Subgroups — C₅×#71667 #14301304

Order 1920.

740 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#520	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#949	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#837	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5001	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4988	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4532	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4530	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1883	—	3	1	no	maximal, Hall
9	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
10	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
11	C₃×C₄×C₅×Q₈	—	2	1	no	—
12	C₃×C₄×C₅×D₄	—	2	1	no	—
13	C₃×C₄×C₅×D₄	—	2	2	no	—
14	C₃×C₅×#117	—	2	1	no	—
15	C₃×C₅×#117	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
17	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₅×#949	—	2	2	no	—
19	C₅×#949	C₄	1	4	yes	complemented
20	C₂×C₅×#215	—	2	1	no	—
21	C₂×C₅×#213	—	2	1	no	—
22	C₂×C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
23	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
24	C₂×C₅×#208	C₂²	1	1	yes	characteristic
25	C₂×C₅×#208	C₂²	1	1	yes	characteristic
26	C₅×#837	—	2	2	no	—
27	C₅×#809	—	2	1	no	—
28	C₅×#809	—	2	1	no	—
29	#71667	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
30	C₂×C₅×AGL(1,ℤ/8)	—	3	1	no	—
31	C₅×#520	D₃	1	1	yes	characteristic, complemented
32	C₂×C₅×#104	—	3	1	no	—
33	C₅×#418	—	3	1	no	—
34	C₅×#390	—	3	1	no	—
35	C₅×#343	—	3	1	no	—
36	C₅×#339	—	3	1	no	—
37	C₂³×C₅×D₃	—	2	1	no	—
38	C₃×C₅×#41	—	2	1	no	—
39	C₃×C₅×#41	—	2	1	no	—
40	C₃×C₅×#41	C₂×C₄	1	2	yes	—
41	C₃×C₅×#41	D₄	1	2	yes	—
42	C₂×C₃×C₅×Q₈	D₄	1	1	yes	characteristic
43	C₂×C₃×C₅×D₄	—	2	1	no	—
44	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
45	C₂²×C₃×C₄×C₅	—	2	1	no	—
46	C₂²×C₃×C₄×C₅	—	2	2	no	—
47	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
48	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
49	C₂²×C₅×Dic₃	—	2	1	no	—
50	C₂×C₅×D₁₂	—	2	1	no	—
51	C₂×C₅×D₁₂	—	2	1	no	—
52	C₂×C₅×D₁₂	—	2	1	no	—
53	C₂×C₅×D₁₂	—	2	1	no	—
54	C₂×C₅×D₁₂	—	2	1	no	—
55	C₂×C₅×D₁₂	C₂×C₄	1	2	yes	complemented
56	C₃×C₅×C₄⋊C₄	—	2	2	no	—
57	C₃×C₅×C₄⋊C₄	—	2	1	no	—
58	C₃×C₅×C₄⋊C₄	—	2	1	no	—
59	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
60	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
61	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
62	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
63	C₃×C₄²×C₅	—	2	2	no	—
64	C₃×C₄²×C₅	—	2	1	no	—
65	C₅×#215	—	2	4	no	—
