4	no	—
402	C₂×C₄	—	12	8	no	—
403	C₂×C₄	C₂×C₄×C₅×D₃	1	4	yes	—
404	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
405	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
406	C₂×C₄	C₅×D₃×Q₈	1	2	yes	—
407	C₂×C₃	C₂²×C₅×C₄⋊C₄	1	1	yes	characteristic
408	C₂×C₃	C₅×#520	1	2	yes	—
409	C₂×C₃	C₅×#535	1	1	yes	characteristic
410	C₂×C₃	C₅×#536	1	1	yes	characteristic
411	C₂×C₃	C₅×#544	1	2	yes	—
412	D₃	—	2	4	no	—
413	C₅	#74225	1	1	yes	characteristic, direct product factor, Sylow
414	C₂²	—	3	4	no	—
415	C₂²	—	6	2	no	—
416	C₂²	—	6	2	no	—
417	C₂²	—	6	4	no	—
418	C₂²	—	6	4	no	—
419	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
420	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
421	C₂²	C₂×C₅×D₃×Q₈	1	1	yes	characteristic
422	C₂²	C₅×#1009	1	2	yes	—
423	C₂²	C₅×#1010	1	2	yes	—
424	C₄	—	2	4	no	—
425	C₄	—	3	4	no	—
426	C₄	—	4	2	no	—
427	C₄	—	4	2	no	—
428	C₄	—	6	4	no	—
429	C₄	—	12	2	no	—
430	C₄	—	12	2	no	—
431	C₄	C₅×D₃×C₄⋊C₄	1	4	yes	—
432	C₃	C₅×#2317	1	1	yes	characteristic, complemented, Sylow
433	C₂	—	6	4	no	—
434	C₂	C₂×C₅×D₃×C₄⋊C₄	1	1	yes	characteristic
435	C₂	C₅×#5523	1	2	yes	—
436	C₂	C₅×#5674	1	1	yes	characteristic
437	C₂	C₅×#5675	1	1	yes	characteristic
438	C₂	C₅×#5689	1	2	yes	—

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂³	C₂³×C₅×D₃
Fitting	C₃×C₅×#382	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂³×C₅×D₃	C₂³
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₅×#382	D₃
hypocenter	C₃	C₅×#2317
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₅×#382

Complements

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

N	H ≅ G/N	type
4. C₃×C₅×#382	C₂	semidirect
5. C₅×#4977	C₂	semidirect
6. C₅×#4975	C₂	semidirect
7. C₅×#4935	C₂	semidirect
9. C₅×#4647	C₂	semidirect
28. C₅×#872	C₄	semidirect
31. #74225	C₅	direct (N × H)
40. C₅×#382	D₃	semidirect
57. C₃×C₄²×C₅	C₂×C₄	semidirect
65. C₅×Dic₃⋊C₄	C₂×C₄	semidirect
67. C₄×C₅×Dic₃	C₂×C₄	semidirect
71. C₃×#382	C₂×C₅	semidirect
72. #4977	C₂×C₅	semidirect
73. #4975	C₂×C₅	semidirect
74. #4935	C₂×C₅	semidirect
76. #4647	C₂×C₅	semidirect
125. C₄×C₅×D₃	C₄⋊C₄	semidirect
143. #872	C₄×C₅	semidirect
172. C₄²×C₅	C₄×D₃	semidirect
181. #382	C₅×D₃	semidirect
216. C₃×C₄²	C₂×C₄×C₅	semidirect
224. Dic₃⋊C₄	C₂×C₄×C₅	semidirect
226. C₄×Dic₃	C₂×C₄×C₅	semidirect
308. C₄×D₃	C₅×C₄⋊C₄	semidirect
353. C₄²	C₄×C₅×D₃	semidirect
354. C₃×C₅	#2317	semidirect
413. C₅	#74225	direct (N × H)
432. C₃	C₅×#2317	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#892	2
C₂×C₅×D₃×C₄⋊C₄	2
C₂×C₅×#872	2
C₃×C₅×#382	2
C₅×#4977	2
C₅×#4975	2
C₅×#4935	2
C₅×#4668	2
C₅×#4647	2
C₅×#2317	3
#74225	5

Subgroups — C5×#74225 #14322893

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#74225 #14322893