Subgroups — C₅×#81845 #14439129

Order 1920.

1312 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#914	C₂	1	2	yes	maximal, complemented
2	C₂×C₅×#911	C₂	1	2	yes	maximal, complemented
3	C₅×D₃×#127	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5668	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#496	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5175	C₂	1	2	yes	maximal, complemented
7	C₅×#5151	C₂	1	2	yes	maximal, complemented
8	C₅×#5074	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#5058	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4712	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4707	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3151	—	3	1	no	maximal, Hall
13	C₂×C₅×#239	C₂²	1	1	yes	characteristic
14	C₂×C₅×#237	C₂²	1	1	yes	characteristic
15	C₂×C₅×D₃×D₄	—	2	2	no	—
16	C₂×C₅×D₃×D₄	C₂²	1	2	yes	—
17	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	complemented
18	C₂×C₃×C₅×D₈	C₂²	1	2	yes	complemented
19	C₃×C₅×#127	C₂²	1	1	yes	characteristic
20	C₃×C₅×#124	C₂²	1	1	yes	characteristic, complemented
21	C₅×#944	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₅×#215	C₂²	1	2	yes	complemented
23	C₅×#940	—	2	2	no	—
24	C₅×#940	C₂²	1	2	yes	—
25	C₅×#940	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₅×#214	C₂²	1	2	yes	complemented
27	C₂×C₅×#213	C₂²	1	2	yes	complemented
28	C₂×C₅×#213	C₂²	1	2	yes	complemented
29	C₅×#914	—	2	8	no	—
30	C₅×#911	—	2	8	no	—
31	C₂×C₅×D₂₄	C₂²	1	2	yes	complemented
32	C₂×C₅×#204	C₂²	1	2	yes	complemented
33	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	—
34	C₅×#884	—	2	2	no	—
35	C₅×#67⋊C₄	—	2	2	no	—
36	C₅×#875	C₂²	1	1	yes	characteristic, complemented
37	C₅×#874	C₂²	1	1	yes	characteristic
38	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
39	C₃×C₅×#97	C₂²	1	1	yes	characteristic, complemented
40	C₅×C₈×Dic₃	C₂²	1	2	yes	complemented
41	C₅×#803	C₂²	1	1	yes	characteristic, complemented
42	#81845	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
43	C₂×C₅×AGL(1,ℤ/8)	—	3	2	no	—
44	C₂×C₅×AGL(1,ℤ/8)	—	3	2	no	—
45	C₅×#532	—	3	1	no	—
46	C₂×C₅×#127	—	3	1	no	—
47	C₅×#496	—	3	1	no	—
48	C₅×#496	—	3	1	no	—
49	C₅×#496	—	3	1	no	—
50	C₅×#496	D₃	1	1	yes	characteristic, complemented
51	C₅×#493	—	3	2	no	—
52	C₅×#492	—	3	2	no	—
53	C₄×C₅×M₁₆	—	3	1	no	—
54	C₂³×C₅×D₃	—	2	2	no	—
55	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
56	C₂×C₃×C₅×D₄	—	2	2	no	—
57	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
58	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
