Subgroups — C₅×#83277 #14415840

Order 1920.

984 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#532	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#948	C₂	1	2	yes	maximal, complemented
3	C₅×#5234	C₂	1	2	yes	maximal, complemented
4	C₅×#5012	C₂	1	2	yes	maximal, complemented
5	C₅×#5011	C₂	1	4	yes	maximal, complemented
6	C₅×D₄×C₃⋊C₈	C₂	1	2	yes	maximal, complemented
7	C₂×C₅×C₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×C₅×#208	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#2935	—	3	1	no	maximal, Hall
10	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
11	C₃×C₅×C₄⋊Q₈	C₄	1	1	yes	characteristic
12	C₃×C₅×#127	C₄	1	1	yes	characteristic
13	C₃×C₅×#124	C₄	1	2	yes	—
14	C₃×C₅×#121	C₄	1	2	yes	—
15	C₃×C₅×#121	C₄	1	2	yes	—
16	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
17	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
18	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
19	C₅×#948	—	2	8	no	—
20	C₂×C₅×#208	C₂²	1	1	yes	characteristic
21	C₂×C₅×#208	C₂²	1	4	yes	—
22	C₂×C₅×#208	C₂²	1	1	yes	characteristic
23	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	—
24	C₂²×C₅×C₃⋊C₈	C₂²	1	4	yes	—
25	C₅×#830	C₂²	1	4	yes	—
26	C₅×#830	C₂²	1	4	yes	—
27	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
28	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	2	yes	—
29	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
30	C₅×#803	C₂²	1	2	yes	—
31	C₄×C₅×C₃⋊C₈	C₂²	1	2	yes	—
32	#83277	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
33	C₂×C₅×#131	—	3	2	no	—
34	C₅×#532	D₃	1	1	yes	characteristic
35	C₅×#436	—	3	2	no	—
36	C₅×#435	—	3	4	no	—
37	C₅×C₈×D₄	—	3	2	no	—
38	C₂×C₅×C₄⋊C₈	—	3	1	no	—
39	C₅×#408	—	3	2	no	—
40	C₄×C₅×M₁₆	—	3	1	no	—
41	C₃×C₅×#41	—	2	4	no	—
42	C₃×C₅×#41	—	2	4	no	—
43	C₂×C₃×C₅×Q₈	C₂×C₄	1	2	yes	—
44	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
45	C₂×C₃×C₅×D₄	C₂×C₄	1	4	yes	—
46	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
47	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
48	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
50	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
51	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
52	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
53	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
54	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	4	yes	—
55	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	4	yes	—
56	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
57	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
58	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
59	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
60	C₅×#208	—	2	2	no	—
61	C₅×#208	—	2	8	no	—
62	C₅×#208	D₄	1	4	yes	complemented
63	C₂×C₅×C₃⋊C₈	—	2	4	no	—
64	C₂×C₅×C₃⋊C₈	—	2	8	no	—
65	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
66	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
67	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
68	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
69	C₃×#532	C₂×C₅	1	1	yes	characteristic
70	C₂×#948	C₂×C₅	1	2	yes	complemented
71	#5234	C₂×C₅	1	2	yes	complemented
72	#5012	C₂×C₅	1	2	yes	complemented
