Subgroups — C₅×#69448 #14295277

Order 1920.

696 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×#208	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#830	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×#803	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄×C₅×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4524	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4524	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1753	—	3	1	no	maximal, Hall
9	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₅×C₂²⋊C₄	C₄	1	2	yes	—
11	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
13	C₂×C₅×#208	—	2	2	no	—
14	C₂×C₅×#208	—	2	2	no	—
15	C₂×C₅×#208	C₄	1	4	yes	complemented
16	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
17	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
18	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
19	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
20	C₃×C₅×#95	C₄	1	2	yes	—
21	C₅×#830	C₄	1	4	yes	complemented
22	C₅×#803	—	2	2	no	—
23	C₄×C₅×C₃⋊C₈	—	2	2	no	—
24	#69448	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₂²×C₅×M₁₆	—	3	1	no	—
26	C₂×C₅×C₂²⋊C₈	—	3	1	no	—
27	C₂×C₅×#97	—	3	1	no	—
28	C₂×C₄×C₅×C₈	—	3	1	no	—
29	C₄×C₅×C₂²⋊C₄	D₃	1	1	yes	characteristic
30	C₅×#336	—	3	1	no	—
31	C₅×#336	—	3	1	no	—
32	C₂⁴×C₃×C₅	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₃×C₄×C₅	—	2	1	no	—
34	C₂²×C₃×C₄×C₅	—	2	1	no	—
35	C₂²×C₃×C₄×C₅	—	2	1	no	—
36	C₂²×C₃×C₄×C₅	—	2	1	no	—
37	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
38	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
40	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
41	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
42	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
43	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
44	C₃×C₄²×C₅	—	2	1	no	—
45	C₃×C₄²×C₅	—	2	1	no	—
46	C₃×C₄²×C₅	—	2	1	no	—
47	C₃×C₄²×C₅	—	2	1	no	—
48	C₅×#208	—	2	8	no	—
49	C₂×C₅×C₃⋊C₈	—	2	1	no	—
50	C₂×C₅×C₃⋊C₈	—	2	1	no	—
51	C₂×C₅×C₃⋊C₈	—	2	1	no	—
52	C₂×C₅×C₃⋊C₈	—	2	1	no	—
53	C₂×C₅×C₃⋊C₈	—	2	1	no	—
54	C₂×C₅×C₃⋊C₈	—	2	1	no	—
55	C₂×C₅×C₃⋊C₈	C₂×C₄	1	2	yes	—
56	C₂×C₅×C₃⋊C₈	C₂×C₄	1	2	yes	—
57	C₂×C₅×C₃⋊C₈	C₂×C₄	1	2	yes	—
58	C₂×C₅×C₃⋊C₈	C₂×C₄	1	2	yes	—
59	C₂×C₅×C₃⋊C₈	D₄	1	2	yes	—
60	C₂×C₅×C₃⋊C₈	D₄	1	2	yes	—
61	C₂²×#208	C₂×C₅	1	1	yes	characteristic
62	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic
63	C₂×#830	C₂×C₅	1	1	yes	characteristic
64	C₂×#803	C₂×C₅	1	1	yes	characteristic, complemented
