Subgroups — C₅×#68992 #14302140

Order 1920.

780 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#895	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#823	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#823	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5126	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#343	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4530	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1900	—	3	1	no	maximal, Hall
9	C₂²×C₅×D₁₂	C₄	1	2	yes	—
10	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
11	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₂×C₅×(C₂×D₃)⋊C₄	C₄	1	2	yes	—
16	C₂×C₅×#208	C₂²	1	1	yes	characteristic
17	C₂×C₅×#208	C₂²	1	1	yes	characteristic
18	C₅×D₃×M₁₆	—	2	2	no	—
19	C₅×D₃×M₁₆	—	2	2	no	—
20	C₂×C₅×ΓL(1,𝔽₂₅)	—	2	1	no	—
21	C₂×C₅×D₃×C₈	—	2	1	no	—
22	C₅×#895	—	2	1	no	—
23	C₅×#895	—	2	1	no	—
24	C₅×#895	—	2	1	no	—
25	C₅×#895	—	2	1	no	—
26	C₅×#823	—	2	2	no	—
27	C₅×#823	—	2	2	no	—
28	C₅×(C₂×D₃)⋊C₈	—	2	1	no	—
29	C₅×(C₂×D₃)⋊C₈	—	2	1	no	—
30	#68992	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
31	C₂²×C₅×M₁₆	—	3	1	no	—
32	C₂×C₅×#121	—	3	1	no	—
33	C₂×C₅×#100	—	3	1	no	—
34	C₂×C₅×#100	—	3	1	no	—
35	C₅×#407	—	3	1	no	—
36	C₅×#343	—	3	1	no	—
37	C₅×#343	D₃	1	1	yes	characteristic, complemented
38	C₂³×C₅×D₃	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₅×D₃	C₂×C₄	1	2	yes	—
40	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
41	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
42	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
43	C₂×C₅×D₁₂	—	2	2	no	—
44	C₂×C₅×D₁₂	—	2	2	no	—
45	C₂×C₅×D₁₂	—	2	1	no	—
46	C₂×C₅×D₁₂	—	2	1	no	—
47	C₂×C₅×D₁₂	—	2	1	no	—
48	C₂×C₅×D₁₂	—	2	1	no	—
49	C₂×C₅×D₁₂	—	2	1	no	—
50	C₂×C₅×D₁₂	—	2	1	no	—
51	C₂×C₅×D₁₂	—	4	4	no	—
52	C₂×C₄×C₅×D₃	—	2	1	no	—
53	C₂×C₄×C₅×D₃	—	2	1	no	—
54	C₂×C₄×C₅×D₃	—	2	1	no	—
55	C₂×C₄×C₅×D₃	—	2	1	no	—
56	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
57	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
58	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
59	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
60	C₃×C₅×M₁₆	—	2	1	no	—
61	C₃×C₅×M₁₆	—	2	1	no	—
62	C₃×C₅×M₁₆	—	2	1	no	—
63	C₃×C₅×M₁₆	D₄	1	2	yes	complemented
64	C₂×C₃×C₅×C₈	—	2	1	no	—
65	C₂×C₃×C₅×C₈	—	2	1	no	—
66	C₃×C₅×C₄⋊C₄	—	2	1	no	—
67	C₃×C₅×C₄⋊C₄	—	2	1	no	—
68	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
69	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
70	C₅×#208	—	2	1	no	—
71	C₅×#208	—	2	1	no	—
72	C₅×#208	—	2	1	no	—
73	C₅×#208	D₄	1	2	yes	complemented
74	C₂×C₅×C₃⋊C₈	—	2	1	no	—
75	C₂×C₅×C₃⋊C₈	—	2	1	no	—
76	C₅×ΓL(1,𝔽₂₅)	—	2	4	no	—
77	C₅×D₃×C₈	—	2	4	no	—