66	C₅×#213	—	2	4	no	—
67	C₅×(C₂×D₃)⋊C₄	—	4	4	no	—
68	C₄×C₅×Dic₃	—	2	1	no	—
69	C₄×C₅×Dic₃	—	2	1	no	—
70	C₅×#208	—	2	1	no	—
71	C₅×#208	—	2	1	no	—
72	C₅×#208	—	2	1	no	—
73	C₅×#208	C₂×C₄	1	2	yes	complemented
74	C₂×C₅×C₃⋊C₈	—	2	1	no	—
75	C₂×C₅×C₃⋊C₈	—	2	1	no	—
76	C₃×#520	C₂×C₅	1	1	yes	characteristic, complemented
77	C₂×#949	C₂×C₅	1	1	yes	characteristic
78	C₂×#837	C₂×C₅	1	1	yes	characteristic, complemented
79	#5001	C₂×C₅	1	1	yes	characteristic, complemented
80	#4988	C₂×C₅	1	1	yes	characteristic, complemented
81	#4532	C₂×C₅	1	1	yes	characteristic, complemented
82	#4530	C₂×C₅	1	1	yes	characteristic, complemented
83	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
84	C₂²×C₅×D₄	—	3	1	no	—
85	C₅×AGL(1,ℤ/8)	—	3	4	no	—
86	C₅×AGL(1,ℤ/8)	—	6	2	no	—
87	C₂×C₅×SD₁₆	—	6	1	no	—
88	C₂×C₅×D₈	—	6	1	no	—
89	C₂×C₅×M₁₆	—	3	1	no	—
90	C₂×C₅×M₁₆	—	3	1	no	—
91	C₄×C₅×Q₈	—	2	1	no	—
92	C₄×C₅×D₄	—	2	1	no	—
93	C₄×C₅×D₄	—	2	2	no	—
94	C₅×#117	—	2	1	no	—
95	C₅×#117	C₂×D₃	1	1	yes	characteristic
96	C₂×C₅×C₄⋊C₄	—	2	1	no	—
97	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
98	C₂×C₅×C₂²⋊C₄	—	6	2	no	—
99	C₂×C₄²×C₅	—	3	1	no	—
100	C₅×#104	—	6	2	no	—
101	C₅×#102	—	6	1	no	—
102	C₅×#102	—	6	1	no	—
103	#1883	—	3	1	no	Sylow
104	C₂³×C₃×C₅	—	2	1	no	—
105	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₅×D₃	—	2	2	no	—
107	C₂²×C₅×D₃	—	4	2	no	—
108	C₂²×C₅×D₃	—	4	2	no	—
109	C₂²×C₅×D₃	—	4	1	no	—
110	C₂²×C₅×D₃	—	4	1	no	—
111	C₃×C₅×Q₈	—	2	1	no	—
112	C₃×C₅×Q₈	C₂²⋊C₄	1	2	yes	complemented
113	C₃×C₅×D₄	—	2	2	no	—
114	C₃×C₅×D₄	—	2	2	no	—
115	C₃×C₅×D₄	—	2	1	no	—
116	C₃×C₅×D₄	C₂²⋊C₄	1	2	yes	complemented
117	C₂×C₃×C₄×C₅	—	2	1	no	—
118	C₂×C₃×C₄×C₅	—	2	2	no	—
119	C₂×C₃×C₄×C₅	—	2	2	no	—
120	C₂×C₃×C₄×C₅	—	2	1	no	—
121	C₂×C₃×C₄×C₅	—	2	2	no	—
122	C₂×C₃×C₄×C₅	—	2	1	no	—
123	C₂×C₃×C₄×C₅	—	4	2	no	—
124	C₂×C₃×C₄×C₅	—	8	2	no	—
125	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
127	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
128	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
129	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
130	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
131	C₂×C₅×Dic₃	—	2	2	no	—
132	C₂×C₅×Dic₃	—	4	1	no	—
133	C₂×C₅×Dic₃	—	4	1	no	—
134	C₅×D₁₂	—	2	2	no	—
135	C₅×D₁₂	—	2	2	no	—
136	C₅×D₁₂	—	4	1	no	—
137	C₅×D₁₂	—	4	1	no	—
138	C₅×C₃⋊C₈	—	2	2	no	—
139	C₅×C₃⋊C₈	—	4	1	no	—
140	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
141	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
142	C₃×C₄×Q₈	—	2	1	no	—
143	C₃×C₄×D₄	—	2	1	no	—
144	C₃×C₄×D₄	—	2	2	no	—