65	C₂×C₄×C₃⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
66	#4524	C₂×C₅	1	1	yes	characteristic, complemented
67	#4524	C₂×C₅	1	1	yes	characteristic, complemented
68	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
69	C₂×C₅×M₁₆	—	3	4	no	—
70	C₂×C₅×M₁₆	—	6	2	no	—
71	C₂×C₅×M₁₆	—	6	2	no	—
72	C₂²×C₅×C₈	—	3	1	no	—
73	C₂²×C₅×C₈	—	3	1	no	—
74	C₂²×C₅×C₈	—	3	1	no	—
75	C₂²×C₅×C₈	—	3	1	no	—
76	C₂×C₅×C₂²⋊C₄	Dic₃	1	2	yes	—
77	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
78	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
79	C₅×C₂²⋊C₈	—	3	4	no	—
80	C₅×#97	—	6	2	no	—
81	C₄×C₅×C₈	—	6	2	no	—
82	C₅×#95	Dic₃	1	2	yes	—
83	#1753	—	3	1	no	Sylow
84	C₂³×C₃×C₅	—	2	1	no	—
85	C₂³×C₃×C₅	—	2	1	no	—
86	C₂³×C₃×C₅	—	2	2	no	—
87	C₂³×C₃×C₅	—	2	2	no	—
88	C₂³×C₃×C₅	C₄²	1	2	yes	—
89	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
90	C₂×C₃×C₄×C₅	—	2	2	no	—
91	C₂×C₃×C₄×C₅	—	2	1	no	—
92	C₂×C₃×C₄×C₅	—	2	1	no	—
93	C₂×C₃×C₄×C₅	—	2	2	no	—
94	C₂×C₃×C₄×C₅	—	2	2	no	—
95	C₂×C₃×C₄×C₅	—	2	2	no	—
96	C₂×C₃×C₄×C₅	—	2	2	no	—
97	C₂×C₃×C₄×C₅	—	2	2	no	—
98	C₂×C₃×C₄×C₅	—	2	2	no	—
99	C₂×C₃×C₄×C₅	—	2	2	no	—
100	C₂×C₃×C₄×C₅	—	2	2	no	—
101	C₂×C₃×C₄×C₅	C₄²	1	2	yes	—
102	C₂×C₃×C₄×C₅	M₁₆	1	4	yes	complemented
103	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
106	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
107	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
108	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
109	C₅×C₃⋊C₈	—	2	2	no	—
110	C₅×C₃⋊C₈	—	2	2	no	—
111	C₅×C₃⋊C₈	—	2	2	no	—
112	C₅×C₃⋊C₈	C₂²⋊C₄	1	4	yes	complemented
113	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
114	C₂×C₃×C₂²⋊C₄	C₄×C₅	1	2	yes	—
115	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
116	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
117	C₂×#208	—	2	2	no	—
118	C₂×#208	—	2	2	no	—
119	C₂×#208	C₄×C₅	1	4	yes	complemented
120	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
121	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
122	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
123	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
124	C₃×#95	C₄×C₅	1	2	yes	—
125	#830	C₄×C₅	1	4	yes	complemented
126	#803	—	2	2	no	—
127	C₄×C₃⋊C₈	—	2	2	no	—
128	C₂⁴×C₅	C₂×Dic₃	1	1	yes	characteristic
129	C₂²×C₄×C₅	—	2	1	no	—
130	C₂²×C₄×C₅	—	2	1	no	—
131	C₂²×C₄×C₅	—	2	1	no	—
132	C₂²×C₄×C₅	—	2	1	no	—
133	C₂²×C₄×C₅	C₄×D₃	1	2	yes	—
134	C₂²×C₄×C₅	C₄×D₃	1	2	yes	—
135	C₂²×C₄×C₅	C₂×Dic₃	1	2	yes	—
136	C₂²×C₄×C₅	C₂×Dic₃	1	2	yes	—
137	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
