Subgroups — C₅×#81588 #14471906

Order 1920.

784 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5722	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5718	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#486	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5084	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5075	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4762	C₂	1	2	yes	maximal, complemented
7	C₅×#4761	C₂	1	2	yes	maximal, complemented
8	C₅×#4760	C₂	1	2	yes	maximal, complemented
9	C₅×#4758	C₂	1	2	yes	maximal, complemented
10	C₄×C₅×#204	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×C₈×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3362	—	3	1	no	maximal, Hall
13	C₂×C₅×#237	—	2	1	no	—
14	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₃×C₅×#127	C₂²	1	1	yes	characteristic
16	C₅×#944	—	2	2	no	—
17	C₅×#940	C₂²	1	2	yes	—
18	C₅×#939	—	2	2	no	—
19	C₅×#938	—	2	1	no	—
20	C₅×D₄×Dic₃	C₂²	1	2	yes	—
21	C₂×C₅×#214	C₂²	1	2	yes	—
22	C₂×C₅×#204	C₂²	1	1	yes	characteristic
23	C₅×#888	—	2	1	no	—
24	C₅×#888	C₂²	1	2	yes	—
25	C₅×#887	—	2	1	no	—
26	C₅×#887	C₂²	1	2	yes	—
27	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
28	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
29	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
30	C₃×C₅×#102	C₂²	1	2	yes	—
31	C₃×C₅×#102	C₂²	1	2	yes	—
32	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
33	C₅×#832	C₂²	1	2	yes	—
34	C₅×#821	C₂²	1	1	yes	characteristic
35	C₅×#817	C₂²	1	1	yes	characteristic
36	C₅×#816	C₂²	1	1	yes	characteristic
37	C₅×Dic₃⋊C₈	C₂²	1	2	yes	—
38	C₅×C₈×Dic₃	C₂²	1	2	yes	—
39	C₅×#809	C₂²	1	2	yes	—
40	C₅×#808	C₂²	1	2	yes	—
41	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
42	#81588	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
43	C₅×Q₈²	—	3	1	no	—
44	C₅×#550	—	3	1	no	—
45	C₅×#486	—	3	2	no	—
46	C₅×#486	D₃	1	1	yes	characteristic, complemented
47	C₅×#476	—	3	2	no	—
48	C₅×#476	—	3	1	no	—
49	C₅×#460	—	3	2	no	—
50	C₅×#460	—	3	1	no	—
51	C₅×C₈×Q₈	—	3	1	no	—
52	C₄×C₅×SD₁₆	—	3	2	no	—
53	C₄×C₅×SD₁₆	—	3	1	no	—
54	C₂×C₃×C₅×Q₈	—	2	1	no	—
55	C₂×C₃×C₅×D₄	—	2	1	no	—
56	C₂×C₃×C₅×D₄	—	2	1	no	—
57	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
58	C₂×C₅×#67	—	2	2	no	—
59	C₂×C₅×#67	—	2	2	no	—
60	C₂²×C₅×Dic₃	—	2	2	no	—
61	C₅×#237	—	4	4	no	—
62	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
63	C₂×C₄×C₅×D₃	—	2	1	no	—
64	C₂×C₅×Dic₆	—	2	2	no	—
65	C₂×C₅×Dic₆	D₄	1	1	yes	characteristic
66	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
67	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
68	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
69	C₃×C₅×C₄⋊C₄	—	2	1	no	—
70	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
71	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
72	C₅×#217	—	2	2	no	—
73	C₅×#214	—	2	4	no	—