73	#5011	C₂×C₅	1	4	yes	complemented
74	D₄×C₃⋊C₈	C₂×C₅	1	2	yes	complemented
75	C₂×C₄⋊(C₃⋊C₈)	C₂×C₅	1	1	yes	characteristic, complemented
76	C₄×#208	C₂×C₅	1	1	yes	characteristic, complemented
77	C₂×C₅×#41	C₂×D₃	1	2	yes	—
78	C₅×#131	—	6	8	no	—
79	C₂×C₅×M₁₆	—	3	1	no	—
80	C₂×C₅×M₁₆	—	3	1	no	—
81	C₂×C₅×M₁₆	—	3	4	no	—
82	C₂²×C₅×C₈	—	3	2	no	—
83	C₂²×C₅×C₈	—	3	4	no	—
84	C₅×C₄⋊Q₈	Dic₃	1	1	yes	characteristic
85	C₅×#127	Dic₃	1	1	yes	characteristic
86	C₅×#124	Dic₃	1	2	yes	—
87	C₅×#121	Dic₃	1	2	yes	—
88	C₅×#121	Dic₃	1	2	yes	—
89	C₄×C₅×D₄	C₂×D₃	1	2	yes	—
90	C₄×C₅×D₄	C₂×D₃	1	2	yes	—
91	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
92	C₅×C₄⋊C₈	—	3	1	no	—
93	C₅×C₄⋊C₈	—	3	2	no	—
94	C₅×C₄⋊C₈	—	3	1	no	—
95	C₅×C₂²⋊C₈	—	3	4	no	—
96	C₅×C₂²⋊C₈	—	3	4	no	—
97	C₅×#97	—	3	2	no	—
98	C₄×C₅×C₈	—	3	2	no	—
99	#2935	—	3	1	no	Sylow
100	C₂³×C₃×C₅	C₂²×C₄	1	4	yes	—
101	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
102	C₃×C₅×Q₈	—	2	4	no	—
103	C₃×C₅×D₄	—	2	8	no	—
104	C₃×C₅×D₄	—	2	4	no	—
105	C₃×C₅×D₄	—	2	4	no	—
106	C₃×C₅×D₄	—	4	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	—	4	1	no	—
111	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
115	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
118	C₂×C₃×C₄×C₅	#41	1	2	yes	—
119	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
120	C₅×C₃⋊C₈	—	2	2	no	—
121	C₅×C₃⋊C₈	—	2	2	no	—
122	C₅×C₃⋊C₈	—	2	2	no	—
123	C₅×C₃⋊C₈	C₂×D₄	1	4	yes	—
124	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
125	C₃×C₄⋊Q₈	C₄×C₅	1	1	yes	characteristic
126	C₃×#127	C₄×C₅	1	1	yes	characteristic
127	C₃×#124	C₄×C₅	1	2	yes	—
128	C₃×#121	C₄×C₅	1	2	yes	—
129	C₃×#121	C₄×C₅	1	2	yes	—
130	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
131	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
132	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
133	#948	—	2	8	no	—
134	C₂×#208	C₂²×C₅	1	1	yes	characteristic
135	C₂×#208	C₂²×C₅	1	4	yes	—
136	C₂×#208	C₂²×C₅	1	1	yes	characteristic
137	C₂²×C₃⋊C₈	C₂²×C₅	1	2	yes	—
138	C₂²×C₃⋊C₈	C₂²×C₅	1	4	yes	—
139	#830	C₂²×C₅	1	4	yes	—
140	#830	C₂²×C₅	1	4	yes	—
141	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic
142	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	2	yes	—
143	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic
144	#803	C₂²×C₅	1	2	yes	—
145	C₄×C₃⋊C₈	C₂²×C₅	1	2	yes	—
146	C₅×#41	—	2	4	no	—
147	C₅×#41	—	2	4	no	—
148	C₂×C₅×Q₈	C₂×Dic₃	1	2	yes	—
149	C₂×C₅×D₄	C₂×Dic₃	1	2	yes	—
150	C₂×C₅×D₄	C₂×Dic₃	1	4	yes	—
151	C₂×C₅×D₄	C₂×Dic₃	1	2	yes	—
152	C₂×C₅×D₄	C₂×Dic₃	1	2	yes	—
153	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
154	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
155	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
156	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
157	C₅×M₁₆	—	3	4	no	—
158	C₅×M₁₆	—	6	8	no	—
159	C₅×M₁₆	—	6	2	no	—
160	C₂×C₅×C₈	—	3	2	no	—
161	C₂×C₅×C₈	—	3	2	no	—
162	C₂×C₅×C₈	—	3	2	no	—
163	C₂×C₅×C₈	—	3	2	no	—
164	C₂×C₅×C₈	—	6	8	no	—
165	C₂×C₅×C₈	—	6	4	no	—
166	C₅×C₄⋊C₄	C₂×Dic₃	1	2	yes	—
167	C₅×C₄⋊C₄	C₂×Dic₃	1	2	yes	—
168	C₅×C₂²⋊C₄	C₂×Dic₃	1	4	yes	—
169	C₅×C₂²⋊C₄	C₂×Dic₃	1	4	yes	—
170	C₄²×C₅	C₂×Dic₃	1	1	yes	characteristic
171	C₄²×C₅	C₂×Dic₃	1	1	yes	characteristic