59	C₂×C₅×#67	—	2	1	no	—
60	C₂×C₅×#67	—	2	2	no	—
61	C₂×C₅×#67	—	2	2	no	—
62	C₂×C₅×#67	—	2	4	no	—
63	C₂²×C₅×Dic₃	—	2	1	no	—
64	C₅×#239	—	2	4	no	—
65	C₅×#237	—	2	4	no	—
66	C₅×D₃×D₄	—	2	4	no	—
67	C₅×D₃×D₄	—	2	4	no	—
68	C₅×D₃×D₄	—	4	8	no	—
69	C₂×C₅×D₁₂	—	2	1	no	—
70	C₂×C₅×D₁₂	—	2	2	no	—
71	C₂×C₅×D₁₂	C₂³	1	2	yes	—
72	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
73	C₂×C₄×C₅×D₃	—	2	1	no	—
74	C₂×C₄×C₅×D₃	D₄	1	2	yes	—
75	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
76	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
77	C₃×C₅×SD₁₆	—	2	4	no	—
78	C₃×C₅×D₈	—	2	4	no	—
79	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
80	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
81	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
82	C₅×#215	—	2	4	no	—
83	C₅×#214	—	2	4	no	—
84	C₅×#213	—	2	4	no	—
85	C₅×#213	—	2	4	no	—
86	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
87	C₅×Dic₃⋊C₄	—	2	2	no	—
88	C₄×C₅×Dic₃	D₄	1	2	yes	—
89	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
90	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
91	C₅×D₂₄	—	2	4	no	—
92	C₅×#204	—	2	4	no	—
93	C₅×ΓL(1,𝔽₂₅)	D₄	1	8	yes	complemented
94	C₂×#914	C₂×C₅	1	2	yes	complemented
95	C₂×#911	C₂×C₅	1	2	yes	complemented
96	D₃×#127	C₂×C₅	1	1	yes	characteristic, complemented
97	#5668	C₂×C₅	1	1	yes	characteristic, complemented
98	C₃×#496	C₂×C₅	1	1	yes	characteristic, complemented
99	#5175	C₂×C₅	1	2	yes	complemented
100	#5151	C₂×C₅	1	2	yes	complemented
101	#5074	C₂×C₅	1	1	yes	characteristic, complemented
102	#5058	C₂×C₅	1	1	yes	characteristic, complemented
103	#4712	C₂×C₅	1	1	yes	characteristic, complemented
104	#4707	C₂×C₅	1	1	yes	characteristic, complemented
105	C₂×C₅×#41	—	3	1	no	—
106	C₂×C₅×#41	—	3	1	no	—
107	C₂²×C₅×D₄	—	3	2	no	—
108	C₂²×C₅×D₄	—	6	2	no	—
109	C₅×AGL(1,ℤ/8)	—	6	8	no	—
110	C₅×AGL(1,ℤ/8)	—	6	8	no	—
111	C₂×C₅×SD₁₆	—	3	2	no	—
112	C₂×C₅×SD₁₆	—	3	2	no	—
113	C₂×C₅×SD₁₆	—	3	2	no	—
114	C₂×C₅×SD₁₆	C₂×D₃	1	2	yes	complemented
115	C₂×C₅×D₈	—	3	2	no	—
116	C₂×C₅×D₈	—	3	2	no	—
117	C₂×C₅×D₈	—	3	2	no	—
118	C₂×C₅×D₈	C₂×D₃	1	2	yes	complemented
119	C₂×C₅×M₁₆	—	3	2	no	—
120	C₅×C₄⋊Q₈	—	3	1	no	—
121	C₅×#127	—	3	2	no	—
122	C₅×#127	—	3	1	no	—
123	C₅×#127	—	3	1	no	—
124	C₅×#127	—	6	2	no	—
125	C₅×#127	C₂×D₃	1	1	yes	characteristic
126	C₅×#124	—	3	1	no	—
127	C₅×#124	C₂×D₃	1	1	yes	characteristic, complemented
128	C₅×#121	—	6	2	no	—
129	C₄×C₅×D₄	—	6	2	no	—
130	C₂×C₄²×C₅	—	3	1	no	—
131	C₅×#97	—	3	1	no	—
132	C₅×#97	C₂×D₃	1	1	yes	characteristic, complemented