74	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
75	C₅×C₄⋊Dic₃	D₄	1	1	yes	characteristic
76	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
77	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
78	C₅×Dic₃⋊C₄	—	2	1	no	—
79	C₅×Dic₃⋊C₄	—	2	2	no	—
80	C₅×Dic₃⋊C₄	—	2	2	no	—
81	C₅×Dic₃⋊C₄	D₄	1	2	yes	—
82	C₄×C₅×Dic₃	—	2	1	no	—
83	C₄×C₅×Dic₃	—	2	2	no	—
84	C₄×C₅×Dic₃	C₂³	1	2	yes	—
85	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
86	C₅×#204	—	2	2	no	—
87	#5722	C₂×C₅	1	1	yes	characteristic, complemented
88	#5718	C₂×C₅	1	1	yes	characteristic
89	C₃×#486	C₂×C₅	1	1	yes	characteristic, complemented
90	#5084	C₂×C₅	1	1	yes	characteristic, complemented
91	#5075	C₂×C₅	1	1	yes	characteristic, complemented
92	#4762	C₂×C₅	1	2	yes	complemented
93	#4761	C₂×C₅	1	2	yes	complemented
94	#4760	C₂×C₅	1	2	yes	complemented
95	#4758	C₂×C₅	1	2	yes	complemented
96	C₄×#204	C₂×C₅	1	1	yes	characteristic, complemented
97	C₈×Dic₆	C₂×C₅	1	1	yes	characteristic, complemented
98	C₂×C₅×#41	—	6	1	no	—
99	C₂×C₅×SD₁₆	—	3	2	no	—
100	C₂×C₅×SD₁₆	—	3	1	no	—
101	C₅×C₄⋊Q₈	—	3	2	no	—
102	C₅×C₄⋊Q₈	—	6	1	no	—
103	C₅×C₄⋊Q₈	—	6	2	no	—
104	C₅×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic
105	C₅×#127	—	3	2	no	—
106	C₅×#127	C₂×D₃	1	1	yes	characteristic
107	C₅×#121	—	6	1	no	—
108	C₅×#121	—	6	2	no	—
109	C₄×C₅×Q₈	—	3	1	no	—
110	C₄×C₅×Q₈	—	3	2	no	—
111	C₄×C₅×Q₈	—	3	1	no	—
112	C₄×C₅×Q₈	—	6	1	no	—
113	C₄×C₅×D₄	—	3	2	no	—
114	C₄×C₅×D₄	—	3	1	no	—
115	C₅×#106	—	3	1	no	—
116	C₅×#106	—	3	2	no	—
117	C₅×C₄⋊C₈	—	3	2	no	—
118	C₅×C₄⋊C₈	—	3	1	no	—
119	C₅×#103	—	3	1	no	—
120	C₅×#102	—	3	2	no	—
121	C₅×#102	—	3	1	no	—
122	C₅×#102	—	3	2	no	—
123	C₅×#102	C₂×D₃	1	2	yes	—
124	C₅×#102	C₂×D₃	1	2	yes	—
125	C₄×C₅×C₈	—	3	2	no	—
126	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
127	#3362	—	3	1	no	Sylow
128	C₂³×C₃×C₅	—	2	2	no	—
129	C₂²×C₅×D₃	—	2	1	no	—
130	C₃×C₅×Q₈	—	8	1	no	—
131	C₃×C₅×D₄	—	2	2	no	—
132	C₃×C₅×D₄	—	2	2	no	—
133	C₃×C₅×D₄	—	4	2	no	—
134	C₃×C₅×D₄	—	8	1	no	—
135	C₂×C₃×C₄×C₅	—	2	2	no	—
136	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
137	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
138	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
139	C₅×#67	—	4	4	no	—
140	C₅×#67	—	8	2	no	—
141	C₂×C₅×Dic₃	—	2	1	no	—
142	C₂×C₅×Dic₃	—	2	1	no	—
143	C₂×C₅×Dic₃	—	2	1	no	—
144	C₂×C₅×Dic₃	—	4	4	no	—
145	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
146	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
147	C₅×D₁₂	—	2	1	no	—
148	C₅×D₁₂	—	2	1	no	—
149	C₄×C₅×D₃	—	4	2	no	—
150	C₅×Dic₆	—	2	1	no	—
151	C₅×Dic₆	—	8	2	no	—
152	C₅×Dic₆	SD₁₆	1	4	yes	complemented
153	C₅×Dic₆	#41	1	2	yes	complemented
154	C₃×C₅×C₈	—	2	1	no	—
155	C₃×C₅×C₈	—	2	1	no	—
156	C₅×C₃⋊C₈	—	2	2	no	—
157	C₂×#237	—	2	1	no	—
158	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
159	C₃×#127	C₂²×C₅	1	1	yes	characteristic