172	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
173	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
174	C₂×#131	—	3	2	no	—
175	#532	C₅×D₃	1	1	yes	characteristic
176	#436	—	3	2	no	—
177	#435	—	3	4	no	—
178	C₈×D₄	—	3	2	no	—
179	C₂×C₄⋊C₈	—	3	1	no	—
180	#408	—	3	2	no	—
181	C₄×M₁₆	—	3	1	no	—
182	C₂²×C₃×C₅	—	2	1	no	—
183	C₂²×C₃×C₅	—	2	1	no	—
184	C₂²×C₃×C₅	—	2	4	no	—
185	C₂²×C₃×C₅	—	2	4	no	—
186	C₂²×C₃×C₅	—	2	4	no	—
187	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
188	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
189	C₃×C₄×C₅	—	2	4	no	—
190	C₃×C₄×C₅	—	2	1	no	—
191	C₃×C₄×C₅	—	2	1	no	—
192	C₃×C₄×C₅	—	2	1	no	—
193	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
194	C₃×C₄×C₅	#131	1	2	yes	complemented
195	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
196	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
197	C₃×#41	—	2	4	no	—
198	C₃×#41	—	2	4	no	—
199	C₂×C₃×Q₈	C₂×C₄×C₅	1	2	yes	—
200	C₂×C₃×D₄	C₂×C₄×C₅	1	2	yes	—
201	C₂×C₃×D₄	C₂×C₄×C₅	1	4	yes	—
202	C₂×C₃×D₄	C₂×C₄×C₅	1	2	yes	—
203	C₂×C₃×D₄	C₂×C₄×C₅	1	2	yes	—
204	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
205	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
206	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
207	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
208	C₃×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
209	C₃×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
210	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	4	yes	—
211	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	4	yes	—
212	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
213	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
214	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
215	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
216	#208	—	2	2	no	—
217	#208	—	2	8	no	—
218	#208	C₅×D₄	1	4	yes	complemented
219	C₂×C₃⋊C₈	—	2	4	no	—
220	C₂×C₃⋊C₈	—	2	8	no	—
221	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
222	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
223	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
224	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
225	C₂³×C₅	C₂²×Dic₃	1	4	yes	—
226	C₂³×C₅	C₂²×Dic₃	1	1	yes	characteristic
227	C₅×Q₈	—	2	4	no	—
228	C₅×D₄	—	2	8	no	—
229	C₅×D₄	—	2	4	no	—
230	C₅×D₄	—	2	4	no	—
231	C₅×D₄	—	4	2	no	—
232	C₂×C₄×C₅	—	2	2	no	—
233	C₂×C₄×C₅	—	2	4	no	—
234	C₂×C₄×C₅	—	2	4	no	—
235	C₂×C₄×C₅	—	4	1	no	—
236	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
237	C₂×C₄×C₅	#237	1	2	yes	—
238	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
239	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
240	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
241	C₂×C₄×C₅	C₂²×Dic₃	1	4	yes	—
242	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
243	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
244	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
245	C₅×C₈	—	3	4	no	—
246	C₅×C₈	—	6	2	no	—
247	C₅×C₈	—	6	2	no	—
248	C₅×C₈	—	6	2	no	—
249	C₂×#41	C₂×C₅×D₃	1	2	yes	—
250	#131	—	6	8	no	—
251	C₂×M₁₆	—	3	1	no	—
252	C₂×M₁₆	—	3	4	no	—
253	C₂×M₁₆	—	3	1	no	—
254	C₂²×C₈	—	3	2	no	—
255	C₂²×C₈	—	3	4	no	—