78	C₂×D₃×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
79	C₂×#895	C₂×C₅	1	1	yes	characteristic
80	C₂×#823	C₂×C₅	1	1	yes	characteristic, complemented
81	C₂×#823	C₂×C₅	1	1	yes	characteristic, complemented
82	#5126	C₂×C₅	1	1	yes	characteristic, complemented
83	C₃×#343	C₂×C₅	1	1	yes	characteristic, complemented
84	#4530	C₂×C₅	1	1	yes	characteristic, complemented
85	C₂²×C₅×D₄	—	3	2	no	—
86	C₂²×C₅×D₄	—	3	1	no	—
87	C₂³×C₄×C₅	—	3	1	no	—
88	C₂×C₅×M₁₆	—	3	1	no	—
89	C₂×C₅×M₁₆	—	3	1	no	—
90	C₂×C₅×M₁₆	—	6	1	no	—
91	C₂×C₅×M₁₆	—	6	2	no	—
92	C₂×C₅×M₁₆	—	6	2	no	—
93	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
94	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
95	C₂²×C₅×C₈	—	6	1	no	—
96	C₅×#121	—	6	1	no	—
97	C₅×#121	—	6	1	no	—
98	C₅×#121	—	6	1	no	—
99	C₅×#121	—	6	1	no	—
100	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
101	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
102	C₅×#100	—	6	2	no	—
103	C₅×#100	—	6	2	no	—
104	C₅×C₂²⋊C₈	—	6	1	no	—
105	C₅×C₂²⋊C₈	—	6	1	no	—
106	#1900	—	3	1	no	Sylow
107	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₅×D₃	—	2	1	no	—
109	C₂²×C₅×D₃	—	2	1	no	—
110	C₂²×C₅×D₃	—	2	2	no	—
111	C₂²×C₅×D₃	—	2	2	no	—
112	C₂²×C₅×D₃	—	2	2	no	—
113	C₂²×C₅×D₃	—	2	2	no	—
114	C₂²×C₅×D₃	—	4	1	no	—
115	C₂²×C₅×D₃	—	4	2	no	—
116	C₂²×C₅×D₃	—	4	2	no	—
117	C₂²×C₅×D₃	C₂²⋊C₄	1	1	yes	characteristic
118	C₂²×C₅×D₃	C₂²⋊C₄	1	1	yes	characteristic
119	C₂×C₃×C₄×C₅	—	2	2	no	—
120	C₂×C₃×C₄×C₅	—	4	2	no	—
121	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
122	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
123	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
124	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
125	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
126	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
127	C₂×C₅×Dic₃	—	2	1	no	—
128	C₂×C₅×Dic₃	—	2	1	no	—
129	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
130	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
131	C₅×D₁₂	—	4	4	no	—
132	C₅×D₁₂	—	4	4	no	—
133	C₅×D₁₂	—	4	1	no	—
134	C₅×D₁₂	—	4	1	no	—
135	C₅×D₁₂	—	4	1	no	—
136	C₅×D₁₂	—	4	1	no	—
137	C₄×C₅×D₃	—	2	1	no	—
138	C₄×C₅×D₃	—	2	1	no	—
139	C₄×C₅×D₃	—	2	1	no	—
140	C₄×C₅×D₃	—	2	1	no	—
141	C₄×C₅×D₃	—	2	1	no	—
142	C₄×C₅×D₃	—	2	1	no	—
143	C₄×C₅×D₃	—	2	1	no	—
144	C₄×C₅×D₃	—	2	1	no	—
145	C₃×C₅×C₈	—	2	2	no	—
146	C₃×C₅×C₈	—	4	1	no	—
147	C₅×C₃⋊C₈	—	2	2	no	—
148	C₅×C₃⋊C₈	—	4	1	no	—
149	C₂²×D₁₂	C₄×C₅	1	2	yes	—
150	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
151	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
152	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
153	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