160	#944	—	2	2	no	—
161	#940	C₂²×C₅	1	2	yes	—
162	#939	—	2	2	no	—
163	#938	—	2	1	no	—
164	D₄×Dic₃	C₂²×C₅	1	2	yes	—
165	C₂×#214	C₂²×C₅	1	2	yes	—
166	C₂×#204	C₂²×C₅	1	1	yes	characteristic
167	#888	—	2	1	no	—
168	#888	C₂²×C₅	1	2	yes	—
169	#887	—	2	1	no	—
170	#887	C₂²×C₅	1	2	yes	—
171	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
172	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic
173	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic
174	C₃×#102	C₂²×C₅	1	2	yes	—
175	C₃×#102	C₂²×C₅	1	2	yes	—
176	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
177	#832	C₂²×C₅	1	2	yes	—
178	#821	C₂²×C₅	1	1	yes	characteristic
179	#817	C₂²×C₅	1	1	yes	characteristic
180	#816	C₂²×C₅	1	1	yes	characteristic
181	Dic₃⋊C₈	C₂²×C₅	1	2	yes	—
182	C₈×Dic₃	C₂²×C₅	1	2	yes	—
183	#809	C₂²×C₅	1	2	yes	—
184	#808	C₂²×C₅	1	2	yes	—
185	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic
186	C₅×#41	—	12	4	no	—
187	C₂×C₅×Q₈	—	2	1	no	—
188	C₂×C₅×Q₈	—	3	1	no	—
189	C₂×C₅×Q₈	—	3	1	no	—
190	C₂×C₅×Q₈	—	6	2	no	—
191	C₂×C₅×D₄	—	2	1	no	—
192	C₂×C₅×D₄	—	2	1	no	—
193	C₂×C₅×D₄	—	3	1	no	—
194	C₂×C₅×D₄	—	6	2	no	—
195	C₂×C₅×D₄	—	6	2	no	—
196	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
197	C₂²×C₄×C₅	—	6	2	no	—
198	C₂²×C₄×C₅	—	6	1	no	—
199	C₅×SD₁₆	—	6	2	no	—
200	C₅×SD₁₆	—	6	4	no	—
201	C₂×C₅×C₈	—	3	2	no	—
202	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
203	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
204	C₅×C₄⋊C₄	—	2	1	no	—
205	C₅×C₄⋊C₄	—	3	2	no	—
206	C₅×C₄⋊C₄	—	3	1	no	—
207	C₅×C₄⋊C₄	—	3	1	no	—
208	C₅×C₄⋊C₄	—	3	1	no	—
209	C₅×C₄⋊C₄	—	6	2	no	—
210	C₅×C₄⋊C₄	—	6	2	no	—
211	C₅×C₄⋊C₄	—	6	1	no	—
212	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
213	C₅×C₂²⋊C₄	—	6	2	no	—
214	C₅×C₂²⋊C₄	—	6	1	no	—
215	C₄²×C₅	—	3	2	no	—
216	C₄²×C₅	—	6	2	no	—
217	C₄²×C₅	—	6	1	no	—
218	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
219	Q₈²	—	3	1	no	—
220	#550	—	3	1	no	—
221	#486	—	3	2	no	—
222	#486	C₅×D₃	1	1	yes	characteristic, complemented
223	#476	—	3	1	no	—
224	#476	—	3	2	no	—
225	#460	—	3	1	no	—
226	#460	—	3	2	no	—
227	C₈×Q₈	—	3	1	no	—
228	C₄×SD₁₆	—	3	2	no	—
229	C₄×SD₁₆	—	3	1	no	—
230	C₂²×C₃×C₅	—	4	2	no	—
231	C₂²×C₃×C₅	—	4	2	no	—
232	C₂²×C₃×C₅	—	4	2	no	—
233	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₅×D₃	—	4	1	no	—
235	C₂×C₅×D₃	—	4	1	no	—
236	C₂×C₅×D₃	—	4	1	no	—
237	C₃×C₄×C₅	—	2	1	no	—
238	C₃×C₄×C₅	—	4	2	no	—
239	C₃×C₄×C₅	C₂×SD₁₆	1	2	yes	—
240	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
241	C₃×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
242	C₅×Dic₃	—	2	2	no	—
243	C₅×Dic₃	—	2	2	no	—
244	C₅×Dic₃	—	4	1	no	—
245	C₅×Dic₃	—	4	1	no	—
246	C₅×Dic₃	C₂×SD₁₆	1	4	yes	—
247	C₂×C₃×Q₈	—	2	1	no	—
248	C₂×C₃×D₄	—	2	1	no	—
249	C₂×C₃×D₄	—	2	1	no	—
250	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
251	C₂×#67	—	2	2	no	—
252	C₂×#67	—	2	2	no	—
