Subgroups — C₅×#83128 #14419592

Order 1920.

744 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#529	C₂	1	1	yes	maximal, characteristic
2	C₅×#5024	C₂	1	2	yes	maximal, complemented
3	C₅×#5011	C₂	1	2	yes	maximal, complemented
4	C₅×#5011	C₂	1	2	yes	maximal, complemented
5	C₅×D₄×C₃⋊C₈	C₂	1	2	yes	maximal, complemented
6	C₅×#5000	C₂	1	2	yes	maximal, complemented
7	C₅×#4997	C₂	1	2	yes	maximal, complemented
8	C₅×#4925	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×#803	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#2968	—	3	1	no	maximal, Hall
11	C₃×C₅×#126	C₄	1	2	yes	—
12	C₃×C₅×#125	C₄	1	1	yes	characteristic
13	C₃×C₅×#124	C₄	1	1	yes	characteristic
14	C₃×C₅×#123	C₄	1	2	yes	—
15	C₃×C₅×C₂²⋊Q₈	C₄	1	1	yes	characteristic
16	C₃×C₅×#121	C₄	1	1	yes	characteristic
17	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
18	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
19	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
20	C₃×C₅×#117	C₂²	1	2	yes	—
21	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
22	C₂×C₅×#208	C₂²	1	2	yes	—
23	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	—
24	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	—
25	C₅×#830	C₂²	1	1	yes	characteristic
26	C₅×#830	C₂²	1	1	yes	characteristic
27	C₅×#830	C₂²	1	2	yes	—
28	C₅×#830	C₂²	1	2	yes	—
29	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	2	yes	—
30	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	2	yes	—
31	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	2	yes	—
32	C₅×#803	C₂²	1	1	yes	characteristic
33	C₅×#803	C₂²	1	1	yes	characteristic
34	C₅×#803	C₂²	1	2	yes	—
35	C₅×#803	C₂²	1	2	yes	—
36	C₄×C₅×C₃⋊C₈	C₂²	1	2	yes	—
37	C₄×C₅×C₃⋊C₈	C₂²	1	2	yes	—
38	#83128	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
39	C₅×#529	D₃	1	1	yes	characteristic
40	C₅×#446	—	3	2	no	—
41	C₅×#435	—	3	2	no	—
42	C₅×#435	—	3	2	no	—
43	C₅×C₈×D₄	—	3	2	no	—
44	C₅×#433	—	3	2	no	—
45	C₅×#431	—	3	1	no	—
46	C₅×#405	—	3	2	no	—
47	C₂×C₅×#97	—	3	1	no	—
48	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
49	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
50	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
53	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
54	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
55	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
56	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
57	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
58	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
59	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
60	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
61	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
62	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
63	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
64	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
65	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
