Subgroups — C₅×#81679 #14437989

Order 1920.

784 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5728	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5668	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#489	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5089	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5055	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4804	C₂	1	2	yes	maximal, complemented
7	C₅×#4797	C₂	1	2	yes	maximal, complemented
8	C₅×#4772	C₂	1	2	yes	maximal, complemented
9	C₅×#4764	C₂	1	2	yes	maximal, complemented
10	C₅×#4714	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×D₃×#97	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3135	—	3	1	no	maximal, Hall
13	C₂×C₅×#239	C₂²	1	1	yes	characteristic
14	C₂×C₅×#237	C₂²	1	1	yes	characteristic
15	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₃×C₅×#124	C₂²	1	1	yes	characteristic
17	C₅×#946	—	2	1	no	—
18	C₅×Q₈×Dic₃	—	2	1	no	—
19	C₅×#944	C₂²	1	1	yes	characteristic
20	C₅×#940	C₂²	1	1	yes	characteristic
21	C₂×C₅×D₃×C₈	C₂²	1	2	yes	—
22	C₅×#897	—	2	1	no	—
23	C₅×#892	C₂²	1	2	yes	—
24	C₅×#890	C₂²	1	2	yes	—
25	C₅×#887	—	2	1	no	—
26	C₅×#884	—	2	1	no	—
27	C₅×#884	—	2	1	no	—
28	C₅×#67⋊C₄	—	2	1	no	—
29	C₅×#67⋊C₄	—	2	1	no	—
30	C₅×#875	C₂²	1	1	yes	characteristic
31	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
32	C₅×#869	C₂²	1	1	yes	characteristic
33	C₃×C₅×#103	C₂²	1	2	yes	—
34	C₃×C₅×#102	C₂²	1	2	yes	—
35	C₃×C₅×#97	C₂²	1	1	yes	characteristic
36	C₅×#835	C₂²	1	2	yes	—
37	C₅×#832	C₂²	1	2	yes	—
38	C₅×#821	C₂²	1	2	yes	—
39	C₅×#816	C₂²	1	2	yes	—
40	C₅×#815	C₂²	1	2	yes	—
41	C₅×#810	C₂²	1	2	yes	—
42	C₅×#809	C₂²	1	2	yes	—
43	C₅×#803	C₂²	1	1	yes	characteristic
44	#81679	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
45	C₅×#533	—	3	1	no	—
46	C₅×#532	—	3	1	no	—
47	C₅×#491	—	3	2	no	—
48	C₅×#490	—	3	2	no	—
49	C₅×#489	—	3	1	no	—
50	C₅×#489	—	3	1	no	—
51	C₅×#489	—	3	1	no	—
52	C₅×#489	D₃	1	1	yes	characteristic, complemented
53	C₅×#416	—	3	2	no	—
54	C₅×#416	—	3	2	no	—
55	C₂×C₅×#97	—	3	1	no	—
56	C₂×C₃×C₅×Q₈	—	2	1	no	—
57	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
58	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
59	C₂×C₅×#67	—	2	1	no	—
60	C₂×C₅×#67	—	2	1	no	—
61	C₂×C₅×#67	—	2	1	no	—
62	C₂²×C₅×Dic₃	—	2	1	no	—
63	C₅×#239	—	2	4	no	—
64	C₅×#237	—	2	4	no	—
65	C₂×C₅×D₁₂	—	2	1	no	—
66	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
67	C₂×C₄×C₅×D₃	—	2	1	no	—
68	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
69	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