253	C₂²×Dic₃	—	2	2	no	—
254	#237	—	4	4	no	—
255	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
256	C₂×C₄×D₃	—	2	1	no	—
257	C₂×Dic₆	—	2	2	no	—
258	C₂×Dic₆	C₅×D₄	1	1	yes	characteristic
259	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
260	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
261	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
262	C₃×C₄⋊C₄	—	2	1	no	—
263	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
264	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
265	#217	—	2	2	no	—
266	#214	—	2	4	no	—
267	(C₂×D₃)⋊C₄	—	2	1	no	—
268	C₄⋊Dic₃	C₅×D₄	1	1	yes	characteristic
269	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
270	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
271	Dic₃⋊C₄	—	2	1	no	—
272	Dic₃⋊C₄	—	2	2	no	—
273	Dic₃⋊C₄	—	2	2	no	—
274	Dic₃⋊C₄	C₅×D₄	1	2	yes	—
275	C₄×Dic₃	—	2	1	no	—
276	C₄×Dic₃	—	2	2	no	—
277	C₄×Dic₃	C₂³×C₅	1	2	yes	—
278	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
279	#204	—	2	2	no	—
280	C₂³×C₅	—	2	2	no	—
281	C₂³×C₅	—	6	1	no	—
282	C₅×Q₈	—	3	4	no	—
283	C₅×Q₈	—	3	2	no	—
284	C₅×Q₈	—	6	1	no	—
285	C₅×Q₈	—	8	1	no	—
286	C₅×Q₈	—	24	2	no	—
287	C₅×D₄	—	2	2	no	—
288	C₅×D₄	—	2	2	no	—
289	C₅×D₄	—	4	2	no	—
290	C₅×D₄	—	6	1	no	—
291	C₅×D₄	—	6	1	no	—
292	C₅×D₄	—	8	1	no	—
293	C₅×D₄	—	12	4	no	—
294	C₅×D₄	—	24	2	no	—
295	C₂×C₄×C₅	—	2	2	no	—
296	C₂×C₄×C₅	—	3	2	no	—
297	C₂×C₄×C₅	—	3	2	no	—
298	C₂×C₄×C₅	—	6	1	no	—
299	C₂×C₄×C₅	—	6	1	no	—
300	C₂×C₄×C₅	—	6	1	no	—
301	C₂×C₄×C₅	—	12	4	no	—
302	C₂×C₄×C₅	—	12	2	no	—
303	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
304	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
305	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
306	C₅×C₈	—	2	1	no	—
307	C₅×C₈	—	2	1	no	—
308	C₅×C₈	—	6	2	no	—
309	C₂×#41	—	6	1	no	—
310	C₂×SD₁₆	—	3	2	no	—
311	C₂×SD₁₆	—	3	1	no	—
312	C₄⋊Q₈	—	3	2	no	—
313	C₄⋊Q₈	—	6	1	no	—
314	C₄⋊Q₈	—	6	2	no	—
315	C₄⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic
316	#127	—	3	2	no	—
317	#127	C₂×C₅×D₃	1	1	yes	characteristic
318	#121	—	6	1	no	—
319	#121	—	6	2	no	—
320	C₄×Q₈	—	3	1	no	—
321	C₄×Q₈	—	3	2	no	—
322	C₄×Q₈	—	3	1	no	—
323	C₄×Q₈	—	6	1	no	—
324	C₄×D₄	—	3	2	no	—
325	C₄×D₄	—	3	1	no	—
326	#106	—	3	1	no	—
327	#106	—	3	2	no	—
328	C₄⋊C₈	—	3	2	no	—
329	C₄⋊C₈	—	3	1	no	—
330	#103	—	3	1	no	—
331	#102	—	3	2	no	—
332	#102	—	3	1	no	—
333	#102	—	3	2	no	—
334	#102	C₂×C₅×D₃	1	2	yes	—
335	#102	C₂×C₅×D₃	1	2	yes	—
336	C₄×C₈	—	3	2	no	—
337	C₄×C₈	C₂×C₅×D₃	1	1	yes	characteristic
338	C₂×C₃×C₅	—	8	2	no	—
339	C₂×C₃×C₅	#548	1	1	yes	characteristic
340	C₂×C₃×C₅	C₂²×SD₁₆	1	1	yes	characteristic
341	C₂×C₃×C₅	#576	1	1	yes	characteristic
342	C₅×D₃	—	8	1	no	—
343	C₂³×C₃	—	2	2	no	—
344	C₂²×D₃	—	2	1	no	—
345	C₃×Q₈	—	8	1	no	—
346	C₃×D₄	—	2	2	no	—
347	C₃×D₄	—	2	2	no	—
348	C₃×D₄	—	4	2	no	—
349	C₃×D₄	—	8	1	no	—
350	C₂×C₃×C₄	—	2	2	no	—