154	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
155	C₂×(C₂×D₃)⋊C₄	C₄×C₅	1	2	yes	—
156	C₂×#208	C₂²×C₅	1	1	yes	characteristic
157	C₂×#208	C₂²×C₅	1	1	yes	characteristic
158	D₃×M₁₆	—	2	2	no	—
159	D₃×M₁₆	—	2	2	no	—
160	C₂×ΓL(1,𝔽₂₅)	—	2	1	no	—
161	C₂×D₃×C₈	—	2	1	no	—
162	#895	—	2	1	no	—
163	#895	—	2	1	no	—
164	#895	—	2	1	no	—
165	#895	—	2	1	no	—
166	#823	—	2	2	no	—
167	#823	—	2	2	no	—
168	(C₂×D₃)⋊C₈	—	2	1	no	—
169	(C₂×D₃)⋊C₈	—	2	1	no	—
170	C₂⁴×C₅	—	3	1	no	—
171	C₂⁴×C₅	—	3	2	no	—
172	C₂×C₅×D₄	—	6	2	no	—
173	C₂×C₅×D₄	—	6	2	no	—
174	C₂×C₅×D₄	—	6	1	no	—
175	C₂×C₅×D₄	—	6	1	no	—
176	C₂×C₅×D₄	—	6	1	no	—
177	C₂×C₅×D₄	—	6	1	no	—
178	C₂×C₅×D₄	—	6	1	no	—
179	C₂×C₅×D₄	—	6	1	no	—
180	C₂×C₅×D₄	—	12	4	no	—
181	C₂²×C₄×C₅	—	3	1	no	—
182	C₂²×C₄×C₅	—	3	1	no	—
183	C₂²×C₄×C₅	—	3	1	no	—
184	C₂²×C₄×C₅	—	3	1	no	—
185	C₂²×C₄×C₅	—	3	1	no	—
186	C₂²×C₄×C₅	—	6	1	no	—
187	C₂²×C₄×C₅	—	6	1	no	—
188	C₂²×C₄×C₅	—	6	1	no	—
189	C₂²×C₄×C₅	—	6	1	no	—
190	C₂²×C₄×C₅	C₄×D₃	1	2	yes	—
191	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
192	C₅×M₁₆	—	2	1	no	—
193	C₅×M₁₆	—	2	1	no	—
194	C₅×M₁₆	—	2	1	no	—
195	C₅×M₁₆	—	3	2	no	—
196	C₅×M₁₆	—	6	4	no	—
197	C₅×M₁₆	—	6	1	no	—
198	C₅×M₁₆	—	6	1	no	—
199	C₅×M₁₆	—	6	1	no	—
200	C₅×M₁₆	D₁₂	1	2	yes	complemented
201	C₂×C₅×C₈	—	2	1	no	—
202	C₂×C₅×C₈	—	2	1	no	—
203	C₂×C₅×C₈	—	6	4	no	—
204	C₂×C₅×C₈	—	6	1	no	—
205	C₂×C₅×C₈	—	6	1	no	—
206	C₅×C₄⋊C₄	—	2	1	no	—
207	C₅×C₄⋊C₄	—	2	1	no	—
208	C₅×C₂²⋊C₄	—	6	2	no	—
209	C₅×C₂²⋊C₄	—	6	2	no	—
210	C₂²×M₁₆	—	3	1	no	—
211	C₂×#121	—	3	1	no	—
212	C₂×#100	—	3	1	no	—
213	C₂×#100	—	3	1	no	—
214	#407	—	3	1	no	—
215	#343	—	3	1	no	—
216	#343	C₅×D₃	1	1	yes	characteristic, complemented
217	C₂²×C₃×C₅	—	2	1	no	—
218	C₂²×C₃×C₅	—	2	1	no	—
219	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
220	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
221	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
222	C₂×C₅×D₃	—	2	1	no	—
223	C₂×C₅×D₃	—	2	1	no	—
224	C₂×C₅×D₃	—	2	1	no	—
225	C₂×C₅×D₃	—	2	1	no	—
226	C₂×C₅×D₃	—	2	1	no	—
227	C₂×C₅×D₃	—	4	2	no	—
228	C₂×C₅×D₃	—	4	2	no	—
229	C₂×C₅×D₃	—	4	2	no	—
230	C₂×C₅×D₃	—	4	2	no	—
231	C₂×C₅×D₃	—	4	2	no	—
232	C₂×C₅×D₃	—	8	2	no	—
233	C₂×C₅×D₃	—	8	2	no	—
234	C₂×C₅×D₃	#100	1	2	yes	complemented
235	C₃×C₄×C₅	—	4	2	no	—
236	C₃×C₄×C₅	#120	1	1	yes	characteristic
237	C₃×C₄×C₅	#121	1	1	yes	characteristic
238	C₃×C₄×C₅	#121	1	1	yes	characteristic
239	C₃×C₄×C₅	#123	1	1	yes	characteristic
240	C₅×Dic₃	—	2	1	no	—
241	C₅×Dic₃	—	2	1	no	—
242	C₂³×D₃	C₂×C₄×C₅	1	1	yes	characteristic
243	C₂³×D₃	C₂×C₄×C₅	1	2	yes	—
244	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
245	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
246	C₂²×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