133	C₄×C₅×C₈	—	3	2	no	—
134	#3151	—	3	1	no	Sylow
135	C₂³×C₃×C₅	—	2	1	no	—
136	C₂³×C₃×C₅	—	2	2	no	—
137	C₂²×C₅×D₃	—	2	1	no	—
138	C₂²×C₅×D₃	—	2	2	no	—
139	C₂²×C₅×D₃	—	4	8	no	—
140	C₂²×C₅×D₃	—	4	4	no	—
141	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
142	C₃×C₅×Q₈	—	2	2	no	—
143	C₃×C₅×D₄	—	2	2	no	—
144	C₃×C₅×D₄	—	2	2	no	—
145	C₃×C₅×D₄	—	2	2	no	—
146	C₃×C₅×D₄	—	4	4	no	—
147	C₂×C₃×C₄×C₅	—	2	1	no	—
148	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
149	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
150	C₅×#67	—	4	2	no	—
151	C₅×#67	—	4	4	no	—
152	C₅×#67	—	4	8	no	—
153	C₅×#67	—	4	4	no	—
154	C₂×C₅×Dic₃	—	2	1	no	—
155	C₂×C₅×Dic₃	—	4	2	no	—
156	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
157	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
158	C₅×D₁₂	—	2	2	no	—
159	C₅×D₁₂	—	2	2	no	—
160	C₅×D₁₂	—	2	2	no	—
161	C₅×D₁₂	—	4	4	no	—
162	C₅×D₁₂	—	4	2	no	—
163	C₄×C₅×D₃	—	2	4	no	—
164	C₄×C₅×D₃	—	4	2	no	—
165	C₄×C₅×D₃	C₂×D₄	1	4	yes	—
166	C₅×Dic₆	—	2	2	no	—
167	C₃×C₅×C₈	C₂×D₄	1	4	yes	complemented
168	C₅×C₃⋊C₈	C₂×D₄	1	4	yes	complemented
169	C₂×#239	C₂²×C₅	1	1	yes	characteristic
170	C₂×#237	C₂²×C₅	1	1	yes	characteristic
171	C₂×D₃×D₄	—	2	2	no	—
172	C₂×D₃×D₄	C₂²×C₅	1	2	yes	—
173	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	complemented
174	C₂×C₃×D₈	C₂²×C₅	1	2	yes	complemented
175	C₃×#127	C₂²×C₅	1	1	yes	characteristic
176	C₃×#124	C₂²×C₅	1	1	yes	characteristic, complemented
177	#944	C₂²×C₅	1	1	yes	characteristic, complemented
178	C₂×#215	C₂²×C₅	1	2	yes	complemented
179	#940	—	2	2	no	—
180	#940	C₂²×C₅	1	2	yes	—
181	#940	C₂²×C₅	1	1	yes	characteristic, complemented
182	C₂×#214	C₂²×C₅	1	2	yes	complemented
183	C₂×#213	C₂²×C₅	1	2	yes	complemented
184	C₂×#213	C₂²×C₅	1	2	yes	complemented
185	#914	—	2	8	no	—
186	#911	—	2	8	no	—
187	C₂×D₂₄	C₂²×C₅	1	2	yes	complemented
188	C₂×#204	C₂²×C₅	1	2	yes	complemented
189	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	2	yes	—
190	#884	—	2	2	no	—
191	#67⋊C₄	—	2	2	no	—
192	#875	C₂²×C₅	1	1	yes	characteristic, complemented
193	#874	C₂²×C₅	1	1	yes	characteristic
194	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
195	C₃×#97	C₂²×C₅	1	1	yes	characteristic, complemented
196	C₈×Dic₃	C₂²×C₅	1	2	yes	complemented
197	#803	C₂²×C₅	1	1	yes	characteristic, complemented
198	C₂⁴×C₅	—	6	2	no	—
199	C₅×#41	—	6	4	no	—
200	C₅×#41	—	6	4	no	—
201	C₂×C₅×Q₈	—	3	1	no	—
202	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
203	C₂×C₅×D₄	—	2	2	no	—
204	C₂×C₅×D₄	—	3	1	no	—
205	C₂×C₅×D₄	—	3	2	no	—