145	C₃×#117	—	2	1	no	—
146	C₃×#117	C₂²×C₅	1	1	yes	characteristic
147	C₂×C₃×C₄⋊C₄	—	2	1	no	—
148	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
149	#949	—	2	2	no	—
150	#949	C₄×C₅	1	4	yes	complemented
151	C₂×#215	—	2	1	no	—
152	C₂×#213	—	2	1	no	—
153	C₂×(C₂×D₃)⋊C₄	—	2	2	no	—
154	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
155	C₂×#208	C₂²×C₅	1	1	yes	characteristic
156	C₂×#208	C₂²×C₅	1	1	yes	characteristic
157	#837	—	2	2	no	—
158	#809	—	2	1	no	—
159	#809	—	2	1	no	—
160	C₂⁴×C₅	—	6	1	no	—
161	C₅×#41	—	2	1	no	—
162	C₅×#41	—	2	1	no	—
163	C₅×#41	C₄×D₃	1	2	yes	—
164	C₅×#41	D₁₂	1	2	yes	—
165	C₂×C₅×Q₈	#67	1	1	yes	characteristic
166	C₂×C₅×D₄	—	2	1	no	—
167	C₂×C₅×D₄	—	3	2	no	—
168	C₂×C₅×D₄	—	6	1	no	—
169	C₂×C₅×D₄	—	6	1	no	—
170	C₂×C₅×D₄	—	6	1	no	—
171	C₂×C₅×D₄	—	6	1	no	—
172	C₂×C₅×D₄	—	6	1	no	—
173	C₂×C₅×D₄	#67	1	1	yes	characteristic
174	C₂²×C₄×C₅	—	2	1	no	—
175	C₂²×C₄×C₅	—	2	2	no	—
176	C₂²×C₄×C₅	—	6	1	no	—
177	C₂²×C₄×C₅	#67	1	2	yes	—
178	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
179	C₅×SD₁₆	—	6	4	no	—
180	C₅×D₈	—	6	4	no	—
181	C₅×M₁₆	—	3	2	no	—
182	C₅×M₁₆	—	6	1	no	—
183	C₅×M₁₆	—	6	1	no	—
184	C₅×M₁₆	—	6	1	no	—
185	C₂×C₅×C₈	—	6	1	no	—
186	C₂×C₅×C₈	—	6	1	no	—
187	C₅×C₄⋊C₄	—	2	2	no	—
188	C₅×C₄⋊C₄	—	2	1	no	—
189	C₅×C₄⋊C₄	—	2	1	no	—
190	C₅×C₄⋊C₄	#67	1	1	yes	characteristic
191	C₅×C₄⋊C₄	#67	1	1	yes	characteristic
192	C₅×C₂²⋊C₄	—	2	2	no	—
193	C₅×C₂²⋊C₄	—	2	1	no	—
194	C₅×C₂²⋊C₄	—	12	4	no	—
195	C₄²×C₅	—	2	2	no	—
196	C₄²×C₅	—	2	1	no	—
197	C₄²×C₅	—	6	1	no	—
198	C₄²×C₅	—	6	1	no	—
199	C₂×AGL(1,ℤ/8)	—	3	1	no	—
200	#520	C₅×D₃	1	1	yes	characteristic, complemented
201	C₂×#104	—	3	1	no	—
202	#418	—	3	1	no	—
203	#390	—	3	1	no	—
204	#343	—	3	1	no	—
205	#339	—	3	1	no	—
206	C₂²×C₃×C₅	—	2	1	no	—
207	C₂²×C₃×C₅	—	2	1	no	—
208	C₂²×C₃×C₅	—	2	2	no	—
209	C₂²×C₃×C₅	—	4	1	no	—
210	C₂²×C₃×C₅	—	4	1	no	—
211	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
212	C₂²×C₃×C₅	#120	1	1	yes	characteristic
213	C₂²×C₃×C₅	#121	1	1	yes	characteristic
214	C₂×C₅×D₃	—	4	4	no	—
215	C₂×C₅×D₃	—	4	2	no	—
216	C₂×C₅×D₃	—	8	2	no	—
217	C₂×C₅×D₃	—	8	1	no	—
218	C₂×C₅×D₃	—	8	1	no	—
219	C₃×C₄×C₅	—	2	2	no	—
220	C₃×C₄×C₅	—	4	2	no	—
221	C₃×C₄×C₅	—	4	1	no	—
222	C₃×C₄×C₅	—	4	1	no	—
223	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
224	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
225	C₃×C₄×C₅	#121	1	1	yes	characteristic
226	C₃×C₄×C₅	#123	1	1	yes	characteristic
227	C₅×Dic₃	—	4	2	no	—
228	C₂³×D₃	—	2	1	no	—
229	C₃×#41	—	2	1	no	—
230	C₃×#41	—	2	1	no	—