66	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
67	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
68	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
69	C₃×C₄²×C₅	C₂³	1	2	yes	—
70	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
71	C₅×#208	—	2	4	no	—
72	C₂×C₅×C₃⋊C₈	—	2	4	no	—
73	C₂×C₅×C₃⋊C₈	—	2	4	no	—
74	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
75	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
76	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
77	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
78	C₃×#529	C₂×C₅	1	1	yes	characteristic
79	#5024	C₂×C₅	1	2	yes	complemented
80	#5011	C₂×C₅	1	2	yes	complemented
81	#5011	C₂×C₅	1	2	yes	complemented
82	D₄×C₃⋊C₈	C₂×C₅	1	2	yes	complemented
83	#5000	C₂×C₅	1	2	yes	complemented
84	#4997	C₂×C₅	1	2	yes	complemented
85	#4925	C₂×C₅	1	1	yes	characteristic, complemented
86	C₂×#803	C₂×C₅	1	1	yes	characteristic, complemented
87	C₂×C₅×M₁₆	—	3	2	no	—
88	C₂²×C₅×C₈	—	3	2	no	—
89	C₂²×C₅×C₈	—	3	2	no	—
90	C₅×#126	Dic₃	1	2	yes	—
91	C₅×#125	Dic₃	1	1	yes	characteristic
92	C₅×#124	Dic₃	1	1	yes	characteristic
93	C₅×#123	Dic₃	1	2	yes	—
94	C₅×C₂²⋊Q₈	Dic₃	1	1	yes	characteristic
95	C₅×#121	Dic₃	1	1	yes	characteristic
96	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
97	C₄×C₅×D₄	C₂×D₃	1	2	yes	—
98	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
99	C₅×#117	C₂×D₃	1	2	yes	—
100	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
101	C₅×C₄⋊C₈	—	3	2	no	—
102	C₅×C₄⋊C₈	—	3	2	no	—
103	C₅×C₄⋊C₈	—	3	2	no	—
104	C₅×C₂²⋊C₈	—	3	1	no	—
105	C₅×C₂²⋊C₈	—	3	1	no	—
106	C₅×C₂²⋊C₈	—	3	2	no	—
107	C₅×C₂²⋊C₈	—	3	2	no	—
108	C₅×#97	—	3	1	no	—
109	C₅×#97	—	3	1	no	—
110	C₅×#97	—	3	2	no	—
111	C₅×#97	—	3	2	no	—
112	C₄×C₅×C₈	—	3	2	no	—
113	C₄×C₅×C₈	—	3	2	no	—
114	#2968	—	3	1	no	Sylow
115	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
116	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
117	C₃×C₅×Q₈	—	4	1	no	—
118	C₃×C₅×D₄	—	2	4	no	—
119	C₃×C₅×D₄	—	4	1	no	—
120	C₂×C₃×C₄×C₅	—	2	2	no	—
121	C₂×C₃×C₄×C₅	—	2	2	no	—
122	C₂×C₃×C₄×C₅	—	2	2	no	—
123	C₂×C₃×C₄×C₅	—	2	2	no	—
124	C₂×C₃×C₄×C₅	—	4	1	no	—
125	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
131	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
132	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
133	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
134	C₅×C₃⋊C₈	—	2	2	no	—
135	C₅×C₃⋊C₈	—	2	2	no	—
136	C₅×C₃⋊C₈	—	2	2	no	—
137	C₅×C₃⋊C₈	#41	1	4	yes	—
138	C₃×#126	C₄×C₅	1	2	yes	—
139	C₃×#125	C₄×C₅	1	1	yes	characteristic
140	C₃×#124	C₄×C₅	1	1	yes	characteristic
141	C₃×#123	C₄×C₅	1	2	yes	—
142	C₃×C₂²⋊Q₈	C₄×C₅	1	1	yes	characteristic
143	C₃×#121	C₄×C₅	1	1	yes	characteristic
144	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
145	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
146	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