206	C₂×C₅×D₄	—	6	1	no	—
207	C₂×C₅×D₄	—	6	4	no	—
208	C₂×C₅×D₄	—	6	4	no	—
209	C₂×C₅×D₄	—	6	2	no	—
210	C₂×C₅×D₄	—	6	4	no	—
211	C₂×C₅×D₄	—	6	2	no	—
212	C₂×C₅×D₄	—	6	1	no	—
213	C₂×C₅×D₄	—	6	2	no	—
214	C₂×C₅×D₄	—	12	8	no	—
215	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
216	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
217	C₂²×C₄×C₅	—	3	1	no	—
218	C₂²×C₄×C₅	—	3	2	no	—
219	C₂²×C₄×C₅	—	6	1	no	—
220	C₂²×C₄×C₅	—	6	1	no	—
221	C₅×SD₁₆	—	2	4	no	—
222	C₅×SD₁₆	—	6	4	no	—
223	C₅×SD₁₆	—	6	4	no	—
224	C₅×SD₁₆	—	6	4	no	—
225	C₅×D₈	—	2	4	no	—
226	C₅×D₈	—	6	4	no	—
227	C₅×D₈	—	6	4	no	—
228	C₅×D₈	—	6	4	no	—
229	C₅×M₁₆	—	3	8	no	—
230	C₂×C₅×C₈	—	3	2	no	—
231	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
232	C₅×C₄⋊C₄	—	6	2	no	—
233	C₅×C₂²⋊C₄	—	2	2	no	—
234	C₅×C₂²⋊C₄	—	6	2	no	—
235	C₄²×C₅	—	3	2	no	—
236	C₄²×C₅	—	3	1	no	—
237	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
238	C₂×AGL(1,ℤ/8)	—	3	2	no	—
239	C₂×AGL(1,ℤ/8)	—	3	2	no	—
240	#532	—	3	1	no	—
241	C₂×#127	—	3	1	no	—
242	#496	—	3	1	no	—
243	#496	—	3	1	no	—
244	#496	—	3	1	no	—
245	#496	C₅×D₃	1	1	yes	characteristic, complemented
246	#493	—	3	2	no	—
247	#492	—	3	2	no	—
248	C₄×M₁₆	—	3	1	no	—
249	C₂²×C₃×C₅	—	4	1	no	—
250	C₂²×C₃×C₅	—	4	2	no	—
251	C₂²×C₃×C₅	—	4	4	no	—
252	C₂²×C₃×C₅	—	4	2	no	—
253	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
254	C₂×C₅×D₃	—	2	2	no	—
255	C₂×C₅×D₃	—	4	1	no	—
256	C₂×C₅×D₃	—	4	2	no	—
257	C₂×C₅×D₃	—	4	4	no	—
258	C₂×C₅×D₃	—	4	2	no	—
259	C₂×C₅×D₃	—	8	8	no	—
260	C₂×C₅×D₃	#127	1	2	yes	—
261	C₃×C₄×C₅	—	2	2	no	—
262	C₃×C₄×C₅	—	4	1	no	—
263	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
264	C₅×Dic₃	—	4	1	no	—
265	C₅×Dic₃	#127	1	2	yes	—
266	C₅×Dic₃	AGL(1,ℤ/8)	1	4	yes	complemented
267	C₂³×D₃	—	2	2	no	—
268	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
269	C₂×C₃×D₄	—	2	2	no	—
270	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
271	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
272	C₂×#67	—	2	1	no	—
273	C₂×#67	—	2	2	no	—
274	C₂×#67	—	2	2	no	—
275	C₂×#67	—	2	4	no	—
276	C₂²×Dic₃	—	2	1	no	—
277	#239	—	2	4	no	—
278	#237	—	2	4	no	—
279	D₃×D₄	—	2	4	no	—
280	D₃×D₄	—	2	4	no	—
281	D₃×D₄	—	4	8	no	—
282	C₂×D₁₂	—	2	1	no	—
283	C₂×D₁₂	—	2	2	no	—
284	C₂×D₁₂	C₂³×C₅	1	2	yes	—
285	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
286	C₂×C₄×D₃	—	2	1	no	—
287	C₂×C₄×D₃	C₅×D₄	1	2	yes	—
288	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
289	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
290	C₃×SD₁₆	—	2	4	no	—
291	C₃×D₈	—	2	4	no	—