231	C₃×#41	C₂×C₄×C₅	1	2	yes	—
232	C₃×#41	C₅×D₄	1	2	yes	—
233	C₂×C₃×Q₈	C₅×D₄	1	1	yes	characteristic
234	C₂×C₃×D₄	—	2	1	no	—
235	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
236	C₂²×C₃×C₄	—	2	1	no	—
237	C₂²×C₃×C₄	—	2	2	no	—
238	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
239	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
240	C₂²×Dic₃	—	2	1	no	—
241	C₂×D₁₂	—	2	1	no	—
242	C₂×D₁₂	—	2	1	no	—
243	C₂×D₁₂	—	2	1	no	—
244	C₂×D₁₂	—	2	1	no	—
245	C₂×D₁₂	—	2	1	no	—
246	C₂×D₁₂	C₂×C₄×C₅	1	2	yes	complemented
247	C₃×C₄⋊C₄	—	2	2	no	—
248	C₃×C₄⋊C₄	—	2	1	no	—
249	C₃×C₄⋊C₄	—	2	1	no	—
250	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
251	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
252	C₃×C₂²⋊C₄	—	2	2	no	—
253	C₃×C₂²⋊C₄	—	2	1	no	—
254	C₃×C₄²	—	2	2	no	—
255	C₃×C₄²	—	2	1	no	—
256	#215	—	2	4	no	—
257	#213	—	2	4	no	—
258	(C₂×D₃)⋊C₄	—	4	4	no	—
259	C₄×Dic₃	—	2	1	no	—
260	C₄×Dic₃	—	2	1	no	—
261	#208	—	2	1	no	—
262	#208	—	2	1	no	—
263	#208	—	2	1	no	—
264	#208	C₂×C₄×C₅	1	2	yes	complemented
265	C₂×C₃⋊C₈	—	2	1	no	—
266	C₂×C₃⋊C₈	—	2	1	no	—
267	C₂³×C₅	—	2	1	no	—
268	C₂³×C₅	—	6	2	no	—
269	C₂³×C₅	—	12	2	no	—
270	C₂³×C₅	—	12	2	no	—
271	C₂³×C₅	—	12	1	no	—
272	C₂³×C₅	—	12	1	no	—
273	C₂³×C₅	C₂×#67	1	1	yes	characteristic
274	C₅×Q₈	—	2	1	no	—
275	C₅×Q₈	(C₂×D₃)⋊C₄	1	2	yes	complemented
276	C₅×D₄	—	2	2	no	—
277	C₅×D₄	—	2	2	no	—
278	C₅×D₄	—	2	1	no	—
279	C₅×D₄	—	6	2	no	—
280	C₅×D₄	—	6	2	no	—
281	C₅×D₄	—	12	1	no	—
282	C₅×D₄	—	12	1	no	—
283	C₅×D₄	(C₂×D₃)⋊C₄	1	2	yes	complemented
284	C₂×C₄×C₅	—	2	1	no	—
285	C₂×C₄×C₅	—	2	2	no	—
286	C₂×C₄×C₅	—	2	2	no	—
287	C₂×C₄×C₅	—	2	1	no	—
288	C₂×C₄×C₅	—	2	2	no	—
289	C₂×C₄×C₅	—	2	1	no	—
290	C₂×C₄×C₅	—	4	2	no	—
291	C₂×C₄×C₅	—	6	2	no	—
292	C₂×C₄×C₅	—	8	2	no	—
293	C₂×C₄×C₅	—	12	1	no	—
294	C₂×C₄×C₅	—	12	1	no	—
295	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
296	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
297	C₂×C₄×C₅	#235	1	1	yes	characteristic
298	C₂×C₄×C₅	#235	1	1	yes	characteristic
299	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
300	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
301	C₅×C₈	—	6	2	no	—
302	C₅×C₈	—	12	1	no	—
303	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
304	C₂²×D₄	—	3	1	no	—
305	AGL(1,ℤ/8)	—	3	4	no	—
306	AGL(1,ℤ/8)	—	6	2	no	—
307	C₂×SD₁₆	—	6	1	no	—
308	C₂×D₈	—	6	1	no	—
309	C₂×M₁₆	—	3	1	no	—
310	C₂×M₁₆	—	3	1	no	—
311	C₄×Q₈	—	2	1	no	—
312	C₄×D₄	—	2	1	no	—
313	C₄×D₄	—	2	2	no	—
314	#117	—	2	1	no	—
315	#117	C₂×C₅×D₃	1	1	yes	characteristic
316	C₂×C₄⋊C₄	—	2	1	no	—
