Subgroups — C₅×#81455 #14435427

Order 1920.

772 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5624	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#887	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#484	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5050	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4968	C₂	1	1	yes	maximal, characteristic
6	C₅×#4889	C₂	1	2	yes	maximal, complemented
7	C₅×#4877	C₂	1	2	yes	maximal, complemented
8	C₅×#4798	C₂	1	2	yes	maximal, complemented
9	C₅×#4789	C₂	1	2	yes	maximal, complemented
10	C₅×#4738	C₂	1	1	yes	maximal, characteristic
11	C₅×#4719	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3117	—	3	1	no	maximal, Hall
13	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
14	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₅×#947	C₂²	1	1	yes	characteristic
17	C₅×Q₈×Dic₃	C₂²	1	1	yes	characteristic
18	C₂×C₅×#216	C₂²	1	2	yes	—
19	C₅×#930	C₂²	1	1	yes	characteristic
20	C₂×C₅×Dic₃⋊C₄	—	2	1	no	—
21	C₂×C₄×C₅×Dic₃	—	2	1	no	—
22	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
23	C₂×C₅×#204	C₂²	1	2	yes	—
24	C₅×#898	—	2	1	no	—
25	C₅×#893	C₂²	1	1	yes	characteristic
26	C₅×#892	—	2	1	no	—
27	C₅×#890	C₂²	1	1	yes	characteristic
28	C₅×#887	—	2	1	no	—
29	C₅×#887	—	2	1	no	—
30	C₅×#887	C₂²	1	2	yes	—
31	C₅×#887	C₂²	1	2	yes	—
32	C₅×#886	—	2	1	no	—
33	C₅×#67⋊C₄	—	2	1	no	—
34	C₃×C₅×#107	C₂²	1	2	yes	—
35	C₃×C₅×#103	C₂²	1	2	yes	—
36	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
37	C₅×#830	C₂²	1	1	yes	characteristic
38	C₅×#816	C₂²	1	2	yes	—
39	C₅×#815	C₂²	1	2	yes	—
40	C₅×Dic₃⋊C₈	C₂²	1	2	yes	—
41	C₅×#810	C₂²	1	2	yes	—
42	C₅×#809	C₂²	1	2	yes	—
43	C₅×#808	C₂²	1	2	yes	—
44	#81455	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
45	C₅×#529	—	3	1	no	—
46	C₂×C₄×C₅×Q₈	—	3	1	no	—
47	C₅×#484	D₃	1	1	yes	characteristic, complemented
48	C₅×#481	—	3	1	no	—
49	C₅×#479	—	3	2	no	—
50	C₅×#464	—	3	2	no	—
51	C₅×#451	—	3	1	no	—
52	C₅×#448	—	3	1	no	—
53	C₅×#441	—	3	2	no	—
54	C₅×#440	—	3	2	no	—
55	C₅×#432	—	3	1	no	—
56	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
57	C₂²×C₃×C₄×C₅	—	2	1	no	—
58	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
59	C₂×C₅×#67	—	2	1	no	—
60	C₂²×C₅×Dic₃	—	2	1	no	—
61	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
62	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
63	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
64	C₂×C₄×C₅×D₃	—	2	1	no	—
65	C₂×C₅×Dic₆	—	2	1	no	—
66	C₂×C₅×Dic₆	—	2	4	no	—
67	C₂×C₅×Dic₆	C₂³	1	2	yes	—
68	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
69	C₃×C₅×C₄⋊C₄	—	2	1	no	—
70	C₃×C₅×C₄⋊C₄	—	2	1	no	—
71	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
72	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
73	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
74	C₅×#216	—	2	4	no	—
75	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
76	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