70	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
71	C₂×C₅×Dic₆	—	2	1	no	—
72	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
73	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
74	C₃×C₅×C₄⋊C₄	—	2	1	no	—
75	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
76	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
77	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
78	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
79	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
80	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
81	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
82	C₅×C₄⋊Dic₃	—	2	1	no	—
83	C₅×C₄⋊Dic₃	—	2	2	no	—
84	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
85	C₅×Dic₃⋊C₄	—	2	1	no	—
86	C₅×Dic₃⋊C₄	—	2	1	no	—
87	C₅×Dic₃⋊C₄	—	2	2	no	—
88	C₄×C₅×Dic₃	—	2	2	no	—
89	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
90	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
91	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
92	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
93	C₅×D₃×C₈	—	2	4	no	—
94	#5728	C₂×C₅	1	1	yes	characteristic, complemented
95	#5668	C₂×C₅	1	1	yes	characteristic
96	C₃×#489	C₂×C₅	1	1	yes	characteristic, complemented
97	#5089	C₂×C₅	1	1	yes	characteristic, complemented
98	#5055	C₂×C₅	1	1	yes	characteristic, complemented
99	#4804	C₂×C₅	1	2	yes	complemented
100	#4797	C₂×C₅	1	2	yes	complemented
101	#4772	C₂×C₅	1	2	yes	complemented
102	#4764	C₂×C₅	1	2	yes	complemented
103	#4714	C₂×C₅	1	1	yes	characteristic, complemented
104	D₃×#97	C₂×C₅	1	1	yes	characteristic, complemented
105	C₂×C₅×#41	—	3	1	no	—
106	C₂×C₅×#41	—	3	1	no	—
107	C₂²×C₅×C₈	—	3	2	no	—
108	C₅×C₄⋊Q₈	—	3	1	no	—
109	C₅×C₄⋊Q₈	—	3	1	no	—
110	C₅×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic
111	C₅×#127	—	3	1	no	—
112	C₅×#125	—	3	2	no	—
113	C₅×#124	—	3	1	no	—
114	C₅×#124	C₂×D₃	1	1	yes	characteristic
115	C₅×C₂²⋊Q₈	—	6	1	no	—
116	C₅×C₂²⋊Q₈	—	6	1	no	—
117	C₅×#121	—	6	1	no	—
118	C₅×#121	—	6	1	no	—
119	C₄×C₅×Q₈	—	6	1	no	—
120	C₄×C₅×Q₈	—	6	1	no	—
121	C₄×C₅×D₄	—	6	1	no	—
122	C₄×C₅×D₄	—	6	1	no	—
123	C₅×#117	—	3	2	no	—
124	C₂×C₄²×C₅	—	3	1	no	—
125	C₅×#103	—	3	2	no	—
126	C₅×#103	—	3	2	no	—
127	C₅×#103	—	3	2	no	—
128	C₅×#103	C₂×D₃	1	2	yes	—
129	C₅×#102	—	3	2	no	—
130	C₅×#102	—	3	2	no	—
131	C₅×#102	—	3	2	no	—
132	C₅×#102	C₂×D₃	1	2	yes	—
133	C₅×#97	—	3	2	no	—
134	C₅×#97	—	3	1	no	—
135	C₅×#97	C₂×D₃	1	1	yes	characteristic
136	#3135	—	3	1	no	Sylow
137	C₂³×C₃×C₅	—	2	1	no	—
138	C₂²×C₅×D₃	—	2	1	no	—
139	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