147	C₃×#117	C₂²×C₅	1	2	yes	—
148	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
149	C₂×#208	C₂²×C₅	1	2	yes	—
150	C₂²×C₃⋊C₈	C₂²×C₅	1	2	yes	—
151	C₂²×C₃⋊C₈	C₂²×C₅	1	2	yes	—
152	#830	C₂²×C₅	1	1	yes	characteristic
153	#830	C₂²×C₅	1	1	yes	characteristic
154	#830	C₂²×C₅	1	2	yes	—
155	#830	C₂²×C₅	1	2	yes	—
156	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	2	yes	—
157	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	2	yes	—
158	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	2	yes	—
159	#803	C₂²×C₅	1	1	yes	characteristic
160	#803	C₂²×C₅	1	1	yes	characteristic
161	#803	C₂²×C₅	1	2	yes	—
162	#803	C₂²×C₅	1	2	yes	—
163	C₄×C₃⋊C₈	C₂²×C₅	1	2	yes	—
164	C₄×C₃⋊C₈	C₂²×C₅	1	2	yes	—
165	C₂×C₅×Q₈	C₂×Dic₃	1	1	yes	characteristic
166	C₂×C₅×D₄	C₂×Dic₃	1	2	yes	—
167	C₂×C₅×D₄	C₂×Dic₃	1	1	yes	characteristic
168	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
169	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
170	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
171	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
172	C₅×M₁₆	—	6	4	no	—
173	C₂×C₅×C₈	—	3	2	no	—
174	C₂×C₅×C₈	—	3	2	no	—
175	C₂×C₅×C₈	—	3	2	no	—
176	C₂×C₅×C₈	—	3	2	no	—
177	C₂×C₅×C₈	—	6	4	no	—
178	C₂×C₅×C₈	—	6	4	no	—
179	C₅×C₄⋊C₄	C₂×Dic₃	1	2	yes	—
180	C₅×C₄⋊C₄	C₂×Dic₃	1	2	yes	—
181	C₅×C₄⋊C₄	C₂×Dic₃	1	1	yes	characteristic
182	C₅×C₄⋊C₄	C₂×Dic₃	1	2	yes	—
183	C₅×C₄⋊C₄	C₂×Dic₃	1	1	yes	characteristic
184	C₅×C₄⋊C₄	C₂×Dic₃	1	2	yes	—
185	C₅×C₂²⋊C₄	C₂×Dic₃	1	2	yes	—
186	C₅×C₂²⋊C₄	C₂×Dic₃	1	2	yes	—
187	C₅×C₂²⋊C₄	C₂×Dic₃	1	2	yes	—
188	C₅×C₂²⋊C₄	C₂×Dic₃	1	2	yes	—
189	C₅×C₂²⋊C₄	C₂×Dic₃	1	2	yes	—
190	C₄²×C₅	C₂×Dic₃	1	1	yes	characteristic
191	C₄²×C₅	C₂×Dic₃	1	1	yes	characteristic
192	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
193	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
194	C₄²×C₅	C₂²×D₃	1	2	yes	—
195	#529	C₅×D₃	1	1	yes	characteristic
196	#446	—	3	2	no	—
197	#435	—	3	2	no	—
198	#435	—	3	2	no	—
199	C₈×D₄	—	3	2	no	—
200	#433	—	3	2	no	—
201	#431	—	3	1	no	—
202	#405	—	3	2	no	—
203	C₂×#97	—	3	1	no	—
204	C₂²×C₃×C₅	—	2	1	no	—
205	C₂²×C₃×C₅	—	2	1	no	—
206	C₂²×C₃×C₅	—	2	2	no	—
207	C₂²×C₃×C₅	—	2	2	no	—
208	C₂²×C₃×C₅	—	2	2	no	—
209	C₂²×C₃×C₅	#131	1	2	yes	—
210	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
211	C₃×C₄×C₅	—	2	1	no	—
212	C₃×C₄×C₅	—	2	2	no	—
213	C₃×C₄×C₅	—	2	1	no	—
214	C₃×C₄×C₅	—	2	1	no	—
215	C₃×C₄×C₅	—	2	2	no	—
216	C₃×C₄×C₅	—	2	1	no	—
217	C₃×C₄×C₅	—	2	1	no	—
218	C₃×C₄×C₅	—	2	2	no	—
219	C₃×C₄×C₅	C₂×#41	1	2	yes	—
220	C₂×C₃×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
221	C₂×C₃×D₄	C₂×C₄×C₅	1	2	yes	—
222	C₂×C₃×D₄	C₂×C₄×C₅	1	1	yes	characteristic
223	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
224	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
225	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
226	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
227	C₃×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