317	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
318	C₂×C₂²⋊C₄	—	6	2	no	—
319	C₂×C₄²	—	3	1	no	—
320	#104	—	6	2	no	—
321	#102	—	6	1	no	—
322	#102	—	6	1	no	—
323	C₂×C₃×C₅	—	2	1	no	—
324	C₂×C₃×C₅	—	2	1	no	—
325	C₂×C₃×C₅	—	4	2	no	—
326	C₂×C₃×C₅	#386	1	1	yes	characteristic
327	C₂×C₃×C₅	#453	1	1	yes	characteristic
328	C₂×C₃×C₅	#454	1	1	yes	characteristic
329	C₅×D₃	—	8	2	no	—
330	C₂³×C₃	—	2	1	no	—
331	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
332	C₂²×D₃	—	2	2	no	—
333	C₂²×D₃	—	4	2	no	—
334	C₂²×D₃	—	4	2	no	—
335	C₂²×D₃	—	4	1	no	—
336	C₂²×D₃	—	4	1	no	—
337	C₃×Q₈	—	2	1	no	—
338	C₃×Q₈	C₅×C₂²⋊C₄	1	2	yes	complemented
339	C₃×D₄	—	2	2	no	—
340	C₃×D₄	—	2	2	no	—
341	C₃×D₄	—	2	1	no	—
342	C₃×D₄	C₅×C₂²⋊C₄	1	2	yes	complemented
343	C₂×C₃×C₄	—	2	1	no	—
344	C₂×C₃×C₄	—	2	2	no	—
345	C₂×C₃×C₄	—	2	2	no	—
346	C₂×C₃×C₄	—	2	1	no	—
347	C₂×C₃×C₄	—	2	2	no	—
348	C₂×C₃×C₄	—	2	1	no	—
349	C₂×C₃×C₄	—	4	2	no	—
350	C₂×C₃×C₄	—	8	2	no	—
351	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
352	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
353	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
354	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
355	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
356	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
357	C₂×Dic₃	—	2	2	no	—
358	C₂×Dic₃	—	4	1	no	—
359	C₂×Dic₃	—	4	1	no	—
360	D₁₂	—	2	2	no	—
361	D₁₂	—	2	2	no	—
362	D₁₂	—	4	1	no	—
363	D₁₂	—	4	1	no	—
364	C₃⋊C₈	—	2	2	no	—
365	C₃⋊C₈	—	4	1	no	—
366	C₂²×C₅	—	2	1	no	—
367	C₂²×C₅	—	2	1	no	—
368	C₂²×C₅	—	2	2	no	—
369	C₂²×C₅	—	4	1	no	—
370	C₂²×C₅	—	4	1	no	—
371	C₂²×C₅	—	12	4	no	—
372	C₂²×C₅	—	12	2	no	—
373	C₂²×C₅	—	24	2	no	—
374	C₂²×C₅	—	24	1	no	—
375	C₂²×C₅	—	24	1	no	—
376	C₂²×C₅	C₄×#67	1	1	yes	characteristic
377	C₂²×C₅	#930	1	1	yes	characteristic
378	C₂²×C₅	#953	1	1	yes	characteristic
379	C₄×C₅	—	2	2	no	—
380	C₄×C₅	—	4	2	no	—
381	C₄×C₅	—	4	1	no	—
382	C₄×C₅	—	4	1	no	—
383	C₄×C₅	—	12	2	no	—
384	C₄×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
385	C₄×C₅	C₄×#67	1	1	yes	characteristic
386	C₄×C₅	#929	1	1	yes	characteristic
387	C₄×C₅	#930	1	1	yes	characteristic
388	C₂⁴	—	6	1	no	—
389	#41	—	2	1	no	—
390	#41	—	2	1	no	—
391	#41	C₄×C₅×D₃	1	2	yes	—
392	#41	C₅×D₁₂	1	2	yes	—
393	C₂×Q₈	C₅×#67	1	1	yes	characteristic
394	C₂×D₄	—	2	1	no	—
395	C₂×D₄	—	3	2	no	—
396	C₂×D₄	—	6	1	no	—
397	C₂×D₄	—	6	1	no	—
398	C₂×D₄	—	6	1	no	—
399	C₂×D₄	—	6	1	no	—
400	C₂×D₄	—	6	1	no	—
401	C₂×D₄	C₅×#67	1	1	yes	characteristic
402	C₂²×C₄	—	2	1	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	6	1	no	—