256	C₄⋊Q₈	C₅×Dic₃	1	1	yes	characteristic
257	#127	C₅×Dic₃	1	1	yes	characteristic
258	#124	C₅×Dic₃	1	2	yes	—
259	#121	C₅×Dic₃	1	2	yes	—
260	#121	C₅×Dic₃	1	2	yes	—
261	C₄×D₄	C₂×C₅×D₃	1	2	yes	—
262	C₄×D₄	C₂×C₅×D₃	1	2	yes	—
263	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
264	C₄⋊C₈	—	3	1	no	—
265	C₄⋊C₈	—	3	2	no	—
266	C₄⋊C₈	—	3	1	no	—
267	C₂²⋊C₈	—	3	4	no	—
268	C₂²⋊C₈	—	3	4	no	—
269	#97	—	3	2	no	—
270	C₄×C₈	—	3	2	no	—
271	C₂×C₃×C₅	—	2	2	no	—
272	C₂×C₃×C₅	—	4	4	no	—
273	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
274	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
275	C₂×C₃×C₅	#568	1	1	yes	characteristic
276	C₂³×C₃	C₂²×C₄×C₅	1	4	yes	—
277	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
278	C₃×Q₈	—	2	4	no	—
279	C₃×D₄	—	2	8	no	—
280	C₃×D₄	—	2	4	no	—
281	C₃×D₄	—	2	4	no	—
282	C₃×D₄	—	4	2	no	—
283	C₂×C₃×C₄	—	2	2	no	—
284	C₂×C₃×C₄	—	2	4	no	—
285	C₂×C₃×C₄	—	2	4	no	—
286	C₂×C₃×C₄	—	4	1	no	—
287	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
288	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
289	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
290	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
291	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
292	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
293	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
294	C₂×C₃×C₄	C₅×#41	1	2	yes	—
295	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
296	C₃⋊C₈	—	2	2	no	—
297	C₃⋊C₈	—	2	2	no	—
298	C₃⋊C₈	—	2	2	no	—
299	C₃⋊C₈	C₂×C₅×D₄	1	4	yes	—
300	C₂²×C₅	—	2	1	no	—
301	C₂²×C₅	—	2	1	no	—
302	C₂²×C₅	—	2	4	no	—
303	C₂²×C₅	—	2	4	no	—
304	C₂²×C₅	—	2	4	no	—
305	C₂²×C₅	D₄×Dic₃	1	2	yes	—
306	C₂²×C₅	C₂³×Dic₃	1	1	yes	characteristic
307	C₄×C₅	—	2	4	no	—
308	C₄×C₅	—	2	1	no	—
309	C₄×C₅	—	2	1	no	—
310	C₄×C₅	—	2	1	no	—
311	C₄×C₅	D₄×Dic₃	1	2	yes	—
312	C₄×C₅	#948	1	2	yes	complemented
313	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
314	C₄×C₅	C₂×#237	1	1	yes	characteristic
315	#41	—	2	4	no	—
316	#41	—	2	4	no	—
317	C₂×Q₈	C₂×C₅×Dic₃	1	2	yes	—
318	C₂×D₄	C₂×C₅×Dic₃	1	2	yes	—
319	C₂×D₄	C₂×C₅×Dic₃	1	4	yes	—
320	C₂×D₄	C₂×C₅×Dic₃	1	2	yes	—
321	C₂×D₄	C₂×C₅×Dic₃	1	2	yes	—
322	C₂²×C₄	C₂×C₅×Dic₃	1	1	yes	characteristic
323	C₂²×C₄	C₂×C₅×Dic₃	1	1	yes	characteristic
324	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
325	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
326	M₁₆	—	3	4	no	—
327	M₁₆	—	6	8	no	—
328	M₁₆	—	6	2	no	—
329	C₂×C₈	—	3	2	no	—
330	C₂×C₈	—	3	2	no	—
331	C₂×C₈	—	3	2	no	—
332	C₂×C₈	—	3	2	no	—
333	C₂×C₈	—	6	8	no	—
334	C₂×C₈	—	6	4	no	—
335	C₄⋊C₄	C₂×C₅×Dic₃	1	2	yes	—
336	C₄⋊C₄	C₂×C₅×Dic₃	1	2	yes	—
337	C₂²⋊C₄	C₂×C₅×Dic₃	1	4	yes	—
338	C₂²⋊C₄	C₂×C₅×Dic₃	1	4	yes	—
339	C₄²	C₂×C₅×Dic₃	1	1	yes	characteristic
340	C₄²	C₂×C₅×Dic₃	1	1	yes	characteristic
341	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
342	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
343	C₃×C₅	#2935	1	1	yes	characteristic, complemented, Hall
344	C₂²×C₃	—	2	1	no	—
345	C₂²×C₃	—	2	1	no	—
346	C₂²×C₃	—	2	4	no	—
347	C₂²×C₃	—	2	4	no	—
348	C₂²×C₃	—	2	4	no	—
349	C₂²×C₃	C₄×C₅×D₄	1	2	yes	—
350	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
351	C₃×C₄	—	2	4	no	—