77	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
78	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
79	C₅×C₄⋊Dic₃	—	2	1	no	—
80	C₅×C₄⋊Dic₃	—	2	1	no	—
81	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
82	C₅×Dic₃⋊C₄	—	2	1	no	—
83	C₅×Dic₃⋊C₄	—	2	2	no	—
84	C₅×Dic₃⋊C₄	—	2	2	no	—
85	C₄×C₅×Dic₃	—	2	1	no	—
86	C₄×C₅×Dic₃	—	2	2	no	—
87	C₄×C₅×Dic₃	—	2	2	no	—
88	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
89	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
90	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
91	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
92	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
93	C₅×#204	—	2	4	no	—
94	#5624	C₂×C₅	1	1	yes	characteristic
95	C₂×#887	C₂×C₅	1	1	yes	characteristic, complemented
96	C₃×#484	C₂×C₅	1	1	yes	characteristic, complemented
97	#5050	C₂×C₅	1	1	yes	characteristic, complemented
98	#4968	C₂×C₅	1	1	yes	characteristic
99	#4889	C₂×C₅	1	2	yes	complemented
100	#4877	C₂×C₅	1	2	yes	complemented
101	#4798	C₂×C₅	1	2	yes	complemented
102	#4789	C₂×C₅	1	2	yes	complemented
103	#4738	C₂×C₅	1	1	yes	characteristic
104	#4719	C₂×C₅	1	1	yes	characteristic, complemented
105	C₂²×C₅×Q₈	—	3	1	no	—
106	C₂×C₅×Q₁₆	—	3	2	no	—
107	C₂×C₅×SD₁₆	—	3	2	no	—
108	C₅×#126	—	6	1	no	—
109	C₅×#125	—	3	1	no	—
110	C₅×#124	—	3	1	no	—
111	C₅×#123	—	6	1	no	—
112	C₅×C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic
113	C₅×#121	—	3	1	no	—
114	C₄×C₅×Q₈	—	3	1	no	—
115	C₄×C₅×Q₈	—	3	2	no	—
116	C₄×C₅×Q₈	—	3	2	no	—
117	C₄×C₅×Q₈	—	6	1	no	—
118	C₄×C₅×Q₈	—	6	1	no	—
119	C₄×C₅×D₄	—	3	1	no	—
120	C₄×C₅×D₄	—	6	1	no	—
121	C₅×#117	—	6	1	no	—
122	C₂×C₅×C₄⋊C₄	—	6	1	no	—
123	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
124	C₂×C₄²×C₅	—	3	1	no	—
125	C₂×C₄²×C₅	—	6	1	no	—
126	C₅×#107	C₂×D₃	1	2	yes	—
127	C₅×#106	—	3	2	no	—
128	C₅×C₄⋊C₈	—	3	2	no	—
129	C₅×#103	—	3	2	no	—
130	C₅×#103	—	3	2	no	—
131	C₅×#103	C₂×D₃	1	2	yes	—
132	C₅×#102	—	3	2	no	—
133	C₅×C₂²⋊C₈	—	3	1	no	—
134	C₅×C₂²⋊C₈	C₂×D₃	1	1	yes	characteristic
135	C₅×#97	—	3	2	no	—
136	#3117	—	3	1	no	Sylow
137	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₅×D₃	—	2	1	no	—
139	C₃×C₅×Q₈	—	2	2	no	—
140	C₂×C₃×C₄×C₅	—	2	2	no	—
141	C₂×C₃×C₄×C₅	—	2	2	no	—
142	C₂×C₃×C₄×C₅	—	2	1	no	—
143	C₂×C₃×C₄×C₅	—	2	1	no	—
144	C₂×C₃×C₄×C₅	—	4	2	no	—
145	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
146	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
147	C₅×#67	—	4	2	no	—
148	C₂×C₅×Dic₃	—	2	4	no	—
149	C₂×C₅×Dic₃	—	2	2	no	—
150	C₂×C₅×Dic₃	—	2	2	no	—
151	C₂×C₅×Dic₃	—	2	1	no	—
152	C₂×C₅×Dic₃	—	4	1	no	—
153	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
154	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
155	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
156	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
157	C₅×D₁₂	—	2	2	no	—
158	C₄×C₅×D₃	—	4	2	no	—
159	C₅×Dic₆	—	2	4	no	—
160	C₅×Dic₆	—	2	2	no	—
161	C₅×Dic₆	#41	1	4	yes	—
162	C₃×C₅×C₈	—	2	2	no	—