405	C₂²×C₄	C₅×#67	1	2	yes	—
406	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
407	SD₁₆	—	6	4	no	—
408	D₈	—	6	4	no	—
409	M₁₆	—	3	2	no	—
410	M₁₆	—	6	1	no	—
411	M₁₆	—	6	1	no	—
412	M₁₆	—	6	1	no	—
413	C₂×C₈	—	6	1	no	—
414	C₂×C₈	—	6	1	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	—	2	1	no	—
417	C₄⋊C₄	—	2	1	no	—
418	C₄⋊C₄	C₅×#67	1	1	yes	characteristic
419	C₄⋊C₄	C₅×#67	1	1	yes	characteristic
420	C₂²⋊C₄	—	2	2	no	—
421	C₂²⋊C₄	—	2	1	no	—
422	C₂²⋊C₄	—	12	4	no	—
423	C₄²	—	2	2	no	—
424	C₄²	—	2	1	no	—
425	C₄²	—	6	1	no	—
426	C₄²	—	6	1	no	—
427	C₃×C₅	#1883	1	1	yes	characteristic, complemented, Hall
428	C₂²×C₃	—	2	1	no	—
429	C₂²×C₃	—	2	1	no	—
430	C₂²×C₃	—	2	2	no	—
431	C₂²×C₃	—	4	1	no	—
432	C₂²×C₃	—	4	1	no	—
433	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
434	C₂²×C₃	C₅×#120	1	1	yes	characteristic
435	C₂²×C₃	C₅×#121	1	1	yes	characteristic
436	C₂×D₃	—	4	4	no	—
437	C₂×D₃	—	4	2	no	—
438	C₂×D₃	—	8	2	no	—
439	C₂×D₃	—	8	1	no	—
440	C₂×D₃	—	8	1	no	—
441	C₃×C₄	—	2	2	no	—
442	C₃×C₄	—	4	2	no	—
443	C₃×C₄	—	4	1	no	—
444	C₃×C₄	—	4	1	no	—
445	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
446	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
447	C₃×C₄	C₅×#121	1	1	yes	characteristic
448	C₃×C₄	C₅×#123	1	1	yes	characteristic
449	Dic₃	—	4	2	no	—
450	C₂×C₅	—	2	1	no	—
451	C₂×C₅	—	2	1	no	—
452	C₂×C₅	—	4	2	no	—
453	C₂×C₅	—	24	2	no	—
454	C₂×C₅	#5213	1	1	yes	characteristic
455	C₂×C₅	#5241	1	1	yes	characteristic
456	C₂×C₅	#5245	1	1	yes	characteristic
457	C₂³	—	2	1	no	—
458	C₂³	—	6	2	no	—
459	C₂³	—	12	2	no	—
460	C₂³	—	12	2	no	—
461	C₂³	—	12	1	no	—
462	C₂³	—	12	1	no	—
463	C₂³	C₂×C₅×#67	1	1	yes	characteristic
464	Q₈	—	2	1	no	—
465	Q₈	C₅×(C₂×D₃)⋊C₄	1	2	yes	complemented
466	D₄	—	2	2	no	—
467	D₄	—	2	2	no	—
468	D₄	—	2	1	no	—
469	D₄	—	6	2	no	—
470	D₄	—	6	2	no	—
471	D₄	—	12	1	no	—
472	D₄	—	12	1	no	—
473	D₄	C₅×(C₂×D₃)⋊C₄	1	2	yes	complemented
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	6	2	no	—
482	C₂×C₄	—	8	2	no	—
483	C₂×C₄	—	12	1	no	—
484	C₂×C₄	—	12	1	no	—
485	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
486	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
487	C₂×C₄	C₅×#235	1	1	yes	characteristic
488	C₂×C₄	C₅×#235	1	1	yes	characteristic
489	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
490	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
491	C₈	—	6	2	no	—
492	C₈	—	12	1	no	—
493	C₂×C₃	—	2	1	no	—
494	C₂×C₃	—	2	1	no	—
495	C₂×C₃	—	4	2	no	—
496	C₂×C₃	C₅×#386	1	1	yes	characteristic
497	C₂×C₃	C₅×#453	1	1	yes	characteristic