140	C₃×C₅×Q₈	—	2	2	no	—
141	C₃×C₅×Q₈	—	4	2	no	—
142	C₃×C₅×D₄	—	2	2	no	—
143	C₂×C₃×C₄×C₅	—	2	2	no	—
144	C₂×C₃×C₄×C₅	—	2	1	no	—
145	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
146	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
147	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
148	C₅×#67	—	4	2	no	—
149	C₅×#67	—	4	2	no	—
150	C₅×#67	—	4	2	no	—
151	C₂×C₅×Dic₃	—	2	2	no	—
152	C₂×C₅×Dic₃	—	2	1	no	—
153	C₂×C₅×Dic₃	—	4	2	no	—
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	C₅×D₁₂	—	4	2	no	—
159	C₄×C₅×D₃	—	4	1	no	—
160	C₄×C₅×D₃	—	4	1	no	—
161	C₄×C₅×D₃	—	4	2	no	—
162	C₄×C₅×D₃	#41	1	4	yes	—
163	C₅×Dic₆	—	2	2	no	—
164	C₅×Dic₆	—	4	2	no	—
165	C₃×C₅×C₈	—	2	2	no	—
166	C₅×C₃⋊C₈	—	2	2	no	—
167	C₂×#239	C₂²×C₅	1	1	yes	characteristic
168	C₂×#237	C₂²×C₅	1	1	yes	characteristic
169	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
170	C₃×#124	C₂²×C₅	1	1	yes	characteristic
171	#946	—	2	1	no	—
172	Q₈×Dic₃	—	2	1	no	—
173	#944	C₂²×C₅	1	1	yes	characteristic
174	#940	C₂²×C₅	1	1	yes	characteristic
175	C₂×D₃×C₈	C₂²×C₅	1	2	yes	—
176	#897	—	2	1	no	—
177	#892	C₂²×C₅	1	2	yes	—
178	#890	C₂²×C₅	1	2	yes	—
179	#887	—	2	1	no	—
180	#884	—	2	1	no	—
181	#884	—	2	1	no	—
182	#67⋊C₄	—	2	1	no	—
183	#67⋊C₄	—	2	1	no	—
184	#875	C₂²×C₅	1	1	yes	characteristic
185	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
186	#869	C₂²×C₅	1	1	yes	characteristic
187	C₃×#103	C₂²×C₅	1	2	yes	—
188	C₃×#102	C₂²×C₅	1	2	yes	—
189	C₃×#97	C₂²×C₅	1	1	yes	characteristic
190	#835	C₂²×C₅	1	2	yes	—
191	#832	C₂²×C₅	1	2	yes	—
192	#821	C₂²×C₅	1	2	yes	—
193	#816	C₂²×C₅	1	2	yes	—
194	#815	C₂²×C₅	1	2	yes	—
195	#810	C₂²×C₅	1	2	yes	—
196	#809	C₂²×C₅	1	2	yes	—
197	#803	C₂²×C₅	1	1	yes	characteristic
198	C₅×#41	—	6	4	no	—
199	C₅×#41	—	6	4	no	—
200	C₂×C₅×Q₈	—	2	1	no	—
201	C₂×C₅×Q₈	—	3	1	no	—
202	C₂×C₅×Q₈	—	6	1	no	—
203	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
204	C₂×C₅×D₄	—	3	1	no	—
205	C₂×C₅×D₄	—	6	1	no	—
206	C₂×C₅×D₄	—	6	1	no	—
207	C₂×C₅×D₄	—	6	1	no	—
208	C₂×C₅×D₄	—	6	1	no	—
209	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
210	C₂²×C₄×C₅	—	3	1	no	—
211	C₂²×C₄×C₅	—	3	1	no	—
212	C₂²×C₄×C₅	—	3	1	no	—
213	C₂²×C₄×C₅	—	6	1	no	—
214	C₂²×C₄×C₅	—	6	1	no	—
215	C₂×C₅×C₈	—	3	2	no	—
216	C₂×C₅×C₈	—	6	4	no	—
217	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
218	C₅×C₄⋊C₄	—	2	1	no	—
219	C₅×C₄⋊C₄	—	3	2	no	—
220	C₅×C₄⋊C₄	—	6	1	no	—
221	C₅×C₄⋊C₄	—	6	1	no	—
222	C₅×C₄⋊C₄	—	6	2	no	—
223	C₅×C₄⋊C₄	—	6	2	no	—
224	C₅×C₄⋊C₄	—	6	1	no	—
225	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
226	C₅×C₂²⋊C₄	—	2	1	no	—
227	C₅×C₂²⋊C₄	—	2	1	no	—