247	C₂×D₁₂	—	2	2	no	—
248	C₂×D₁₂	—	2	2	no	—
249	C₂×D₁₂	—	2	1	no	—
250	C₂×D₁₂	—	2	1	no	—
251	C₂×D₁₂	—	2	1	no	—
252	C₂×D₁₂	—	2	1	no	—
253	C₂×D₁₂	—	2	1	no	—
254	C₂×D₁₂	—	2	1	no	—
255	C₂×D₁₂	—	4	4	no	—
256	C₂×C₄×D₃	—	2	1	no	—
257	C₂×C₄×D₃	—	2	1	no	—
258	C₂×C₄×D₃	—	2	1	no	—
259	C₂×C₄×D₃	—	2	1	no	—
260	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
261	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
262	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
263	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
264	C₃×M₁₆	—	2	1	no	—
265	C₃×M₁₆	—	2	1	no	—
266	C₃×M₁₆	—	2	1	no	—
267	C₃×M₁₆	C₅×D₄	1	2	yes	complemented
268	C₂×C₃×C₈	—	2	1	no	—
269	C₂×C₃×C₈	—	2	1	no	—
270	C₃×C₄⋊C₄	—	2	1	no	—
271	C₃×C₄⋊C₄	—	2	1	no	—
272	(C₂×D₃)⋊C₄	—	2	2	no	—
273	(C₂×D₃)⋊C₄	—	2	2	no	—
274	#208	—	2	1	no	—
275	#208	—	2	1	no	—
276	#208	—	2	1	no	—
277	#208	C₅×D₄	1	2	yes	complemented
278	C₂×C₃⋊C₈	—	2	1	no	—
279	C₂×C₃⋊C₈	—	2	1	no	—
280	ΓL(1,𝔽₂₅)	—	2	4	no	—
281	D₃×C₈	—	2	4	no	—
282	C₂³×C₅	—	3	1	no	—
283	C₂³×C₅	—	3	1	no	—
284	C₂³×C₅	—	6	2	no	—
285	C₂³×C₅	—	6	1	no	—
286	C₂³×C₅	—	6	1	no	—
287	C₂³×C₅	—	6	2	no	—
288	C₂³×C₅	—	6	2	no	—
289	C₂³×C₅	—	6	2	no	—
290	C₂³×C₅	—	12	1	no	—
291	C₂³×C₅	—	12	2	no	—
292	C₂³×C₅	—	12	2	no	—
293	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
294	C₅×D₄	—	12	4	no	—
295	C₅×D₄	—	12	4	no	—
296	C₅×D₄	—	12	1	no	—
297	C₅×D₄	—	12	1	no	—
298	C₅×D₄	—	12	1	no	—
299	C₅×D₄	—	12	1	no	—
300	C₂×C₄×C₅	—	2	2	no	—
301	C₂×C₄×C₅	—	3	1	no	—
302	C₂×C₄×C₅	—	3	1	no	—
303	C₂×C₄×C₅	—	4	2	no	—
304	C₂×C₄×C₅	—	6	1	no	—
305	C₂×C₄×C₅	—	6	1	no	—
306	C₂×C₄×C₅	—	6	1	no	—
307	C₂×C₄×C₅	—	6	1	no	—
308	C₂×C₄×C₅	—	6	1	no	—
309	C₂×C₄×C₅	—	6	1	no	—
310	C₂×C₄×C₅	—	6	1	no	—
311	C₂×C₄×C₅	—	6	1	no	—
312	C₂×C₄×C₅	—	6	1	no	—
313	C₂×C₄×C₅	—	6	1	no	—
314	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
315	C₂×C₄×C₅	#235	1	1	yes	characteristic
316	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
317	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
318	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
319	C₂×C₄×C₅	#239	1	1	yes	characteristic
320	C₅×C₈	—	2	2	no	—
321	C₅×C₈	—	4	1	no	—
322	C₅×C₈	—	6	2	no	—
323	C₅×C₈	—	12	1	no	—
324	C₂²×D₄	—	3	2	no	—
325	C₂²×D₄	—	3	1	no	—
326	C₂³×C₄	—	3	1	no	—
327	C₂×M₁₆	—	3	1	no	—
328	C₂×M₁₆	—	3	1	no	—
329	C₂×M₁₆	—	6	1	no	—
330	C₂×M₁₆	—	6	2	no	—
331	C₂×M₁₆	—	6	2	no	—
332	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
333	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
334	C₂²×C₈	—	6	1	no	—
335	#121	—	6	1	no	—
336	#121	—	6	1	no	—
337	#121	—	6	1	no	—
338	#121	—	6	1	no	—
339	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
340	C₂×C₂²⋊C₄	—	3	2	no	—