498	C₂×C₃	C₅×#454	1	1	yes	characteristic
499	D₃	—	8	2	no	—
500	C₅	#71667	1	1	yes	characteristic, direct product factor, Sylow
501	C₂²	—	2	1	no	—
502	C₂²	—	2	1	no	—
503	C₂²	—	2	2	no	—
504	C₂²	—	4	1	no	—
505	C₂²	—	4	1	no	—
506	C₂²	—	12	4	no	—
507	C₂²	—	12	2	no	—
508	C₂²	—	24	2	no	—
509	C₂²	—	24	1	no	—
510	C₂²	—	24	1	no	—
511	C₂²	C₄×C₅×#67	1	1	yes	characteristic
512	C₂²	C₅×#930	1	1	yes	characteristic
513	C₂²	C₅×#953	1	1	yes	characteristic
514	C₄	—	2	2	no	—
515	C₄	—	4	2	no	—
516	C₄	—	4	1	no	—
517	C₄	—	4	1	no	—
518	C₄	—	12	2	no	—
519	C₄	C₂×C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
520	C₄	C₄×C₅×#67	1	1	yes	characteristic
521	C₄	C₅×#929	1	1	yes	characteristic
522	C₄	C₅×#930	1	1	yes	characteristic
523	C₃	C₅×#1883	1	1	yes	characteristic, complemented, Sylow
524	C₂	—	2	1	no	—
525	C₂	—	2	1	no	—
526	C₂	—	4	2	no	—
527	C₂	—	24	2	no	—
528	C₂	C₅×#5213	1	1	yes	characteristic
529	C₂	C₅×#5241	1	1	yes	characteristic
530	C₂	C₅×#5245	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	#953
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₃×C₅×#520	C₂
socle	C₂²×C₃×C₅	#120
prime radical	C₂×C₅×#949	C₂
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₅×#520	D₃
hypocenter	C₃	C₅×#1883
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#520

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#520	C₂	semidirect
3. C₂×C₅×#837	C₂	semidirect
4. C₅×#5001	C₂	semidirect
5. C₅×#4988	C₂	semidirect
6. C₅×#4532	C₂	semidirect
7. C₅×#4530	C₂	semidirect
19. C₅×#949	C₄	semidirect
29. #71667	C₅	direct (N × H)
31. C₅×#520	D₃	semidirect
55. C₂×C₅×D₁₂	C₂×C₄	semidirect
73. C₅×#208	C₂×C₄	semidirect
76. C₃×#520	C₂×C₅	semidirect
78. C₂×#837	C₂×C₅	semidirect
79. #5001	C₂×C₅	semidirect
80. #4988	C₂×C₅	semidirect
81. #4532	C₂×C₅	semidirect
82. #4530	C₂×C₅	semidirect
112. C₃×C₅×Q₈	C₂²⋊C₄	semidirect
116. C₃×C₅×D₄	C₂²⋊C₄	semidirect
150. #949	C₄×C₅	semidirect
200. #520	C₅×D₃	semidirect
246. C₂×D₁₂	C₂×C₄×C₅	semidirect
264. #208	C₂×C₄×C₅	semidirect
275. C₅×Q₈	(C₂×D₃)⋊C₄	semidirect
283. C₅×D₄	(C₂×D₃)⋊C₄	semidirect
338. C₃×Q₈	C₅×C₂²⋊C₄	semidirect
342. C₃×D₄	C₅×C₂²⋊C₄	semidirect
427. C₃×C₅	#1883	semidirect
465. Q₈	C₅×(C₂×D₃)⋊C₄	semidirect
473. D₄	C₅×(C₂×D₃)⋊C₄	semidirect
500. C₅	#71667	direct (N × H)
523. C₃	C₅×#1883	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#520	2
C₂×C₅×#949	2
C₂×C₅×#837	2
C₅×#5001	2
C₅×#4988	2
C₅×#4532	2
C₅×#4530	2
C₅×#1883	3
#71667	5

Subgroups — C5×#71667 #14301304

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#71667 #14301304