352	C₃×C₄	—	2	1	no	—
353	C₃×C₄	—	2	1	no	—
354	C₃×C₄	—	2	1	no	—
355	C₃×C₄	C₄×C₅×D₄	1	2	yes	—
356	C₃×C₄	C₅×#131	1	2	yes	complemented
357	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
358	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
359	C₂×C₅	—	2	2	no	—
360	C₂×C₅	—	4	4	no	—
361	C₂×C₅	C₂×D₄×Dic₃	1	1	yes	characteristic
362	C₂×C₅	C₂×#948	1	1	yes	characteristic
363	C₂×C₅	#5819	1	1	yes	characteristic
364	C₂³	C₂²×C₅×Dic₃	1	4	yes	—
365	C₂³	C₂²×C₅×Dic₃	1	1	yes	characteristic
366	Q₈	—	2	4	no	—
367	D₄	—	2	8	no	—
368	D₄	—	2	4	no	—
369	D₄	—	2	4	no	—
370	D₄	—	4	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
376	C₂×C₄	C₅×#237	1	2	yes	—
377	C₂×C₄	C₂²×C₅×Dic₃	1	1	yes	characteristic
378	C₂×C₄	C₂²×C₅×Dic₃	1	1	yes	characteristic
379	C₂×C₄	C₂²×C₅×Dic₃	1	1	yes	characteristic
380	C₂×C₄	C₂²×C₅×Dic₃	1	4	yes	—
381	C₂×C₄	C₂²×C₅×Dic₃	1	1	yes	characteristic
382	C₂×C₄	C₂²×C₅×Dic₃	1	1	yes	characteristic
383	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
384	C₈	—	3	4	no	—
385	C₈	—	6	2	no	—
386	C₈	—	6	2	no	—
387	C₈	—	6	2	no	—
388	C₂×C₃	—	2	2	no	—
389	C₂×C₃	—	4	4	no	—
390	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
391	C₂×C₃	C₂×C₅×#131	1	1	yes	characteristic
392	C₂×C₃	C₅×#568	1	1	yes	characteristic
393	C₅	#83277	1	1	yes	characteristic, direct product factor, Sylow
394	C₂²	—	2	1	no	—
395	C₂²	—	2	1	no	—
396	C₂²	—	2	4	no	—
397	C₂²	—	2	4	no	—
398	C₂²	—	2	4	no	—
399	C₂²	C₅×D₄×Dic₃	1	2	yes	—
400	C₂²	C₂³×C₅×Dic₃	1	1	yes	characteristic
401	C₄	—	2	4	no	—
402	C₄	—	2	1	no	—
403	C₄	—	2	1	no	—
404	C₄	—	2	1	no	—
405	C₄	C₅×D₄×Dic₃	1	2	yes	—
406	C₄	C₅×#948	1	2	yes	complemented
407	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
408	C₄	C₂×C₅×#237	1	1	yes	characteristic
409	C₃	C₅×#2935	1	1	yes	characteristic, complemented, Sylow
410	C₂	—	2	2	no	—
411	C₂	—	4	4	no	—
412	C₂	C₂×C₅×D₄×Dic₃	1	1	yes	characteristic
413	C₂	C₂×C₅×#948	1	1	yes	characteristic
414	C₂	C₅×#5819	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting, prime radical	C₃×C₅×#532	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₅×#532	D₃
hypocenter	C₃	C₅×#2935
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₅×#532

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#948	C₂	semidirect
3. C₅×#5234	C₂	semidirect
4. C₅×#5012	C₂	semidirect
5. C₅×#5011	C₂	semidirect
6. C₅×D₄×C₃⋊C₈	C₂	semidirect
7. C₂×C₅×C₄⋊(C₃⋊C₈)	C₂	semidirect
8. C₄×C₅×#208	C₂	semidirect
32. #83277	C₅	direct (N × H)
62. C₅×#208	D₄	semidirect
70. C₂×#948	C₂×C₅	semidirect
71. #5234	C₂×C₅	semidirect
72. #5012	C₂×C₅	semidirect
73. #5011	C₂×C₅	semidirect
74. D₄×C₃⋊C₈	C₂×C₅	semidirect
75. C₂×C₄⋊(C₃⋊C₈)	C₂×C₅	semidirect
76. C₄×#208	C₂×C₅	semidirect
194. C₃×C₄×C₅	#131	semidirect
218. #208	C₅×D₄	semidirect
312. C₄×C₅	#948	semidirect
343. C₃×C₅	#2935	semidirect
356. C₃×C₄	C₅×#131	semidirect
393. C₅	#83277	direct (N × H)
406. C₄	C₅×#948	semidirect
409. C₃	C₅×#2935	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#532	2
C₂×C₅×#948	2
C₅×#5234	2
C₅×#5012	2
C₅×#5011	2
C₅×D₄×C₃⋊C₈	2
C₂×C₅×C₄⋊(C₃⋊C₈)	2
C₄×C₅×#208	2
C₅×#2935	3
#83277	5

Subgroups — C5×#83277 #14415840

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#83277 #14415840