341	#100	—	6	2	no	—
342	#100	—	6	2	no	—
343	C₂²⋊C₈	—	6	1	no	—
344	C₂²⋊C₈	—	6	1	no	—
345	C₂×C₃×C₅	—	2	1	no	—
346	C₂×C₃×C₅	—	2	1	no	—
347	C₂×C₃×C₅	#386	1	1	yes	characteristic
348	C₂×C₃×C₅	C₂×#100	1	1	yes	characteristic
349	C₂×C₃×C₅	#413	1	1	yes	characteristic
350	C₅×D₃	—	2	2	no	—
351	C₅×D₃	—	4	1	no	—
352	C₅×D₃	—	8	2	no	—
353	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
354	C₂²×D₃	—	2	1	no	—
355	C₂²×D₃	—	2	1	no	—
356	C₂²×D₃	—	2	2	no	—
357	C₂²×D₃	—	2	2	no	—
358	C₂²×D₃	—	2	2	no	—
359	C₂²×D₃	—	2	2	no	—
360	C₂²×D₃	—	4	1	no	—
361	C₂²×D₃	—	4	2	no	—
362	C₂²×D₃	—	4	2	no	—
363	C₂²×D₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
364	C₂²×D₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
365	C₂×C₃×C₄	—	2	2	no	—
366	C₂×C₃×C₄	—	4	2	no	—
367	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
368	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
369	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
370	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
371	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
372	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
373	C₂×Dic₃	—	2	1	no	—
374	C₂×Dic₃	—	2	1	no	—
375	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
376	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
377	D₁₂	—	4	4	no	—
378	D₁₂	—	4	4	no	—
379	D₁₂	—	4	1	no	—
380	D₁₂	—	4	1	no	—
381	D₁₂	—	4	1	no	—
382	D₁₂	—	4	1	no	—
383	C₄×D₃	—	2	1	no	—
384	C₄×D₃	—	2	1	no	—
385	C₄×D₃	—	2	1	no	—
386	C₄×D₃	—	2	1	no	—
387	C₄×D₃	—	2	1	no	—
388	C₄×D₃	—	2	1	no	—
389	C₄×D₃	—	2	1	no	—
390	C₄×D₃	—	2	1	no	—
391	C₃×C₈	—	2	2	no	—
392	C₃×C₈	—	4	1	no	—
393	C₃⋊C₈	—	2	2	no	—
394	C₃⋊C₈	—	4	1	no	—
395	C₂²×C₅	—	2	1	no	—
396	C₂²×C₅	—	2	1	no	—
397	C₂²×C₅	—	3	2	no	—
398	C₂²×C₅	—	6	1	no	—
399	C₂²×C₅	—	6	1	no	—
400	C₂²×C₅	—	6	1	no	—
401	C₂²×C₅	—	6	1	no	—
402	C₂²×C₅	—	6	1	no	—
403	C₂²×C₅	—	12	2	no	—
404	C₂²×C₅	—	12	2	no	—
405	C₂²×C₅	—	12	2	no	—
406	C₂²×C₅	—	12	2	no	—
407	C₂²×C₅	—	12	2	no	—
408	C₂²×C₅	—	24	2	no	—
409	C₂²×C₅	—	24	2	no	—
410	C₂²×C₅	C₄×D₁₂	1	1	yes	characteristic
411	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
412	C₂²×C₅	#893	1	1	yes	characteristic
413	C₄×C₅	—	4	2	no	—
414	C₄×C₅	—	6	1	no	—
415	C₄×C₅	—	6	1	no	—
416	C₄×C₅	#882	1	1	yes	characteristic
417	C₄×C₅	#884	1	1	yes	characteristic
418	C₄×C₅	#894	1	1	yes	characteristic
419	C₄×C₅	#895	1	1	yes	characteristic
420	C₂⁴	—	3	1	no	—
421	C₂⁴	—	3	2	no	—
422	C₂×D₄	—	6	2	no	—
423	C₂×D₄	—	6	2	no	—
424	C₂×D₄	—	6	1	no	—
425	C₂×D₄	—	6	1	no	—
426	C₂×D₄	—	6	1	no	—
427	C₂×D₄	—	6	1	no	—
428	C₂×D₄	—	6	1	no	—
429	C₂×D₄	—	6	1	no	—
430	C₂×D₄	—	12	4	no	—
431	C₂²×C₄	—	3	1	no	—
432	C₂²×C₄	—	3	1	no	—
433	C₂²×C₄	—	3	1	no	—
434	C₂²×C₄	—	3	1	no	—