228	C₃×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
229	C₃×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
230	C₃×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
231	C₃×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
232	C₃×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
233	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
234	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
235	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
236	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
237	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
238	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
239	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
240	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
241	C₃×C₄²	C₂³×C₅	1	2	yes	—
242	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
243	#208	—	2	4	no	—
244	C₂×C₃⋊C₈	—	2	4	no	—
245	C₂×C₃⋊C₈	—	2	4	no	—
246	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
247	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
248	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
249	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
250	C₂³×C₅	C₂²×Dic₃	1	2	yes	—
251	C₂³×C₅	C₂²×Dic₃	1	1	yes	characteristic
252	C₅×Q₈	—	4	1	no	—
253	C₅×D₄	—	2	4	no	—
254	C₅×D₄	—	4	1	no	—
255	C₂×C₄×C₅	—	2	2	no	—
256	C₂×C₄×C₅	—	2	2	no	—
257	C₂×C₄×C₅	—	2	2	no	—
258	C₂×C₄×C₅	—	2	2	no	—
259	C₂×C₄×C₅	—	4	1	no	—
260	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
261	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
262	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
263	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
264	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
265	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
266	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
267	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
268	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
269	C₅×C₈	—	3	4	no	—
270	C₅×C₈	—	6	2	no	—
271	C₅×C₈	—	6	2	no	—
272	C₅×C₈	—	6	2	no	—
273	C₂×M₁₆	—	3	2	no	—
274	C₂²×C₈	—	3	2	no	—
275	C₂²×C₈	—	3	2	no	—
276	#126	C₅×Dic₃	1	2	yes	—
277	#125	C₅×Dic₃	1	1	yes	characteristic
278	#124	C₅×Dic₃	1	1	yes	characteristic
279	#123	C₅×Dic₃	1	2	yes	—
280	C₂²⋊Q₈	C₅×Dic₃	1	1	yes	characteristic
281	#121	C₅×Dic₃	1	1	yes	characteristic
282	C₄×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
283	C₄×D₄	C₂×C₅×D₃	1	2	yes	—
284	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
285	#117	C₂×C₅×D₃	1	2	yes	—
286	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
287	C₄⋊C₈	—	3	2	no	—
288	C₄⋊C₈	—	3	2	no	—
289	C₄⋊C₈	—	3	2	no	—
290	C₂²⋊C₈	—	3	1	no	—
291	C₂²⋊C₈	—	3	1	no	—
292	C₂²⋊C₈	—	3	2	no	—
293	C₂²⋊C₈	—	3	2	no	—
294	#97	—	3	1	no	—
295	#97	—	3	1	no	—
296	#97	—	3	2	no	—
297	#97	—	3	2	no	—
298	C₄×C₈	—	3	2	no	—
299	C₄×C₈	—	3	2	no	—
300	C₂×C₃×C₅	—	2	2	no	—