351	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
352	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
353	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
354	#67	—	4	4	no	—
355	#67	—	8	2	no	—
356	C₂×Dic₃	—	2	1	no	—
357	C₂×Dic₃	—	2	1	no	—
358	C₂×Dic₃	—	2	1	no	—
359	C₂×Dic₃	—	4	4	no	—
360	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
361	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
362	D₁₂	—	2	1	no	—
363	D₁₂	—	2	1	no	—
364	C₄×D₃	—	4	2	no	—
365	Dic₆	—	2	1	no	—
366	Dic₆	—	8	2	no	—
367	Dic₆	C₅×SD₁₆	1	4	yes	complemented
368	Dic₆	C₅×#41	1	2	yes	complemented
369	C₃×C₈	—	2	1	no	—
370	C₃×C₈	—	2	1	no	—
371	C₃⋊C₈	—	2	2	no	—
372	C₂²×C₅	—	4	2	no	—
373	C₂²×C₅	—	4	2	no	—
374	C₂²×C₅	—	4	2	no	—
375	C₂²×C₅	—	12	1	no	—
376	C₂²×C₅	—	12	1	no	—
377	C₂²×C₅	—	12	1	no	—
378	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
379	C₄×C₅	—	2	1	no	—
380	C₄×C₅	—	3	4	no	—
381	C₄×C₅	—	4	2	no	—
382	C₄×C₅	—	6	2	no	—
383	C₄×C₅	—	6	2	no	—
384	C₄×C₅	—	12	1	no	—
385	C₄×C₅	—	12	1	no	—
386	C₄×C₅	D₃×SD₁₆	1	2	yes	—
387	C₄×C₅	D₃×#41	1	1	yes	characteristic
388	C₄×C₅	#1010	1	1	yes	characteristic
389	#41	—	12	4	no	—
390	C₂×Q₈	—	2	1	no	—
391	C₂×Q₈	—	3	1	no	—
392	C₂×Q₈	—	3	1	no	—
393	C₂×Q₈	—	6	2	no	—
394	C₂×D₄	—	2	1	no	—
395	C₂×D₄	—	2	1	no	—
396	C₂×D₄	—	3	1	no	—
397	C₂×D₄	—	6	2	no	—
398	C₂×D₄	—	6	2	no	—
399	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
400	C₂²×C₄	—	6	2	no	—
401	C₂²×C₄	—	6	1	no	—
402	SD₁₆	—	6	2	no	—
403	SD₁₆	—	6	4	no	—
404	C₂×C₈	—	3	2	no	—
405	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
406	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	—	3	2	no	—
409	C₄⋊C₄	—	3	1	no	—
410	C₄⋊C₄	—	3	1	no	—
411	C₄⋊C₄	—	3	1	no	—
412	C₄⋊C₄	—	6	2	no	—
413	C₄⋊C₄	—	6	2	no	—
414	C₄⋊C₄	—	6	1	no	—
415	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
416	C₂²⋊C₄	—	6	2	no	—
417	C₂²⋊C₄	—	6	1	no	—
418	C₄²	—	3	2	no	—
419	C₄²	—	6	2	no	—
420	C₄²	—	6	1	no	—
421	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
422	C₃×C₅	#3362	1	1	yes	characteristic, complemented, Hall
423	C₂²×C₃	—	4	2	no	—
424	C₂²×C₃	—	4	2	no	—
425	C₂²×C₃	—	4	2	no	—
426	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
427	C₂×D₃	—	4	1	no	—
428	C₂×D₃	—	4	1	no	—
429	C₂×D₃	—	4	1	no	—
430	C₃×C₄	—	2	1	no	—
431	C₃×C₄	—	4	2	no	—
432	C₃×C₄	C₂×C₅×SD₁₆	1	2	yes	—
433	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
434	C₃×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
435	Dic₃	—	2	2	no	—
436	Dic₃	—	2	2	no	—
437	Dic₃	—	4	1	no	—
438	Dic₃	—	4	1	no	—
439	Dic₃	C₂×C₅×SD₁₆	1	4	yes	—
440	C₂×C₅	—	8	2	no	—
441	C₂×C₅	—	24	1	no	—
442	C₂×C₅	#5677	1	1	yes	characteristic
443	C₂×C₅	#5757	1	1	yes	characteristic
444	C₂×C₅	C₂×D₃×SD₁₆	1	1	yes	characteristic
445	C₂³	—	2	2	no	—
446	C₂³	—	6	1	no	—
447	Q₈	—	3	4	no	—
448	Q₈	—	3	2	no	—
449	Q₈	—	6	1	no	—
450	Q₈	—	8	1	no	—
451	Q₈	—	24	2	no	—
452	D₄	—	2	2	no	—
453	D₄	—	2	2	no	—