292	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
293	C₃×C₂²⋊C₄	—	2	2	no	—
294	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
295	#215	—	2	4	no	—
296	#214	—	2	4	no	—
297	#213	—	2	4	no	—
298	#213	—	2	4	no	—
299	(C₂×D₃)⋊C₄	—	2	2	no	—
300	Dic₃⋊C₄	—	2	2	no	—
301	C₄×Dic₃	C₅×D₄	1	2	yes	—
302	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
303	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
304	D₂₄	—	2	4	no	—
305	#204	—	2	4	no	—
306	ΓL(1,𝔽₂₅)	C₅×D₄	1	8	yes	complemented
307	C₂³×C₅	—	2	1	no	—
308	C₂³×C₅	—	2	2	no	—
309	C₂³×C₅	—	3	1	no	—
310	C₂³×C₅	—	6	1	no	—
311	C₂³×C₅	—	6	2	no	—
312	C₂³×C₅	—	12	4	no	—
313	C₂³×C₅	—	12	8	no	—
314	C₅×Q₈	—	2	2	no	—
315	C₅×Q₈	—	6	2	no	—
316	C₅×D₄	—	2	2	no	—
317	C₅×D₄	—	2	2	no	—
318	C₅×D₄	—	2	2	no	—
319	C₅×D₄	—	4	4	no	—
320	C₅×D₄	—	6	2	no	—
321	C₅×D₄	—	6	2	no	—
322	C₅×D₄	—	6	2	no	—
323	C₅×D₄	—	12	4	no	—
324	C₅×D₄	—	12	4	no	—
325	C₅×D₄	—	12	4	no	—
326	C₅×D₄	—	12	8	no	—
327	C₅×D₄	—	12	2	no	—
328	C₅×D₄	—	12	2	no	—
329	C₂×C₄×C₅	—	2	1	no	—
330	C₂×C₄×C₅	—	3	2	no	—
331	C₂×C₄×C₅	—	3	1	no	—
332	C₂×C₄×C₅	—	3	4	no	—
333	C₂×C₄×C₅	—	6	4	no	—
334	C₂×C₄×C₅	—	6	1	no	—
335	C₂×C₄×C₅	—	12	2	no	—
336	C₂×C₄×C₅	—	12	2	no	—
337	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
338	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
339	C₅×C₈	—	3	4	no	—
340	C₅×C₈	D₃×D₄	1	4	yes	complemented
341	C₂×#41	—	3	1	no	—
342	C₂×#41	—	3	1	no	—
343	C₂²×D₄	—	3	2	no	—
344	C₂²×D₄	—	6	2	no	—
345	AGL(1,ℤ/8)	—	6	8	no	—
346	AGL(1,ℤ/8)	—	6	8	no	—
347	C₂×SD₁₆	—	3	2	no	—
348	C₂×SD₁₆	—	3	2	no	—
349	C₂×SD₁₆	—	3	2	no	—
350	C₂×SD₁₆	C₂×C₅×D₃	1	2	yes	complemented
351	C₂×D₈	—	3	2	no	—
352	C₂×D₈	—	3	2	no	—
353	C₂×D₈	—	3	2	no	—
354	C₂×D₈	C₂×C₅×D₃	1	2	yes	complemented
355	C₂×M₁₆	—	3	2	no	—
356	C₄⋊Q₈	—	3	1	no	—
357	#127	—	3	2	no	—
358	#127	—	3	1	no	—
359	#127	—	3	1	no	—
360	#127	—	6	2	no	—
361	#127	C₂×C₅×D₃	1	1	yes	characteristic
362	#124	—	3	1	no	—
363	#124	C₂×C₅×D₃	1	1	yes	characteristic, complemented
364	#121	—	6	2	no	—
365	C₄×D₄	—	6	2	no	—
366	C₂×C₄²	—	3	1	no	—
367	#97	—	3	1	no	—
368	#97	C₂×C₅×D₃	1	1	yes	characteristic, complemented
369	C₄×C₈	—	3	2	no	—
370	C₂×C₃×C₅	—	8	2	no	—
371	C₂×C₃×C₅	—	8	1	no	—
372	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
373	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	2	yes	—
374	C₅×D₃	—	2	2	no	—
375	C₅×D₃	—	8	1	no	—
376	C₅×D₃	—	8	2	no	—
377	C₂³×C₃	—	2	1	no	—
378	C₂³×C₃	—	2	2	no	—
379	C₂²×D₃	—	2	1	no	—
380	C₂²×D₃	—	2	2	no	—
381	C₂²×D₃	—	4	8	no	—
382	C₂²×D₃	—	4	4	no	—
383	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