138	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
139	C₅×M₁₆	—	6	8	no	—
140	C₂×C₅×C₈	—	3	2	no	—
141	C₂×C₅×C₈	—	3	2	no	—
142	C₂×C₅×C₈	—	3	2	no	—
143	C₂×C₅×C₈	—	3	2	no	—
144	C₂×C₅×C₈	—	3	2	no	—
145	C₂×C₅×C₈	—	3	2	no	—
146	C₂×C₅×C₈	—	6	1	no	—
147	C₂×C₅×C₈	—	6	1	no	—
148	C₂×C₅×C₈	—	6	1	no	—
149	C₂×C₅×C₈	—	6	1	no	—
150	C₂×C₅×C₈	—	6	1	no	—
151	C₂×C₅×C₈	—	6	1	no	—
152	C₅×C₂²⋊C₄	—	2	4	no	—
153	C₄²×C₅	—	2	1	no	—
154	C₄²×C₅	—	2	1	no	—
155	C₄²×C₅	—	2	1	no	—
156	C₄²×C₅	—	2	1	no	—
157	C₂²×M₁₆	—	3	1	no	—
158	C₂×C₂²⋊C₈	—	3	1	no	—
159	C₂×#97	—	3	1	no	—
160	C₂×C₄×C₈	—	3	1	no	—
161	C₄×C₂²⋊C₄	C₅×D₃	1	1	yes	characteristic
162	#336	—	3	1	no	—
163	#336	—	3	1	no	—
164	C₂²×C₃×C₅	—	2	2	no	—
165	C₂²×C₃×C₅	—	2	2	no	—
166	C₂²×C₃×C₅	—	2	2	no	—
167	C₂²×C₃×C₅	—	4	2	no	—
168	C₂²×C₃×C₅	—	4	2	no	—
169	C₂²×C₃×C₅	C₂×C₄²	1	1	yes	characteristic
170	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
171	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
172	C₂²×C₃×C₅	C₂×M₁₆	1	2	yes	—
173	C₂²×C₃×C₅	#131	1	2	yes	—
174	C₃×C₄×C₅	—	2	2	no	—
175	C₃×C₄×C₅	—	2	4	no	—
176	C₃×C₄×C₅	—	4	2	no	—
177	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
178	C₃×C₄×C₅	#117	1	1	yes	characteristic
179	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
180	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
181	C₂⁴×C₃	C₂×C₄×C₅	1	1	yes	characteristic
182	C₂²×C₃×C₄	—	2	1	no	—
183	C₂²×C₃×C₄	—	2	1	no	—
184	C₂²×C₃×C₄	—	2	1	no	—
185	C₂²×C₃×C₄	—	2	1	no	—
186	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
187	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
188	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
189	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
190	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
191	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
192	C₃×C₂²⋊C₄	—	2	4	no	—
193	C₃×C₄²	—	2	1	no	—
194	C₃×C₄²	—	2	1	no	—
195	C₃×C₄²	—	2	1	no	—
196	C₃×C₄²	—	2	1	no	—
197	#208	—	2	8	no	—
198	C₂×C₃⋊C₈	—	2	1	no	—
199	C₂×C₃⋊C₈	—	2	1	no	—
200	C₂×C₃⋊C₈	—	2	1	no	—
201	C₂×C₃⋊C₈	—	2	1	no	—
202	C₂×C₃⋊C₈	—	2	1	no	—
203	C₂×C₃⋊C₈	—	2	1	no	—
204	C₂×C₃⋊C₈	C₂×C₄×C₅	1	2	yes	—
205	C₂×C₃⋊C₈	C₂×C₄×C₅	1	2	yes	—
206	C₂×C₃⋊C₈	C₂×C₄×C₅	1	2	yes	—
207	C₂×C₃⋊C₈	C₂×C₄×C₅	1	2	yes	—
208	C₂×C₃⋊C₈	C₅×D₄	1	2	yes	—
209	C₂×C₃⋊C₈	C₅×D₄	1	2	yes	—
210	C₂³×C₅	—	2	2	no	—
211	C₂³×C₅	—	2	1	no	—
212	C₂³×C₅	—	2	1	no	—
213	C₂³×C₅	—	2	2	no	—
214	C₂³×C₅	C₄×Dic₃	1	2	yes	—
215	C₂³×C₅	C₂²×Dic₃	1	1	yes	characteristic
216	C₂×C₄×C₅	—	2	2	no	—