435	C₂²×C₄	—	3	1	no	—
436	C₂²×C₄	—	6	1	no	—
437	C₂²×C₄	—	6	1	no	—
438	C₂²×C₄	—	6	1	no	—
439	C₂²×C₄	—	6	1	no	—
440	C₂²×C₄	C₄×C₅×D₃	1	2	yes	—
441	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
442	M₁₆	—	2	1	no	—
443	M₁₆	—	2	1	no	—
444	M₁₆	—	2	1	no	—
445	M₁₆	—	3	2	no	—
446	M₁₆	—	6	4	no	—
447	M₁₆	—	6	1	no	—
448	M₁₆	—	6	1	no	—
449	M₁₆	—	6	1	no	—
450	M₁₆	C₅×D₁₂	1	2	yes	complemented
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	2	1	no	—
453	C₂×C₈	—	6	4	no	—
454	C₂×C₈	—	6	1	no	—
455	C₂×C₈	—	6	1	no	—
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₂²⋊C₄	—	6	2	no	—
459	C₂²⋊C₄	—	6	2	no	—
460	C₃×C₅	#1900	1	1	yes	characteristic, complemented, Hall
461	C₂²×C₃	—	2	1	no	—
462	C₂²×C₃	—	2	1	no	—
463	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
464	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
465	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
466	C₂×D₃	—	2	1	no	—
467	C₂×D₃	—	2	1	no	—
468	C₂×D₃	—	2	1	no	—
469	C₂×D₃	—	2	1	no	—
470	C₂×D₃	—	2	1	no	—
471	C₂×D₃	—	4	2	no	—
472	C₂×D₃	—	4	2	no	—
473	C₂×D₃	—	4	2	no	—
474	C₂×D₃	—	4	2	no	—
475	C₂×D₃	—	4	2	no	—
476	C₂×D₃	—	8	2	no	—
477	C₂×D₃	—	8	2	no	—
478	C₂×D₃	C₅×#100	1	2	yes	complemented
479	C₃×C₄	—	4	2	no	—
480	C₃×C₄	C₅×#120	1	1	yes	characteristic
481	C₃×C₄	C₅×#121	1	1	yes	characteristic
482	C₃×C₄	C₅×#121	1	1	yes	characteristic
483	C₃×C₄	C₅×#123	1	1	yes	characteristic
484	Dic₃	—	2	1	no	—
485	Dic₃	—	2	1	no	—
486	C₂×C₅	—	2	1	no	—
487	C₂×C₅	—	2	1	no	—
488	C₂×C₅	—	6	2	no	—
489	C₂×C₅	—	12	1	no	—
490	C₂×C₅	—	24	2	no	—
491	C₂×C₅	#4665	1	1	yes	characteristic
492	C₂×C₅	D₃×#100	1	1	yes	characteristic
493	C₂×C₅	#4751	1	1	yes	characteristic
494	C₂³	—	3	1	no	—
495	C₂³	—	3	1	no	—
496	C₂³	—	6	2	no	—
497	C₂³	—	6	1	no	—
498	C₂³	—	6	1	no	—
499	C₂³	—	6	2	no	—
500	C₂³	—	6	2	no	—
501	C₂³	—	6	2	no	—
502	C₂³	—	12	1	no	—
503	C₂³	—	12	2	no	—
504	C₂³	—	12	2	no	—
505	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
506	D₄	—	12	4	no	—
507	D₄	—	12	4	no	—
508	D₄	—	12	1	no	—
509	D₄	—	12	1	no	—
510	D₄	—	12	1	no	—
511	D₄	—	12	1	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	3	1	no	—
514	C₂×C₄	—	3	1	no	—
515	C₂×C₄	—	4	2	no	—
516	C₂×C₄	—	6	1	no	—
517	C₂×C₄	—	6	1	no	—
518	C₂×C₄	—	6	1	no	—
519	C₂×C₄	—	6	1	no	—
520	C₂×C₄	—	6	1	no	—
521	C₂×C₄	—	6	1	no	—
522	C₂×C₄	—	6	1	no	—
523	C₂×C₄	—	6	1	no	—
524	C₂×C₄	—	6	1	no	—
525	C₂×C₄	—	6	1	no	—
526	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
527	C₂×C₄	C₅×#235	1	1	yes	characteristic
528	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
529	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
530	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
531	C₂×C₄	C₅×#239	1	1	yes	characteristic