228	C₅×C₂²⋊C₄	—	6	2	no	—
229	C₅×C₂²⋊C₄	—	6	1	no	—
230	C₅×C₂²⋊C₄	—	6	1	no	—
231	C₄²×C₅	—	3	1	no	—
232	C₄²×C₅	—	3	1	no	—
233	C₄²×C₅	—	3	1	no	—
234	C₄²×C₅	—	6	2	no	—
235	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
236	#533	—	3	1	no	—
237	#532	—	3	1	no	—
238	#491	—	3	2	no	—
239	#490	—	3	2	no	—
240	#489	—	3	1	no	—
241	#489	—	3	1	no	—
242	#489	—	3	1	no	—
243	#489	C₅×D₃	1	1	yes	characteristic, complemented
244	#416	—	3	2	no	—
245	#416	—	3	2	no	—
246	C₂×#97	—	3	1	no	—
247	C₂²×C₃×C₅	—	4	1	no	—
248	C₂²×C₃×C₅	—	4	1	no	—
249	C₂²×C₃×C₅	—	4	1	no	—
250	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
251	C₂×C₅×D₃	—	2	1	no	—
252	C₂×C₅×D₃	—	2	1	no	—
253	C₂×C₅×D₃	—	4	1	no	—
254	C₂×C₅×D₃	—	4	1	no	—
255	C₂×C₅×D₃	—	4	1	no	—
256	C₂×C₅×D₃	#124	1	2	yes	—
257	C₃×C₄×C₅	—	2	1	no	—
258	C₃×C₄×C₅	—	2	1	no	—
259	C₃×C₄×C₅	—	4	1	no	—
260	C₃×C₄×C₅	—	4	2	no	—
261	C₃×C₄×C₅	C₂×#41	1	2	yes	—
262	C₅×Dic₃	—	2	1	no	—
263	C₅×Dic₃	—	2	1	no	—
264	C₅×Dic₃	—	4	1	no	—
265	C₅×Dic₃	—	4	2	no	—
266	C₅×Dic₃	#124	1	2	yes	—
267	C₂×C₃×Q₈	—	2	1	no	—
268	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
269	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
270	C₂×#67	—	2	1	no	—
271	C₂×#67	—	2	1	no	—
272	C₂×#67	—	2	1	no	—
273	C₂²×Dic₃	—	2	1	no	—
274	#239	—	2	4	no	—
275	#237	—	2	4	no	—
276	C₂×D₁₂	—	2	1	no	—
277	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
278	C₂×C₄×D₃	—	2	1	no	—
279	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
280	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
281	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
282	C₂×Dic₆	—	2	1	no	—
283	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
284	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
285	C₃×C₄⋊C₄	—	2	1	no	—
286	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
287	C₃×C₂²⋊C₄	—	2	1	no	—
288	C₃×C₂²⋊C₄	—	2	1	no	—
289	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
290	(C₂×D₃)⋊C₄	—	2	2	no	—
291	(C₂×D₃)⋊C₄	—	2	1	no	—
292	(C₂×D₃)⋊C₄	—	2	1	no	—
293	C₄⋊Dic₃	—	2	1	no	—
294	C₄⋊Dic₃	—	2	2	no	—
295	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
296	Dic₃⋊C₄	—	2	1	no	—
297	Dic₃⋊C₄	—	2	1	no	—
298	Dic₃⋊C₄	—	2	2	no	—
299	C₄×Dic₃	—	2	2	no	—
300	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
301	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
302	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
303	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
304	D₃×C₈	—	2	4	no	—
305	C₂³×C₅	—	2	1	no	—
306	C₂³×C₅	—	3	1	no	—
307	C₂³×C₅	—	6	1	no	—
308	C₅×Q₈	—	2	2	no	—
309	C₅×Q₈	—	4	2	no	—