217	C₂×C₄×C₅	—	2	1	no	—
218	C₂×C₄×C₅	—	2	1	no	—
219	C₂×C₄×C₅	—	2	2	no	—
220	C₂×C₄×C₅	—	2	2	no	—
221	C₂×C₄×C₅	—	2	2	no	—
222	C₂×C₄×C₅	—	2	2	no	—
223	C₂×C₄×C₅	—	2	2	no	—
224	C₂×C₄×C₅	—	2	2	no	—
225	C₂×C₄×C₅	—	2	2	no	—
226	C₂×C₄×C₅	—	2	2	no	—
227	C₂×C₄×C₅	#208	1	4	yes	complemented
228	C₂×C₄×C₅	C₄×Dic₃	1	2	yes	—
229	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
230	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
231	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
232	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
233	C₂×C₄×C₅	#237	1	1	yes	characteristic
234	C₂×C₄×C₅	#237	1	1	yes	characteristic
235	C₅×C₈	—	3	4	no	—
236	C₅×C₈	—	6	2	no	—
237	C₅×C₈	—	6	2	no	—
238	C₅×C₈	—	6	2	no	—
239	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
240	C₂×M₁₆	—	3	4	no	—
241	C₂×M₁₆	—	6	2	no	—
242	C₂×M₁₆	—	6	2	no	—
243	C₂²×C₈	—	3	1	no	—
244	C₂²×C₈	—	3	1	no	—
245	C₂²×C₈	—	3	1	no	—
246	C₂²×C₈	—	3	1	no	—
247	C₂×C₂²⋊C₄	C₅×Dic₃	1	2	yes	—
248	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
249	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
250	C₂²⋊C₈	—	3	4	no	—
251	#97	—	6	2	no	—
252	C₄×C₈	—	6	2	no	—
253	#95	C₅×Dic₃	1	2	yes	—
254	C₂×C₃×C₅	—	4	2	no	—
255	C₂×C₃×C₅	C₄×C₂²⋊C₄	1	1	yes	characteristic
256	C₂×C₃×C₅	C₄×M₁₆	1	1	yes	characteristic
257	C₂×C₃×C₅	#405	1	1	yes	characteristic
258	C₂×C₃×C₅	#435	1	2	yes	—
259	C₂×C₃×C₅	#436	1	2	yes	—
260	C₂³×C₃	—	2	1	no	—
261	C₂³×C₃	—	2	1	no	—
262	C₂³×C₃	—	2	2	no	—
263	C₂³×C₃	—	2	2	no	—
264	C₂³×C₃	C₄²×C₅	1	2	yes	—
265	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
266	C₂×C₃×C₄	—	2	2	no	—
267	C₂×C₃×C₄	—	2	1	no	—
268	C₂×C₃×C₄	—	2	1	no	—
269	C₂×C₃×C₄	—	2	2	no	—
270	C₂×C₃×C₄	—	2	2	no	—
271	C₂×C₃×C₄	—	2	2	no	—
272	C₂×C₃×C₄	—	2	2	no	—
273	C₂×C₃×C₄	—	2	2	no	—
274	C₂×C₃×C₄	—	2	2	no	—
275	C₂×C₃×C₄	—	2	2	no	—
276	C₂×C₃×C₄	—	2	2	no	—
277	C₂×C₃×C₄	C₄²×C₅	1	2	yes	—
278	C₂×C₃×C₄	C₅×M₁₆	1	4	yes	complemented
279	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
280	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
281	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
282	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
283	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
284	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
285	C₃⋊C₈	—	2	2	no	—
286	C₃⋊C₈	—	2	2	no	—
287	C₃⋊C₈	—	2	2	no	—
288	C₃⋊C₈	C₅×C₂²⋊C₄	1	4	yes	complemented
289	C₂²×C₅	—	2	2	no	—
290	C₂²×C₅	—	2	2	no	—
291	C₂²×C₅	—	2	2	no	—
292	C₂²×C₅	—	4	2	no	—
293	C₂²×C₅	—	4	2	no	—
294	C₂²×C₅	C₂×#208	1	2	yes	—