301	C₂×C₃×C₅	—	4	2	no	—
302	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
303	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
304	C₂×C₃×C₅	#568	1	1	yes	characteristic
305	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
306	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
307	C₃×Q₈	—	4	1	no	—
308	C₃×D₄	—	2	4	no	—
309	C₃×D₄	—	4	1	no	—
310	C₂×C₃×C₄	—	2	2	no	—
311	C₂×C₃×C₄	—	2	2	no	—
312	C₂×C₃×C₄	—	2	2	no	—
313	C₂×C₃×C₄	—	2	2	no	—
314	C₂×C₃×C₄	—	4	1	no	—
315	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
316	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
317	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
318	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
319	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
320	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
321	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
322	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
323	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
324	C₃⋊C₈	—	2	2	no	—
325	C₃⋊C₈	—	2	2	no	—
326	C₃⋊C₈	—	2	2	no	—
327	C₃⋊C₈	C₅×#41	1	4	yes	—
328	C₂²×C₅	—	2	1	no	—
329	C₂²×C₅	—	2	1	no	—
330	C₂²×C₅	—	2	2	no	—
331	C₂²×C₅	—	2	2	no	—
332	C₂²×C₅	—	2	2	no	—
333	C₂²×C₅	#948	1	2	yes	—
334	C₂²×C₅	C₂³×Dic₃	1	1	yes	characteristic
335	C₄×C₅	—	2	1	no	—
336	C₄×C₅	—	2	1	no	—
337	C₄×C₅	—	2	2	no	—
338	C₄×C₅	—	2	1	no	—
339	C₄×C₅	—	2	1	no	—
340	C₄×C₅	—	2	2	no	—
341	C₄×C₅	—	2	1	no	—
342	C₄×C₅	—	2	2	no	—
343	C₄×C₅	D₃×#41	1	2	yes	—
344	C₂×Q₈	C₂×C₅×Dic₃	1	1	yes	characteristic
345	C₂×D₄	C₂×C₅×Dic₃	1	2	yes	—
346	C₂×D₄	C₂×C₅×Dic₃	1	1	yes	characteristic
347	C₂²×C₄	C₂×C₅×Dic₃	1	1	yes	characteristic
348	C₂²×C₄	C₂×C₅×Dic₃	1	1	yes	characteristic
349	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
350	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
351	M₁₆	—	6	4	no	—
352	C₂×C₈	—	3	2	no	—
353	C₂×C₈	—	3	2	no	—
354	C₂×C₈	—	3	2	no	—
355	C₂×C₈	—	3	2	no	—
356	C₂×C₈	—	6	4	no	—
357	C₂×C₈	—	6	4	no	—
358	C₄⋊C₄	C₂×C₅×Dic₃	1	2	yes	—
359	C₄⋊C₄	C₂×C₅×Dic₃	1	2	yes	—
360	C₄⋊C₄	C₂×C₅×Dic₃	1	1	yes	characteristic
361	C₄⋊C₄	C₂×C₅×Dic₃	1	2	yes	—
362	C₄⋊C₄	C₂×C₅×Dic₃	1	1	yes	characteristic
363	C₄⋊C₄	C₂×C₅×Dic₃	1	2	yes	—
364	C₂²⋊C₄	C₂×C₅×Dic₃	1	2	yes	—
365	C₂²⋊C₄	C₂×C₅×Dic₃	1	2	yes	—
366	C₂²⋊C₄	C₂×C₅×Dic₃	1	2	yes	—
367	C₂²⋊C₄	C₂×C₅×Dic₃	1	2	yes	—
368	C₂²⋊C₄	C₂×C₅×Dic₃	1	2	yes	—
369	C₄²	C₂×C₅×Dic₃	1	1	yes	characteristic
370	C₄²	C₂×C₅×Dic₃	1	1	yes	characteristic
371	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
372	C₄²	C₂²×C₅×D₃	1	2	yes	—
373	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
374	C₃×C₅	#2968	1	1	yes	characteristic, complemented, Hall
375	C₂²×C₃	—	2	1	no	—
376	C₂²×C₃	—	2	1	no	—
377	C₂²×C₃	—	2	2	no	—
378	C₂²×C₃	—	2	2	no	—
379	C₂²×C₃	—	2	2	no	—
380	C₂²×C₃	C₅×#131	1	2	yes	—
381	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
382	C₃×C₄	—	2	1	no	—
383	C₃×C₄	—	2	2	no	—
384	C₃×C₄	—	2	1	no	—