310	C₅×Q₈	—	6	2	no	—
311	C₅×Q₈	—	12	2	no	—
312	C₅×D₄	—	2	2	no	—
313	C₅×D₄	—	6	2	no	—
314	C₅×D₄	—	12	2	no	—
315	C₅×D₄	—	12	2	no	—
316	C₅×D₄	—	12	2	no	—
317	C₅×D₄	—	12	2	no	—
318	C₂×C₄×C₅	—	2	2	no	—
319	C₂×C₄×C₅	—	2	1	no	—
320	C₂×C₄×C₅	—	3	1	no	—
321	C₂×C₄×C₅	—	3	4	no	—
322	C₂×C₄×C₅	—	3	1	no	—
323	C₂×C₄×C₅	—	3	1	no	—
324	C₂×C₄×C₅	—	6	2	no	—
325	C₂×C₄×C₅	—	6	1	no	—
326	C₂×C₄×C₅	—	12	1	no	—
327	C₂×C₄×C₅	—	12	1	no	—
328	C₂×C₄×C₅	—	12	2	no	—
329	C₂×C₄×C₅	—	12	2	no	—
330	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
331	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
332	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
333	C₅×C₈	—	2	2	no	—
334	C₅×C₈	—	6	2	no	—
335	C₂×#41	—	3	1	no	—
336	C₂×#41	—	3	1	no	—
337	C₂²×C₈	—	3	2	no	—
338	C₄⋊Q₈	—	3	1	no	—
339	C₄⋊Q₈	—	3	1	no	—
340	C₄⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic
341	#127	—	3	1	no	—
342	#125	—	3	2	no	—
343	#124	—	3	1	no	—
344	#124	C₂×C₅×D₃	1	1	yes	characteristic
345	C₂²⋊Q₈	—	6	1	no	—
346	C₂²⋊Q₈	—	6	1	no	—
347	#121	—	6	1	no	—
348	#121	—	6	1	no	—
349	C₄×Q₈	—	6	1	no	—
350	C₄×Q₈	—	6	1	no	—
351	C₄×D₄	—	6	1	no	—
352	C₄×D₄	—	6	1	no	—
353	#117	—	3	2	no	—
354	C₂×C₄²	—	3	1	no	—
355	#103	—	3	2	no	—
356	#103	—	3	2	no	—
357	#103	—	3	2	no	—
358	#103	C₂×C₅×D₃	1	2	yes	—
359	#102	—	3	2	no	—
360	#102	—	3	2	no	—
361	#102	—	3	2	no	—
362	#102	C₂×C₅×D₃	1	2	yes	—
363	#97	—	3	2	no	—
364	#97	—	3	1	no	—
365	#97	C₂×C₅×D₃	1	1	yes	characteristic
366	C₂×C₃×C₅	—	8	1	no	—
367	C₂×C₃×C₅	C₂×#124	1	1	yes	characteristic
368	C₂×C₃×C₅	#575	1	1	yes	characteristic
369	C₂×C₃×C₅	#575	1	1	yes	characteristic
370	C₅×D₃	—	2	2	no	—
371	C₅×D₃	—	8	1	no	—
372	C₂³×C₃	—	2	1	no	—
373	C₂²×D₃	—	2	1	no	—
374	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
375	C₃×Q₈	—	2	2	no	—
376	C₃×Q₈	—	4	2	no	—
377	C₃×D₄	—	2	2	no	—
378	C₂×C₃×C₄	—	2	2	no	—
379	C₂×C₃×C₄	—	2	1	no	—
380	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
381	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
382	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
383	#67	—	4	2	no	—
384	#67	—	4	2	no	—
385	#67	—	4	2	no	—
386	C₂×Dic₃	—	2	2	no	—
387	C₂×Dic₃	—	2	1	no	—
388	C₂×Dic₃	—	4	2	no	—
389	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
390	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
391	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
392	D₁₂	—	2	2	no	—
393	D₁₂	—	4	2	no	—
394	C₄×D₃	—	4	1	no	—
395	C₄×D₃	—	4	1	no	—
396	C₄×D₃	—	4	2	no	—
397	C₄×D₃	C₅×#41	1	4	yes	—
398	Dic₆	—	2	2	no	—
399	Dic₆	—	4	2	no	—
400	C₃×C₈	—	2	2	no	—
401	C₃⋊C₈	—	2	2	no	—
402	C₂²×C₅	—	3	2	no	—