384	C₃×Q₈	—	2	2	no	—
385	C₃×D₄	—	2	2	no	—
386	C₃×D₄	—	2	2	no	—
387	C₃×D₄	—	2	2	no	—
388	C₃×D₄	—	4	4	no	—
389	C₂×C₃×C₄	—	2	1	no	—
390	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
391	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
392	#67	—	4	2	no	—
393	#67	—	4	4	no	—
394	#67	—	4	8	no	—
395	#67	—	4	4	no	—
396	C₂×Dic₃	—	2	1	no	—
397	C₂×Dic₃	—	4	2	no	—
398	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
399	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
400	D₁₂	—	2	2	no	—
401	D₁₂	—	2	2	no	—
402	D₁₂	—	2	2	no	—
403	D₁₂	—	4	4	no	—
404	D₁₂	—	4	2	no	—
405	C₄×D₃	—	2	4	no	—
406	C₄×D₃	—	4	2	no	—
407	C₄×D₃	C₂×C₅×D₄	1	4	yes	—
408	Dic₆	—	2	2	no	—
409	C₃×C₈	C₂×C₅×D₄	1	4	yes	complemented
410	C₃⋊C₈	C₂×C₅×D₄	1	4	yes	complemented
411	C₂²×C₅	—	3	2	no	—
412	C₂²×C₅	—	4	1	no	—
413	C₂²×C₅	—	4	2	no	—
414	C₂²×C₅	—	4	4	no	—
415	C₂²×C₅	—	4	2	no	—
416	C₂²×C₅	—	6	2	no	—
417	C₂²×C₅	—	12	1	no	—
418	C₂²×C₅	—	12	2	no	—
419	C₂²×C₅	—	12	4	no	—
420	C₂²×C₅	—	12	2	no	—
421	C₂²×C₅	—	24	8	no	—
422	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
423	C₄×C₅	—	2	2	no	—
424	C₄×C₅	—	3	2	no	—
425	C₄×C₅	—	3	4	no	—
426	C₄×C₅	—	4	1	no	—
427	C₄×C₅	—	12	1	no	—
428	C₄×C₅	C₂×D₃×D₄	1	2	yes	—
429	C₂⁴	—	6	2	no	—
430	#41	—	6	4	no	—
431	#41	—	6	4	no	—
432	C₂×Q₈	—	3	1	no	—
433	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
434	C₂×D₄	—	2	2	no	—
435	C₂×D₄	—	3	1	no	—
436	C₂×D₄	—	3	2	no	—
437	C₂×D₄	—	6	1	no	—
438	C₂×D₄	—	6	4	no	—
439	C₂×D₄	—	6	4	no	—
440	C₂×D₄	—	6	2	no	—
441	C₂×D₄	—	6	4	no	—
442	C₂×D₄	—	6	2	no	—
443	C₂×D₄	—	6	1	no	—
444	C₂×D₄	—	6	2	no	—
445	C₂×D₄	—	12	8	no	—
446	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
447	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
448	C₂²×C₄	—	3	1	no	—
449	C₂²×C₄	—	3	2	no	—
450	C₂²×C₄	—	6	1	no	—
451	C₂²×C₄	—	6	1	no	—
452	SD₁₆	—	2	4	no	—
453	SD₁₆	—	6	4	no	—
454	SD₁₆	—	6	4	no	—
455	SD₁₆	—	6	4	no	—
456	D₈	—	2	4	no	—
457	D₈	—	6	4	no	—
458	D₈	—	6	4	no	—
459	D₈	—	6	4	no	—
460	M₁₆	—	3	8	no	—
461	C₂×C₈	—	3	2	no	—
462	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
463	C₄⋊C₄	—	6	2	no	—
464	C₂²⋊C₄	—	2	2	no	—
465	C₂²⋊C₄	—	6	2	no	—
466	C₄²	—	3	2	no	—
467	C₄²	—	3	1	no	—
468	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
469	C₃×C₅	#3151	1	1	yes	characteristic, complemented, Hall
470	C₂²×C₃	—	4	1	no	—
471	C₂²×C₃	—	4	2	no	—
472	C₂²×C₃	—	4	4	no	—
473	C₂²×C₃	—	4	2	no	—
474	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
475	C₂×D₃	—	2	2	no	—
476	C₂×D₃	—	4	1	no	—