295	C₂²×C₅	C₂×C₄×Dic₃	1	1	yes	characteristic
296	C₂²×C₅	D₄×Dic₃	1	1	yes	characteristic
297	C₂²×C₅	D₄×Dic₃	1	1	yes	characteristic
298	C₂²×C₅	#948	1	2	yes	—
299	C₄×C₅	—	2	2	no	—
300	C₄×C₅	—	2	4	no	—
301	C₄×C₅	—	4	2	no	—
302	C₄×C₅	#877	1	1	yes	characteristic
303	C₄×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
304	C₄×C₅	#67⋊C₄	1	1	yes	characteristic
305	C₄×C₅	#67⋊C₄	1	1	yes	characteristic
306	C₂⁴	C₂×C₅×Dic₃	1	1	yes	characteristic
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	C₄×C₅×D₃	1	2	yes	—
312	C₂²×C₄	C₄×C₅×D₃	1	2	yes	—
313	C₂²×C₄	C₂×C₅×Dic₃	1	2	yes	—
314	C₂²×C₄	C₂×C₅×Dic₃	1	2	yes	—
315	C₂²×C₄	C₂×C₅×Dic₃	1	1	yes	characteristic
316	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
317	M₁₆	—	6	8	no	—
318	C₂×C₈	—	3	2	no	—
319	C₂×C₈	—	3	2	no	—
320	C₂×C₈	—	3	2	no	—
321	C₂×C₈	—	3	2	no	—
322	C₂×C₈	—	3	2	no	—
323	C₂×C₈	—	3	2	no	—
324	C₂×C₈	—	6	1	no	—
325	C₂×C₈	—	6	1	no	—
326	C₂×C₈	—	6	1	no	—
327	C₂×C₈	—	6	1	no	—
328	C₂×C₈	—	6	1	no	—
329	C₂×C₈	—	6	1	no	—
330	C₂²⋊C₄	—	2	4	no	—
331	C₄²	—	2	1	no	—
332	C₄²	—	2	1	no	—
333	C₄²	—	2	1	no	—
334	C₄²	—	2	1	no	—
335	C₃×C₅	#1753	1	1	yes	characteristic, complemented, Hall
336	C₂²×C₃	—	2	2	no	—
337	C₂²×C₃	—	2	2	no	—
338	C₂²×C₃	—	2	2	no	—
339	C₂²×C₃	—	4	2	no	—
340	C₂²×C₃	—	4	2	no	—
341	C₂²×C₃	C₂×C₄²×C₅	1	1	yes	characteristic
342	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
343	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
344	C₂²×C₃	C₂×C₅×M₁₆	1	2	yes	—
345	C₂²×C₃	C₅×#131	1	2	yes	—
346	C₃×C₄	—	2	2	no	—
347	C₃×C₄	—	2	4	no	—
348	C₃×C₄	—	4	2	no	—
349	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
350	C₃×C₄	C₅×#117	1	1	yes	characteristic
351	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
352	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
353	C₂×C₅	—	4	2	no	—
354	C₂×C₅	C₄×#208	1	1	yes	characteristic
355	C₂×C₅	Dic₃×C₂²⋊C₄	1	1	yes	characteristic
356	C₂×C₅	#4997	1	1	yes	characteristic
357	C₂×C₅	#5011	1	2	yes	—
358	C₂×C₅	#5012	1	2	yes	—
359	C₂³	—	2	2	no	—
360	C₂³	—	2	1	no	—
361	C₂³	—	2	1	no	—
362	C₂³	—	2	2	no	—
363	C₂³	C₄×C₅×Dic₃	1	2	yes	—
364	C₂³	C₂²×C₅×Dic₃	1	1	yes	characteristic
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	C₅×#208	1	4	yes	complemented
377	C₂×C₄	C₄×C₅×Dic₃	1	2	yes	—
378	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
379	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
380	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
381	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