403	C₂²×C₅	—	4	1	no	—
404	C₂²×C₅	—	4	1	no	—
405	C₂²×C₅	—	4	1	no	—
406	C₂²×C₅	—	6	1	no	—
407	C₂²×C₅	—	6	1	no	—
408	C₂²×C₅	—	12	1	no	—
409	C₂²×C₅	—	12	1	no	—
410	C₂²×C₅	—	12	1	no	—
411	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
412	C₄×C₅	—	2	1	no	—
413	C₄×C₅	—	2	1	no	—
414	C₄×C₅	—	3	2	no	—
415	C₄×C₅	—	4	1	no	—
416	C₄×C₅	—	4	2	no	—
417	C₄×C₅	—	6	1	no	—
418	C₄×C₅	—	6	1	no	—
419	C₄×C₅	—	12	1	no	—
420	C₄×C₅	—	12	2	no	—
421	C₄×C₅	D₃×#41	1	2	yes	—
422	#41	—	6	4	no	—
423	#41	—	6	4	no	—
424	C₂×Q₈	—	2	1	no	—
425	C₂×Q₈	—	3	1	no	—
426	C₂×Q₈	—	6	1	no	—
427	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
428	C₂×D₄	—	3	1	no	—
429	C₂×D₄	—	6	1	no	—
430	C₂×D₄	—	6	1	no	—
431	C₂×D₄	—	6	1	no	—
432	C₂×D₄	—	6	1	no	—
433	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
434	C₂²×C₄	—	3	1	no	—
435	C₂²×C₄	—	3	1	no	—
436	C₂²×C₄	—	3	1	no	—
437	C₂²×C₄	—	6	1	no	—
438	C₂²×C₄	—	6	1	no	—
439	C₂×C₈	—	3	2	no	—
440	C₂×C₈	—	6	4	no	—
441	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
442	C₄⋊C₄	—	2	1	no	—
443	C₄⋊C₄	—	3	2	no	—
444	C₄⋊C₄	—	6	1	no	—
445	C₄⋊C₄	—	6	1	no	—
446	C₄⋊C₄	—	6	2	no	—
447	C₄⋊C₄	—	6	2	no	—
448	C₄⋊C₄	—	6	1	no	—
449	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
450	C₂²⋊C₄	—	2	1	no	—
451	C₂²⋊C₄	—	2	1	no	—
452	C₂²⋊C₄	—	6	2	no	—
453	C₂²⋊C₄	—	6	1	no	—
454	C₂²⋊C₄	—	6	1	no	—
455	C₄²	—	3	1	no	—
456	C₄²	—	3	1	no	—
457	C₄²	—	3	1	no	—
458	C₄²	—	6	2	no	—
459	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
460	C₃×C₅	#3135	1	1	yes	characteristic, complemented, Hall
461	C₂²×C₃	—	4	1	no	—
462	C₂²×C₃	—	4	1	no	—
463	C₂²×C₃	—	4	1	no	—
464	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
465	C₂×D₃	—	2	1	no	—
466	C₂×D₃	—	2	1	no	—
467	C₂×D₃	—	4	1	no	—
468	C₂×D₃	—	4	1	no	—
469	C₂×D₃	—	4	1	no	—
470	C₂×D₃	C₅×#124	1	2	yes	—
471	C₃×C₄	—	2	1	no	—
472	C₃×C₄	—	2	1	no	—
473	C₃×C₄	—	4	1	no	—
474	C₃×C₄	—	4	2	no	—
475	C₃×C₄	C₂×C₅×#41	1	2	yes	—
476	Dic₃	—	2	1	no	—
477	Dic₃	—	2	1	no	—
478	Dic₃	—	4	1	no	—
479	Dic₃	—	4	2	no	—
480	Dic₃	C₅×#124	1	2	yes	—
481	C₂×C₅	—	6	2	no	—
482	C₂×C₅	—	8	1	no	—
483	C₂×C₅	—	24	1	no	—
484	C₂×C₅	D₃×#124	1	1	yes	characteristic
485	C₂×C₅	#5773	1	1	yes	characteristic
486	C₂×C₅	#5777	1	1	yes	characteristic
487	C₂³	—	2	1	no	—
488	C₂³	—	3	1	no	—
489	C₂³	—	6	1	no	—
490	Q₈	—	2	2	no	—
491	Q₈	—	4	2	no	—
492	Q₈	—	6	2	no	—
493	Q₈	—	12	2	no	—
494	D₄	—	2	2	no	—
495	D₄	—	6	2	no	—
496	D₄	—	12	2	no	—
497	D₄	—	12	2	no	—
498	D₄	—	12	2	no	—
499	D₄	—	12	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	3	1	no	—
503	C₂×C₄	—	3	4	no	—
504	C₂×C₄	—	3	1	no	—
505	C₂×C₄	—	3	1	no	—