163	C₅×C₃⋊C₈	—	2	2	no	—
164	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
165	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
166	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
167	#947	C₂²×C₅	1	1	yes	characteristic
168	Q₈×Dic₃	C₂²×C₅	1	1	yes	characteristic
169	C₂×#216	C₂²×C₅	1	2	yes	—
170	#930	C₂²×C₅	1	1	yes	characteristic
171	C₂×Dic₃⋊C₄	—	2	1	no	—
172	C₂×C₄×Dic₃	—	2	1	no	—
173	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
174	C₂×#204	C₂²×C₅	1	2	yes	—
175	#898	—	2	1	no	—
176	#893	C₂²×C₅	1	1	yes	characteristic
177	#892	—	2	1	no	—
178	#890	C₂²×C₅	1	1	yes	characteristic
179	#887	—	2	1	no	—
180	#887	—	2	1	no	—
181	#887	C₂²×C₅	1	2	yes	—
182	#887	C₂²×C₅	1	2	yes	—
183	#886	—	2	1	no	—
184	#67⋊C₄	—	2	1	no	—
185	C₃×#107	C₂²×C₅	1	2	yes	—
186	C₃×#103	C₂²×C₅	1	2	yes	—
187	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
188	#830	C₂²×C₅	1	1	yes	characteristic
189	#816	C₂²×C₅	1	2	yes	—
190	#815	C₂²×C₅	1	2	yes	—
191	Dic₃⋊C₈	C₂²×C₅	1	2	yes	—
192	#810	C₂²×C₅	1	2	yes	—
193	#809	C₂²×C₅	1	2	yes	—
194	#808	C₂²×C₅	1	2	yes	—
195	C₂×C₅×Q₈	—	3	2	no	—
196	C₂×C₅×Q₈	—	6	4	no	—
197	C₂×C₅×Q₈	—	6	1	no	—
198	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
199	C₂×C₅×D₄	—	3	1	no	—
200	C₂×C₅×D₄	—	6	1	no	—
201	C₂²×C₄×C₅	—	2	1	no	—
202	C₂²×C₄×C₅	—	3	1	no	—
203	C₂²×C₄×C₅	—	3	1	no	—
204	C₂²×C₄×C₅	—	6	1	no	—
205	C₂²×C₄×C₅	—	6	1	no	—
206	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
207	C₅×Q₁₆	—	6	4	no	—
208	C₅×SD₁₆	—	6	4	no	—
209	C₂×C₅×C₈	—	3	2	no	—
210	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
211	C₅×C₄⋊C₄	—	2	1	no	—
212	C₅×C₄⋊C₄	—	2	1	no	—
213	C₅×C₄⋊C₄	—	3	1	no	—
214	C₅×C₄⋊C₄	—	6	2	no	—
215	C₅×C₄⋊C₄	—	6	2	no	—
216	C₅×C₄⋊C₄	—	6	1	no	—
217	C₅×C₄⋊C₄	—	6	1	no	—
218	C₅×C₄⋊C₄	—	6	1	no	—
219	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
220	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
221	C₅×C₂²⋊C₄	—	2	1	no	—
222	C₅×C₂²⋊C₄	—	6	1	no	—
223	C₅×C₂²⋊C₄	—	6	1	no	—
224	C₅×C₂²⋊C₄	—	6	1	no	—
225	C₅×C₂²⋊C₄	—	6	1	no	—
226	C₄²×C₅	—	3	1	no	—
227	C₄²×C₅	—	3	1	no	—
228	C₄²×C₅	—	3	1	no	—
229	C₄²×C₅	—	3	1	no	—
230	C₄²×C₅	—	6	2	no	—
231	C₄²×C₅	—	6	2	no	—
232	C₄²×C₅	—	6	1	no	—
233	#529	—	3	1	no	—
234	C₂×C₄×Q₈	—	3	1	no	—
235	#484	C₅×D₃	1	1	yes	characteristic, complemented
236	#481	—	3	1	no	—
237	#479	—	3	2	no	—
238	#464	—	3	2	no	—
239	#451	—	3	1	no	—
240	#448	—	3	1	no	—
241	#441	—	3	2	no	—
242	#440	—	3	2	no	—
243	#432	—	3	1	no	—
244	C₂²×C₃×C₅	—	2	1	no	—
245	C₂²×C₃×C₅	—	2	1	no	—
246	C₂²×C₃×C₅	#137	1	2	yes	—
247	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
248	C₂×C₅×D₃	—	4	1	no	—
249	C₂×C₅×D₃	—	4	1	no	—
250	C₂×C₅×D₃	—	4	1	no	—
251	C₃×C₄×C₅	—	2	1	no	—
252	C₃×C₄×C₅	—	4	1	no	—
253	C₃×C₄×C₅	—	4	1	no	—
254	C₃×C₄×C₅	—	4	2	no	—
255	C₃×C₄×C₅	C₂×#41	1	2	yes	—
256	C₅×Dic₃	—	2	4	no	—
257	C₅×Dic₃	—	2	1	no	—
258	C₅×Dic₃	—	2	1	no	—
259	C₅×Dic₃	—	2	1	no	—
260	C₅×Dic₃	—	2	1	no	—
261	C₅×Dic₃	—	4	1	no	—