382	C₂×C₄	C₅×#237	1	1	yes	characteristic
383	C₂×C₄	C₅×#237	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	—	4	2	no	—
389	C₂×C₃	C₄×C₅×C₂²⋊C₄	1	1	yes	characteristic
390	C₂×C₃	C₄×C₅×M₁₆	1	1	yes	characteristic
391	C₂×C₃	C₅×#405	1	1	yes	characteristic
392	C₂×C₃	C₅×#435	1	2	yes	—
393	C₂×C₃	C₅×#436	1	2	yes	—
394	C₅	#69448	1	1	yes	characteristic, direct product factor, Sylow
395	C₂²	—	2	2	no	—
396	C₂²	—	2	2	no	—
397	C₂²	—	2	2	no	—
398	C₂²	—	4	2	no	—
399	C₂²	—	4	2	no	—
400	C₂²	C₂×C₅×#208	1	2	yes	—
401	C₂²	C₂×C₄×C₅×Dic₃	1	1	yes	characteristic
402	C₂²	C₅×D₄×Dic₃	1	1	yes	characteristic
403	C₂²	C₅×D₄×Dic₃	1	1	yes	characteristic
404	C₂²	C₅×#948	1	2	yes	—
405	C₄	—	2	2	no	—
406	C₄	—	2	4	no	—
407	C₄	—	4	2	no	—
408	C₄	C₅×#877	1	1	yes	characteristic
409	C₄	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
410	C₄	C₅×#67⋊C₄	1	1	yes	characteristic
411	C₄	C₅×#67⋊C₄	1	1	yes	characteristic
412	C₃	C₅×#1753	1	1	yes	characteristic, complemented, Sylow
413	C₂	—	4	2	no	—
414	C₂	C₄×C₅×#208	1	1	yes	characteristic
415	C₂	C₅×Dic₃×C₂²⋊C₄	1	1	yes	characteristic
416	C₂	C₅×#4997	1	1	yes	characteristic
417	C₂	C₅×#5011	1	2	yes	—
418	C₂	C₅×#5012	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₅	C₂²×D₃
commutator	C₂²×C₃	C₂×C₄²×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₃×C₄×C₅×C₂²⋊C₄	C₂
socle	C₂³×C₃×C₅	C₂²×C₄
prime radical	C₂⁴×C₃×C₅	C₂×C₄
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₄×C₅×C₂²⋊C₄	D₃
hypocenter	C₃	C₅×#1753
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ C₄×C₅×C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
4. C₂×C₅×#803	C₂	semidirect
5. C₂×C₄×C₅×C₃⋊C₈	C₂	semidirect
6. C₅×#4524	C₂	semidirect
7. C₅×#4524	C₂	semidirect
15. C₂×C₅×#208	C₄	semidirect
21. C₅×#830	C₄	semidirect
24. #69448	C₅	direct (N × H)
64. C₂×#803	C₂×C₅	semidirect
65. C₂×C₄×C₃⋊C₈	C₂×C₅	semidirect
66. #4524	C₂×C₅	semidirect
67. #4524	C₂×C₅	semidirect
102. C₂×C₃×C₄×C₅	M₁₆	semidirect
112. C₅×C₃⋊C₈	C₂²⋊C₄	semidirect
119. C₂×#208	C₄×C₅	semidirect
125. #830	C₄×C₅	semidirect
227. C₂×C₄×C₅	#208	semidirect
278. C₂×C₃×C₄	C₅×M₁₆	semidirect
288. C₃⋊C₈	C₅×C₂²⋊C₄	semidirect
335. C₃×C₅	#1753	semidirect
376. C₂×C₄	C₅×#208	semidirect
394. C₅	#69448	direct (N × H)
412. C₃	C₅×#1753	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₅×#208	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₂×C₅×#830	2
C₂×C₅×#803	2
C₂×C₄×C₅×C₃⋊C₈	2
C₅×#4524	2
C₅×#1753	3
#69448	5

Subgroups — C5×#69448 #14295277

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#69448 #14295277