506	C₂×C₄	—	6	2	no	—
507	C₂×C₄	—	6	1	no	—
508	C₂×C₄	—	12	1	no	—
509	C₂×C₄	—	12	1	no	—
510	C₂×C₄	—	12	2	no	—
511	C₂×C₄	—	12	2	no	—
512	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
513	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
514	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
515	C₈	—	2	2	no	—
516	C₈	—	6	2	no	—
517	C₂×C₃	—	8	1	no	—
518	C₂×C₃	C₂×C₅×#124	1	1	yes	characteristic
519	C₂×C₃	C₅×#575	1	1	yes	characteristic
520	C₂×C₃	C₅×#575	1	1	yes	characteristic
521	D₃	—	2	2	no	—
522	D₃	—	8	1	no	—
523	C₅	#81679	1	1	yes	characteristic, direct product factor, Sylow
524	C₂²	—	3	2	no	—
525	C₂²	—	4	1	no	—
526	C₂²	—	4	1	no	—
527	C₂²	—	4	1	no	—
528	C₂²	—	6	1	no	—
529	C₂²	—	6	1	no	—
530	C₂²	—	12	1	no	—
531	C₂²	—	12	1	no	—
532	C₂²	—	12	1	no	—
533	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
534	C₄	—	2	1	no	—
535	C₄	—	2	1	no	—
536	C₄	—	3	2	no	—
537	C₄	—	4	1	no	—
538	C₄	—	4	2	no	—
539	C₄	—	6	1	no	—
540	C₄	—	6	1	no	—
541	C₄	—	12	1	no	—
542	C₄	—	12	2	no	—
543	C₄	C₅×D₃×#41	1	2	yes	—
544	C₃	C₅×#3135	1	1	yes	characteristic, complemented, Sylow
545	C₂	—	6	2	no	—
546	C₂	—	8	1	no	—
547	C₂	—	24	1	no	—
548	C₂	C₅×D₃×#124	1	1	yes	characteristic
549	C₂	C₅×#5773	1	1	yes	characteristic
550	C₂	C₅×#5777	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×#489	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₅×#5668	C₂
hypercenter	C₅×#489	D₃
hypocenter	C₃	C₅×#3135
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#489

Complements

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

N	H ≅ G/N	type
1. C₅×#5728	C₂	semidirect
3. C₃×C₅×#489	C₂	semidirect
4. C₅×#5089	C₂	semidirect
5. C₅×#5055	C₂	semidirect
6. C₅×#4804	C₂	semidirect
7. C₅×#4797	C₂	semidirect
8. C₅×#4772	C₂	semidirect
9. C₅×#4764	C₂	semidirect
10. C₅×#4714	C₂	semidirect
11. C₅×D₃×#97	C₂	semidirect
44. #81679	C₅	direct (N × H)
52. C₅×#489	D₃	semidirect
94. #5728	C₂×C₅	semidirect
96. C₃×#489	C₂×C₅	semidirect
97. #5089	C₂×C₅	semidirect
98. #5055	C₂×C₅	semidirect
99. #4804	C₂×C₅	semidirect
100. #4797	C₂×C₅	semidirect
101. #4772	C₂×C₅	semidirect
102. #4764	C₂×C₅	semidirect
103. #4714	C₂×C₅	semidirect
104. D₃×#97	C₂×C₅	semidirect
243. #489	C₅×D₃	semidirect
460. C₃×C₅	#3135	semidirect
523. C₅	#81679	direct (N × H)
544. C₃	C₅×#3135	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5728	2
C₅×#5668	2
C₃×C₅×#489	2
C₅×#5089	2
C₅×#5055	2
C₅×#4804	2
C₅×#4797	2
C₅×#4772	2
C₅×#4764	2
C₅×#4714	2
C₅×D₃×#97	2
C₅×#3135	3
#81679	5

Subgroups — C5×#81679 #14437989

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#81679 #14437989