262	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
263	C₂²×C₃×C₄	—	2	1	no	—
264	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
265	C₂×#67	—	2	1	no	—
266	C₂²×Dic₃	—	2	1	no	—
267	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
268	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
269	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
270	C₂×C₄×D₃	—	2	1	no	—
271	C₂×Dic₆	—	2	1	no	—
272	C₂×Dic₆	—	2	4	no	—
273	C₂×Dic₆	C₂³×C₅	1	2	yes	—
274	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
275	C₃×C₄⋊C₄	—	2	1	no	—
276	C₃×C₄⋊C₄	—	2	1	no	—
277	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
278	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
279	C₃×C₂²⋊C₄	—	2	1	no	—
280	#216	—	2	4	no	—
281	(C₂×D₃)⋊C₄	—	2	1	no	—
282	(C₂×D₃)⋊C₄	—	2	1	no	—
283	(C₂×D₃)⋊C₄	—	2	1	no	—
284	(C₂×D₃)⋊C₄	—	2	1	no	—
285	C₄⋊Dic₃	—	2	1	no	—
286	C₄⋊Dic₃	—	2	1	no	—
287	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
288	Dic₃⋊C₄	—	2	1	no	—
289	Dic₃⋊C₄	—	2	2	no	—
290	Dic₃⋊C₄	—	2	2	no	—
291	C₄×Dic₃	—	2	1	no	—
292	C₄×Dic₃	—	2	2	no	—
293	C₄×Dic₃	—	2	2	no	—
294	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
295	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
296	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
297	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
298	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
299	#204	—	2	4	no	—
300	C₂³×C₅	—	6	1	no	—
301	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
302	C₅×Q₈	—	2	2	no	—
303	C₅×Q₈	—	3	4	no	—
304	C₅×Q₈	—	6	4	no	—
305	C₅×Q₈	—	6	2	no	—
306	C₅×D₄	—	6	2	no	—
307	C₅×D₄	—	12	2	no	—
308	C₂×C₄×C₅	—	2	2	no	—
309	C₂×C₄×C₅	—	2	2	no	—
310	C₂×C₄×C₅	—	2	1	no	—
311	C₂×C₄×C₅	—	2	1	no	—
312	C₂×C₄×C₅	—	3	1	no	—
313	C₂×C₄×C₅	—	3	1	no	—
314	C₂×C₄×C₅	—	3	1	no	—
315	C₂×C₄×C₅	—	3	1	no	—
316	C₂×C₄×C₅	—	4	2	no	—
317	C₂×C₄×C₅	—	6	4	no	—
318	C₂×C₄×C₅	—	6	2	no	—
319	C₂×C₄×C₅	—	6	2	no	—
320	C₂×C₄×C₅	—	6	1	no	—
321	C₂×C₄×C₅	—	12	2	no	—
322	C₂×C₄×C₅	—	12	1	no	—
323	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
324	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
325	C₅×C₈	—	2	2	no	—
326	C₅×C₈	—	6	2	no	—
327	C₂²×Q₈	—	3	1	no	—
328	C₂×Q₁₆	—	3	2	no	—
329	C₂×SD₁₆	—	3	2	no	—
330	#126	—	6	1	no	—
331	#125	—	3	1	no	—
332	#124	—	3	1	no	—
333	#123	—	6	1	no	—
334	C₂²⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic
335	#121	—	3	1	no	—
336	C₄×Q₈	—	3	1	no	—
337	C₄×Q₈	—	3	2	no	—
338	C₄×Q₈	—	3	2	no	—
339	C₄×Q₈	—	6	1	no	—
340	C₄×Q₈	—	6	1	no	—
341	C₄×D₄	—	3	1	no	—
342	C₄×D₄	—	6	1	no	—
343	#117	—	6	1	no	—
344	C₂×C₄⋊C₄	—	6	1	no	—
345	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
346	C₂×C₄²	—	3	1	no	—
347	C₂×C₄²	—	6	1	no	—
348	#107	C₂×C₅×D₃	1	2	yes	—
349	#106	—	3	2	no	—
350	C₄⋊C₈	—	3	2	no	—
351	#103	—	3	2	no	—
352	#103	—	3	2	no	—
353	#103	C₂×C₅×D₃	1	2	yes	—
354	#102	—	3	2	no	—
355	C₂²⋊C₈	—	3	1	no	—
356	C₂²⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
357	#97	—	3	2	no	—