385	C₃×C₄	—	2	1	no	—
386	C₃×C₄	—	2	2	no	—
387	C₃×C₄	—	2	1	no	—
388	C₃×C₄	—	2	1	no	—
389	C₃×C₄	—	2	2	no	—
390	C₃×C₄	C₂×C₅×#41	1	2	yes	—
391	C₂×C₅	—	2	2	no	—
392	C₂×C₅	—	4	2	no	—
393	C₂×C₅	C₂×#948	1	1	yes	characteristic
394	C₂×C₅	#5819	1	1	yes	characteristic
395	C₂×C₅	Dic₃×#41	1	1	yes	characteristic
396	C₂³	C₂²×C₅×Dic₃	1	2	yes	—
397	C₂³	C₂²×C₅×Dic₃	1	1	yes	characteristic
398	Q₈	—	4	1	no	—
399	D₄	—	2	4	no	—
400	D₄	—	4	1	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	C₂²×C₅×Dic₃	1	1	yes	characteristic
407	C₂×C₄	C₂²×C₅×Dic₃	1	1	yes	characteristic
408	C₂×C₄	C₂²×C₅×Dic₃	1	1	yes	characteristic
409	C₂×C₄	C₂²×C₅×Dic₃	1	1	yes	characteristic
410	C₂×C₄	C₂²×C₅×Dic₃	1	1	yes	characteristic
411	C₂×C₄	C₂²×C₅×Dic₃	1	2	yes	—
412	C₂×C₄	C₂²×C₅×Dic₃	1	2	yes	—
413	C₂×C₄	C₂²×C₅×Dic₃	1	2	yes	—
414	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
415	C₈	—	3	4	no	—
416	C₈	—	6	2	no	—
417	C₈	—	6	2	no	—
418	C₈	—	6	2	no	—
419	C₂×C₃	—	2	2	no	—
420	C₂×C₃	—	4	2	no	—
421	C₂×C₃	C₄×C₅×#41	1	1	yes	characteristic
422	C₂×C₃	C₂×C₅×#131	1	1	yes	characteristic
423	C₂×C₃	C₅×#568	1	1	yes	characteristic
424	C₅	#83128	1	1	yes	characteristic, direct product factor, Sylow
425	C₂²	—	2	1	no	—
426	C₂²	—	2	1	no	—
427	C₂²	—	2	2	no	—
428	C₂²	—	2	2	no	—
429	C₂²	—	2	2	no	—
430	C₂²	C₅×#948	1	2	yes	—
431	C₂²	C₂³×C₅×Dic₃	1	1	yes	characteristic
432	C₄	—	2	1	no	—
433	C₄	—	2	1	no	—
434	C₄	—	2	2	no	—
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	2	2	no	—
438	C₄	—	2	1	no	—
439	C₄	—	2	2	no	—
440	C₄	C₅×D₃×#41	1	2	yes	—
441	C₃	C₅×#2968	1	1	yes	characteristic, complemented, Sylow
442	C₂	—	2	2	no	—
443	C₂	—	4	2	no	—
444	C₂	C₂×C₅×#948	1	1	yes	characteristic
445	C₂	C₅×#5819	1	1	yes	characteristic
446	C₂	C₅×Dic₃×#41	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	C₃×C₅×#529	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₃×C₅×#121	C₄
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₅×#529	D₃
hypocenter	C₃	C₅×#2968
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₅×#529

Complements

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

N	H ≅ G/N	type
2. C₅×#5024	C₂	semidirect
3. C₅×#5011	C₂	semidirect
4. C₅×#5011	C₂	semidirect
5. C₅×D₄×C₃⋊C₈	C₂	semidirect
6. C₅×#5000	C₂	semidirect
7. C₅×#4997	C₂	semidirect
8. C₅×#4925	C₂	semidirect
9. C₂×C₅×#803	C₂	semidirect
38. #83128	C₅	direct (N × H)
79. #5024	C₂×C₅	semidirect
80. #5011	C₂×C₅	semidirect
81. #5011	C₂×C₅	semidirect
82. D₄×C₃⋊C₈	C₂×C₅	semidirect
83. #5000	C₂×C₅	semidirect
84. #4997	C₂×C₅	semidirect
85. #4925	C₂×C₅	semidirect
86. C₂×#803	C₂×C₅	semidirect
374. C₃×C₅	#2968	semidirect
424. C₅	#83128	direct (N × H)
441. C₃	C₅×#2968	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#529	2
C₅×#5024	2
C₅×#5011	2
C₅×D₄×C₃⋊C₈	2
C₅×#5000	2
C₅×#4997	2
C₅×#4925	2
C₂×C₅×#803	2
C₅×#2968	3
#83128	5

Subgroups — C5×#83128 #14419592

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#83128 #14419592