532	C₈	—	2	2	no	—
533	C₈	—	4	1	no	—
534	C₈	—	6	2	no	—
535	C₈	—	12	1	no	—
536	C₂×C₃	—	2	1	no	—
537	C₂×C₃	—	2	1	no	—
538	C₂×C₃	C₅×#386	1	1	yes	characteristic
539	C₂×C₃	C₂×C₅×#100	1	1	yes	characteristic
540	C₂×C₃	C₅×#413	1	1	yes	characteristic
541	D₃	—	2	2	no	—
542	D₃	—	4	1	no	—
543	D₃	—	8	2	no	—
544	C₅	#68992	1	1	yes	characteristic, direct product factor, Sylow
545	C₂²	—	2	1	no	—
546	C₂²	—	2	1	no	—
547	C₂²	—	3	2	no	—
548	C₂²	—	6	1	no	—
549	C₂²	—	6	1	no	—
550	C₂²	—	6	1	no	—
551	C₂²	—	6	1	no	—
552	C₂²	—	6	1	no	—
553	C₂²	—	12	2	no	—
554	C₂²	—	12	2	no	—
555	C₂²	—	12	2	no	—
556	C₂²	—	12	2	no	—
557	C₂²	—	12	2	no	—
558	C₂²	—	24	2	no	—
559	C₂²	—	24	2	no	—
560	C₂²	C₄×C₅×D₁₂	1	1	yes	characteristic
561	C₂²	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
562	C₂²	C₅×#893	1	1	yes	characteristic
563	C₄	—	4	2	no	—
564	C₄	—	6	1	no	—
565	C₄	—	6	1	no	—
566	C₄	C₅×#882	1	1	yes	characteristic
567	C₄	C₅×#884	1	1	yes	characteristic
568	C₄	C₅×#894	1	1	yes	characteristic
569	C₄	C₅×#895	1	1	yes	characteristic
570	C₃	C₅×#1900	1	1	yes	characteristic, complemented, Sylow
571	C₂	—	2	1	no	—
572	C₂	—	2	1	no	—
573	C₂	—	6	2	no	—
574	C₂	—	12	1	no	—
575	C₂	—	24	2	no	—
576	C₂	C₅×#4665	1	1	yes	characteristic
577	C₂	C₅×D₃×#100	1	1	yes	characteristic
578	C₂	C₅×#4751	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	D₃×C₂²⋊C₄
commutator	C₂³×C₃	C₂²×C₄×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₃×C₅×#343	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂×C₅×#895	C₂
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₅×#343	D₃
hypocenter	C₃	C₅×#1900
LCS	G ▷ C₂³×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#343

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×D₃×M₁₆	C₂	semidirect
3. C₂×C₅×#823	C₂	semidirect
4. C₂×C₅×#823	C₂	semidirect
5. C₅×#5126	C₂	semidirect
6. C₃×C₅×#343	C₂	semidirect
7. C₅×#4530	C₂	semidirect
30. #68992	C₅	direct (N × H)
37. C₅×#343	D₃	semidirect
63. C₃×C₅×M₁₆	D₄	semidirect
73. C₅×#208	D₄	semidirect
78. C₂×D₃×M₁₆	C₂×C₅	semidirect
80. C₂×#823	C₂×C₅	semidirect
81. C₂×#823	C₂×C₅	semidirect
82. #5126	C₂×C₅	semidirect
83. C₃×#343	C₂×C₅	semidirect
84. #4530	C₂×C₅	semidirect
200. C₅×M₁₆	D₁₂	semidirect
216. #343	C₅×D₃	semidirect
234. C₂×C₅×D₃	#100	semidirect
267. C₃×M₁₆	C₅×D₄	semidirect
277. #208	C₅×D₄	semidirect
450. M₁₆	C₅×D₁₂	semidirect
460. C₃×C₅	#1900	semidirect
478. C₂×D₃	C₅×#100	semidirect
544. C₅	#68992	direct (N × H)
570. C₃	C₅×#1900	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×D₃×M₁₆	2
C₂×C₅×#895	2
C₂×C₅×#823	2
C₅×#5126	2
C₃×C₅×#343	2
C₅×#4530	2
C₅×#1900	3
#68992	5

Subgroups — C5×#68992 #14302140

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#68992 #14302140