454	D₄	—	4	2	no	—
455	D₄	—	6	1	no	—
456	D₄	—	6	1	no	—
457	D₄	—	8	1	no	—
458	D₄	—	12	4	no	—
459	D₄	—	24	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	3	2	no	—
462	C₂×C₄	—	3	2	no	—
463	C₂×C₄	—	6	1	no	—
464	C₂×C₄	—	6	1	no	—
465	C₂×C₄	—	6	1	no	—
466	C₂×C₄	—	12	4	no	—
467	C₂×C₄	—	12	2	no	—
468	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
469	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
470	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
471	C₈	—	2	1	no	—
472	C₈	—	2	1	no	—
473	C₈	—	6	2	no	—
474	C₂×C₃	—	8	2	no	—
475	C₂×C₃	C₅×#548	1	1	yes	characteristic
476	C₂×C₃	C₂²×C₅×SD₁₆	1	1	yes	characteristic
477	C₂×C₃	C₅×#576	1	1	yes	characteristic
478	D₃	—	8	1	no	—
479	C₅	#81588	1	1	yes	characteristic, direct product factor, Sylow
480	C₂²	—	4	2	no	—
481	C₂²	—	4	2	no	—
482	C₂²	—	4	2	no	—
483	C₂²	—	12	1	no	—
484	C₂²	—	12	1	no	—
485	C₂²	—	12	1	no	—
486	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
487	C₄	—	2	1	no	—
488	C₄	—	3	4	no	—
489	C₄	—	4	2	no	—
490	C₄	—	6	2	no	—
491	C₄	—	6	2	no	—
492	C₄	—	12	1	no	—
493	C₄	—	12	1	no	—
494	C₄	C₅×D₃×SD₁₆	1	2	yes	—
495	C₄	C₅×D₃×#41	1	1	yes	characteristic
496	C₄	C₅×#1010	1	1	yes	characteristic
497	C₃	C₅×#3362	1	1	yes	characteristic, complemented, Sylow
498	C₂	—	8	2	no	—
499	C₂	—	24	1	no	—
500	C₂	C₅×#5677	1	1	yes	characteristic
501	C₂	C₅×#5757	1	1	yes	characteristic
502	C₂	C₂×C₅×D₃×SD₁₆	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×#486	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₅×#5718	C₂
hypercenter	C₅×#486	D₃
hypocenter	C₃	C₅×#3362
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#486

Complements

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

N	H ≅ G/N	type
1. C₅×#5722	C₂	semidirect
3. C₃×C₅×#486	C₂	semidirect
4. C₅×#5084	C₂	semidirect
5. C₅×#5075	C₂	semidirect
6. C₅×#4762	C₂	semidirect
7. C₅×#4761	C₂	semidirect
8. C₅×#4760	C₂	semidirect
9. C₅×#4758	C₂	semidirect
10. C₄×C₅×#204	C₂	semidirect
11. C₅×C₈×Dic₆	C₂	semidirect
42. #81588	C₅	direct (N × H)
46. C₅×#486	D₃	semidirect
87. #5722	C₂×C₅	semidirect
89. C₃×#486	C₂×C₅	semidirect
90. #5084	C₂×C₅	semidirect
91. #5075	C₂×C₅	semidirect
92. #4762	C₂×C₅	semidirect
93. #4761	C₂×C₅	semidirect
94. #4760	C₂×C₅	semidirect
95. #4758	C₂×C₅	semidirect
96. C₄×#204	C₂×C₅	semidirect
97. C₈×Dic₆	C₂×C₅	semidirect
152. C₅×Dic₆	SD₁₆	semidirect
153. C₅×Dic₆	#41	semidirect
222. #486	C₅×D₃	semidirect
367. Dic₆	C₅×SD₁₆	semidirect
368. Dic₆	C₅×#41	semidirect
422. C₃×C₅	#3362	semidirect
479. C₅	#81588	direct (N × H)
497. C₃	C₅×#3362	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5722	2
C₅×#5718	2
C₃×C₅×#486	2
C₅×#5084	2
C₅×#5075	2
C₅×#4762	2
C₅×#4761	2
C₅×#4760	2
C₅×#4758	2
C₄×C₅×#204	2
C₅×C₈×Dic₆	2
C₅×#3362	3
#81588	5

Subgroups — C5×#81588 #14471906

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#81588 #14471906