477	C₂×D₃	—	4	2	no	—
478	C₂×D₃	—	4	4	no	—
479	C₂×D₃	—	4	2	no	—
480	C₂×D₃	—	8	8	no	—
481	C₂×D₃	C₅×#127	1	2	yes	—
482	C₃×C₄	—	2	2	no	—
483	C₃×C₄	—	4	1	no	—
484	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
485	Dic₃	—	4	1	no	—
486	Dic₃	C₅×#127	1	2	yes	—
487	Dic₃	C₅×AGL(1,ℤ/8)	1	4	yes	complemented
488	C₂×C₅	—	6	2	no	—
489	C₂×C₅	—	8	2	no	—
490	C₂×C₅	—	8	1	no	—
491	C₂×C₅	—	24	2	no	—
492	C₂×C₅	—	24	1	no	—
493	C₂×C₅	D₃×#127	1	1	yes	characteristic
494	C₂×C₅	D₃×AGL(1,ℤ/8)	1	2	yes	—
495	C₂³	—	2	1	no	—
496	C₂³	—	2	2	no	—
497	C₂³	—	3	1	no	—
498	C₂³	—	6	1	no	—
499	C₂³	—	6	2	no	—
500	C₂³	—	12	4	no	—
501	C₂³	—	12	8	no	—
502	Q₈	—	2	2	no	—
503	Q₈	—	6	2	no	—
504	D₄	—	2	2	no	—
505	D₄	—	2	2	no	—
506	D₄	—	2	2	no	—
507	D₄	—	4	4	no	—
508	D₄	—	6	2	no	—
509	D₄	—	6	2	no	—
510	D₄	—	6	2	no	—
511	D₄	—	12	4	no	—
512	D₄	—	12	4	no	—
513	D₄	—	12	8	no	—
514	D₄	—	12	4	no	—
515	D₄	—	12	2	no	—
516	D₄	—	12	2	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	3	2	no	—
519	C₂×C₄	—	3	1	no	—
520	C₂×C₄	—	3	4	no	—
521	C₂×C₄	—	6	4	no	—
522	C₂×C₄	—	6	1	no	—
523	C₂×C₄	—	12	2	no	—
524	C₂×C₄	—	12	2	no	—
525	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
526	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
527	C₈	—	3	4	no	—
528	C₈	C₅×D₃×D₄	1	4	yes	complemented
529	C₂×C₃	—	8	2	no	—
530	C₂×C₃	—	8	1	no	—
531	C₂×C₃	C₂×C₅×#127	1	1	yes	characteristic
532	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	2	yes	—
533	D₃	—	2	2	no	—
534	D₃	—	8	2	no	—
535	D₃	—	8	1	no	—
536	C₅	#81845	1	1	yes	characteristic, direct product factor, Sylow
537	C₂²	—	3	2	no	—
538	C₂²	—	4	1	no	—
539	C₂²	—	4	2	no	—
540	C₂²	—	4	4	no	—
541	C₂²	—	4	2	no	—
542	C₂²	—	6	2	no	—
543	C₂²	—	12	1	no	—
544	C₂²	—	12	2	no	—
545	C₂²	—	12	4	no	—
546	C₂²	—	12	2	no	—
547	C₂²	—	24	8	no	—
548	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
549	C₄	—	2	2	no	—
550	C₄	—	3	2	no	—
551	C₄	—	3	4	no	—
552	C₄	—	4	1	no	—
553	C₄	—	12	1	no	—
554	C₄	C₂×C₅×D₃×D₄	1	2	yes	—
555	C₃	C₅×#3151	1	1	yes	characteristic, complemented, Sylow
556	C₂	—	6	2	no	—
557	C₂	—	8	2	no	—
558	C₂	—	8	1	no	—
559	C₂	—	24	2	no	—
560	C₂	—	24	1	no	—
561	C₂	C₅×D₃×#127	1	1	yes	characteristic
562	C₂	C₅×D₃×AGL(1,ℤ/8)	1	2	yes	—

	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×#496	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₅×#496	D₃
hypocenter	C₃	C₅×#3151
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#496

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#914	C₂	semidirect
2. C₂×C₅×#911	C₂	semidirect
3. C₅×D₃×#127	C₂	semidirect