358	C₂×C₃×C₅	—	2	2	no	—
359	C₂×C₃×C₅	#525	1	1	yes	characteristic
360	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
361	C₂×C₃×C₅	#575	1	1	yes	characteristic
362	C₅×D₃	—	8	1	no	—
363	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
364	C₂²×D₃	—	2	1	no	—
365	C₃×Q₈	—	2	2	no	—
366	C₂×C₃×C₄	—	2	2	no	—
367	C₂×C₃×C₄	—	2	2	no	—
368	C₂×C₃×C₄	—	2	1	no	—
369	C₂×C₃×C₄	—	2	1	no	—
370	C₂×C₃×C₄	—	4	2	no	—
371	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
372	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
373	#67	—	4	2	no	—
374	C₂×Dic₃	—	2	4	no	—
375	C₂×Dic₃	—	2	2	no	—
376	C₂×Dic₃	—	2	2	no	—
377	C₂×Dic₃	—	2	1	no	—
378	C₂×Dic₃	—	4	1	no	—
379	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
380	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
381	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
382	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
383	D₁₂	—	2	2	no	—
384	C₄×D₃	—	4	2	no	—
385	Dic₆	—	2	4	no	—
386	Dic₆	—	2	2	no	—
387	Dic₆	C₅×#41	1	4	yes	—
388	C₃×C₈	—	2	2	no	—
389	C₃⋊C₈	—	2	2	no	—
390	C₂²×C₅	—	2	1	no	—
391	C₂²×C₅	—	2	1	no	—
392	C₂²×C₅	—	12	1	no	—
393	C₂²×C₅	—	12	1	no	—
394	C₂²×C₅	—	12	1	no	—
395	C₂²×C₅	#918	1	2	yes	—
396	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
397	C₄×C₅	—	2	1	no	—
398	C₄×C₅	—	4	1	no	—
399	C₄×C₅	—	4	2	no	—
400	C₄×C₅	—	4	1	no	—
401	C₄×C₅	—	6	4	no	—
402	C₄×C₅	—	6	1	no	—
403	C₄×C₅	—	6	1	no	—
404	C₄×C₅	—	6	1	no	—
405	C₄×C₅	—	6	1	no	—
406	C₄×C₅	—	12	1	no	—
407	C₄×C₅	D₃×#41	1	2	yes	—
408	C₂×Q₈	—	3	2	no	—
409	C₂×Q₈	—	6	4	no	—
410	C₂×Q₈	—	6	1	no	—
411	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
412	C₂×D₄	—	3	1	no	—
413	C₂×D₄	—	6	1	no	—
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	3	1	no	—
416	C₂²×C₄	—	3	1	no	—
417	C₂²×C₄	—	6	1	no	—
418	C₂²×C₄	—	6	1	no	—
419	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
420	Q₁₆	—	6	4	no	—
421	SD₁₆	—	6	4	no	—
422	C₂×C₈	—	3	2	no	—
423	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
424	C₄⋊C₄	—	2	1	no	—
425	C₄⋊C₄	—	2	1	no	—
426	C₄⋊C₄	—	3	1	no	—
427	C₄⋊C₄	—	6	2	no	—
428	C₄⋊C₄	—	6	2	no	—
429	C₄⋊C₄	—	6	1	no	—
430	C₄⋊C₄	—	6	1	no	—
431	C₄⋊C₄	—	6	1	no	—
432	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
433	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
434	C₂²⋊C₄	—	2	1	no	—
435	C₂²⋊C₄	—	6	1	no	—
436	C₂²⋊C₄	—	6	1	no	—
437	C₂²⋊C₄	—	6	1	no	—
438	C₂²⋊C₄	—	6	1	no	—
439	C₄²	—	3	1	no	—
440	C₄²	—	3	1	no	—
441	C₄²	—	3	1	no	—
442	C₄²	—	3	1	no	—
443	C₄²	—	6	2	no	—
444	C₄²	—	6	2	no	—
445	C₄²	—	6	1	no	—
446	C₃×C₅	#3117	1	1	yes	characteristic, complemented, Hall
447	C₂²×C₃	—	2	1	no	—
448	C₂²×C₃	—	2	1	no	—
449	C₂²×C₃	C₅×#137	1	2	yes	—
450	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
451	C₂×D₃	—	4	1	no	—
452	C₂×D₃	—	4	1	no	—
453	C₂×D₃	—	4	1	no	—
454	C₃×C₄	—	2	1	no	—
455	C₃×C₄	—	4	1	no	—
456	C₃×C₄	—	4	1	no	—
457	C₃×C₄	—	4	2	no	—
458	C₃×C₄	C₂×C₅×#41	1	2	yes	—
459	Dic₃	—	2	4	no	—
460	Dic₃	—	2	1	no	—
461	Dic₃	—	2	1	no	—
462	Dic₃	—	2	1	no	—
463	Dic₃	—	2	1	no	—
464	Dic₃	—	4	1	no	—
465	C₂×C₅	—	2	2	no	—
466	C₂×C₅	—	24	1	no	—
467	C₂×C₅	#5656	1	1	yes	characteristic
468	C₂×C₅	C₂×#918	1	1	yes	characteristic
469	C₂×C₅	#5773	1	1	yes	characteristic
470	C₂³	—	6	1	no	—
471	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
472	Q₈	—	2	2	no	—
473	Q₈	—	3	4	no	—
474	Q₈	—	6	4	no	—
475	Q₈	—	6	2	no	—
476	D₄	—	6	2	no	—
477	D₄	—	12	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	3	1	no	—
483	C₂×C₄	—	3	1	no	—
484	C₂×C₄	—	3	1	no	—
485	C₂×C₄	—	3	1	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	6	4	no	—
488	C₂×C₄	—	6	2	no	—
489	C₂×C₄	—	6	2	no	—
490	C₂×C₄	—	6	1	no	—
491	C₂×C₄	—	12	2	no	—
492	C₂×C₄	—	12	1	no	—
493	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
494	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
495	C₈	—	2	2	no	—
496	C₈	—	6	2	no	—
497	C₂×C₃	—	2	2	no	—
498	C₂×C₃	C₅×#525	1	1	yes	characteristic
499	C₂×C₃	C₂×C₅×#137	1	1	yes	characteristic
500	C₂×C₃	C₅×#575	1	1	yes	characteristic
501	D₃	—	8	1	no	—
502	C₅	#81455	1	1	yes	characteristic, direct product factor, Sylow
503	C₂²	—	2	1	no	—
504	C₂²	—	2	1	no	—
505	C₂²	—	12	1	no	—
506	C₂²	—	12	1	no	—
507	C₂²	—	12	1	no	—
508	C₂²	C₅×#918	1	2	yes	—
509	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
510	C₄	—	2	1	no	—
511	C₄	—	4	1	no	—
512	C₄	—	4	2	no	—
513	C₄	—	4	1	no	—
514	C₄	—	6	4	no	—
515	C₄	—	6	1	no	—
516	C₄	—	6	1	no	—
517	C₄	—	6	1	no	—
518	C₄	—	6	1	no	—
519	C₄	—	12	1	no	—
520	C₄	C₅×D₃×#41	1	2	yes	—
521	C₃	C₅×#3117	1	1	yes	characteristic, complemented, Sylow
522	C₂	—	2	2	no	—
523	C₂	—	24	1	no	—
524	C₂	C₅×#5656	1	1	yes	characteristic
525	C₂	C₂×C₅×#918	1	1	yes	characteristic
526	C₂	C₅×#5773	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂×D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#484	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₅×#930	C₂²
hypercenter	C₅×#484	D₃
hypocenter	C₃	C₅×#3117
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#484

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#887	C₂	semidirect
3. C₃×C₅×#484	C₂	semidirect
4. C₅×#5050	C₂	semidirect
6. C₅×#4889	C₂	semidirect
7. C₅×#4877	C₂	semidirect
8. C₅×#4798	C₂	semidirect
9. C₅×#4789	C₂	semidirect
11. C₅×#4719	C₂	semidirect
44. #81455	C₅	direct (N × H)
47. C₅×#484	D₃	semidirect
95. C₂×#887	C₂×C₅	semidirect
96. C₃×#484	C₂×C₅	semidirect
97. #5050	C₂×C₅	semidirect
99. #4889	C₂×C₅	semidirect
100. #4877	C₂×C₅	semidirect
101. #4798	C₂×C₅	semidirect
102. #4789	C₂×C₅	semidirect
104. #4719	C₂×C₅	semidirect
235. #484	C₅×D₃	semidirect
446. C₃×C₅	#3117	semidirect
502. C₅	#81455	direct (N × H)
521. C₃	C₅×#3117	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5624	2
C₂×C₅×#887	2
C₃×C₅×#484	2
C₅×#5050	2
C₅×#4968	2
C₅×#4889	2
C₅×#4877	2
C₅×#4798	2
C₅×#4789	2
C₅×#4738	2
C₅×#4719	2
C₅×#3117	3
#81455	5

Subgroups — C5×#81455 #14435427

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#81455 #14435427