4. C₅×#5668	C₂	semidirect
5. C₃×C₅×#496	C₂	semidirect
6. C₅×#5175	C₂	semidirect
7. C₅×#5151	C₂	semidirect
8. C₅×#5074	C₂	semidirect
9. C₅×#5058	C₂	semidirect
10. C₅×#4712	C₂	semidirect
11. C₅×#4707	C₂	semidirect
17. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
18. C₂×C₃×C₅×D₈	C₂²	semidirect
20. C₃×C₅×#124	C₂²	semidirect
21. C₅×#944	C₂²	semidirect
22. C₂×C₅×#215	C₂²	semidirect
25. C₅×#940	C₂²	semidirect
26. C₂×C₅×#214	C₂²	semidirect
27. C₂×C₅×#213	C₂²	semidirect
28. C₂×C₅×#213	C₂²	semidirect
31. C₂×C₅×D₂₄	C₂²	semidirect
32. C₂×C₅×#204	C₂²	semidirect
36. C₅×#875	C₂²	semidirect
39. C₃×C₅×#97	C₂²	semidirect
40. C₅×C₈×Dic₃	C₂²	semidirect
41. C₅×#803	C₂²	semidirect
42. #81845	C₅	direct (N × H)
50. C₅×#496	D₃	semidirect
93. C₅×ΓL(1,𝔽₂₅)	D₄	semidirect
94. C₂×#914	C₂×C₅	semidirect
95. C₂×#911	C₂×C₅	semidirect
96. D₃×#127	C₂×C₅	semidirect
97. #5668	C₂×C₅	semidirect
98. C₃×#496	C₂×C₅	semidirect
99. #5175	C₂×C₅	semidirect
100. #5151	C₂×C₅	semidirect
101. #5074	C₂×C₅	semidirect
102. #5058	C₂×C₅	semidirect
103. #4712	C₂×C₅	semidirect
104. #4707	C₂×C₅	semidirect
114. C₂×C₅×SD₁₆	C₂×D₃	semidirect
118. C₂×C₅×D₈	C₂×D₃	semidirect
127. C₅×#124	C₂×D₃	semidirect
132. C₅×#97	C₂×D₃	semidirect
167. C₃×C₅×C₈	C₂×D₄	semidirect
168. C₅×C₃⋊C₈	C₂×D₄	semidirect
173. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
174. C₂×C₃×D₈	C₂²×C₅	semidirect
176. C₃×#124	C₂²×C₅	semidirect
177. #944	C₂²×C₅	semidirect
178. C₂×#215	C₂²×C₅	semidirect
181. #940	C₂²×C₅	semidirect
182. C₂×#214	C₂²×C₅	semidirect
183. C₂×#213	C₂²×C₅	semidirect
184. C₂×#213	C₂²×C₅	semidirect
187. C₂×D₂₄	C₂²×C₅	semidirect
188. C₂×#204	C₂²×C₅	semidirect
192. #875	C₂²×C₅	semidirect
195. C₃×#97	C₂²×C₅	semidirect
196. C₈×Dic₃	C₂²×C₅	semidirect
197. #803	C₂²×C₅	semidirect
245. #496	C₅×D₃	semidirect
266. C₅×Dic₃	AGL(1,ℤ/8)	semidirect
306. ΓL(1,𝔽₂₅)	C₅×D₄	semidirect
340. C₅×C₈	D₃×D₄	semidirect
350. C₂×SD₁₆	C₂×C₅×D₃	semidirect
354. C₂×D₈	C₂×C₅×D₃	semidirect
363. #124	C₂×C₅×D₃	semidirect
368. #97	C₂×C₅×D₃	semidirect
409. C₃×C₈	C₂×C₅×D₄	semidirect
410. C₃⋊C₈	C₂×C₅×D₄	semidirect
469. C₃×C₅	#3151	semidirect
487. Dic₃	C₅×AGL(1,ℤ/8)	semidirect
528. C₈	C₅×D₃×D₄	semidirect
536. C₅	#81845	direct (N × H)
555. C₃	C₅×#3151	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#914	2
C₂×C₅×#911	2
C₅×D₃×#127	2
C₅×#5668	2
C₃×C₅×#496	2
C₅×#5175	2
C₅×#5151	2
C₅×#5074	2
C₅×#5058	2
C₅×#4712	2
C₅×#4707	2
C₅×#3151	3
#81845	5

Subgroups — C5×#81845 #14439129

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#81845 #14439129