Subgroups — C₅×#68909 #14301086

Order 1920.

748 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	C₂²×C₅×#204	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#887	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#4988	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×#810	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#809	C₂	1	1	yes	maximal, characteristic
6	C₃×C₅×#340	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4550	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1880	—	3	1	no	maximal, Hall
9	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
10	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
14	C₂×C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
15	C₂×C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
16	C₂×C₅×Dic₃⋊C₄	—	2	1	no	—
17	C₂×C₄×C₅×Dic₃	—	2	1	no	—
18	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
19	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₅×#204	—	2	2	no	—
21	C₂×C₅×#204	—	2	2	no	—
22	C₂×C₅×#204	C₄	1	4	yes	complemented
23	C₅×#887	—	2	2	no	—
24	C₅×#887	—	2	2	no	—
25	C₅×#810	—	2	2	no	—
26	C₅×#809	—	2	2	no	—
27	#68909	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
28	C₂²×C₅×SD₁₆	—	3	1	no	—
29	C₂×C₄×C₅×Q₈	—	3	1	no	—
30	C₂×C₅×#103	—	3	1	no	—
31	C₂×C₅×#102	—	3	1	no	—
32	C₅×#390	—	3	1	no	—
33	C₅×#340	D₃	1	1	yes	characteristic, complemented
34	C₅×#336	—	3	1	no	—
35	C₂³×C₅×D₃	—	2	1	no	—
36	C₂²×C₃×C₄×C₅	—	2	1	no	—
37	C₂²×C₃×C₄×C₅	—	2	1	no	—
38	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
39	C₂²×C₅×Dic₃	—	2	1	no	—
40	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
41	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
42	C₂×C₅×D₁₂	—	2	1	no	—
43	C₂×C₅×D₁₂	—	2	1	no	—
44	C₂×C₅×D₁₂	—	2	1	no	—
45	C₂×C₅×D₁₂	—	2	1	no	—
46	C₂×C₅×D₁₂	—	2	1	no	—
47	C₂×C₅×D₁₂	C₂×C₄	1	2	yes	—
48	C₂×C₅×Dic₆	—	2	1	no	—
49	C₂×C₅×Dic₆	—	2	1	no	—
50	C₂×C₅×Dic₆	—	2	1	no	—
51	C₂×C₅×Dic₆	C₂×C₄	1	2	yes	—
52	C₂×C₅×Dic₆	D₄	1	2	yes	—
53	C₂×C₅×Dic₆	D₄	1	2	yes	—
54	C₂×C₃×C₅×C₈	—	2	1	no	—
55	C₂×C₃×C₅×C₈	—	2	1	no	—
56	C₂×C₃×C₅×C₈	C₂×C₄	1	2	yes	—
57	C₃×C₅×C₄⋊C₄	—	2	1	no	—
58	C₃×C₅×C₄⋊C₄	—	2	1	no	—
59	C₃×C₅×C₄⋊C₄	—	2	1	no	—
60	C₃×C₅×C₄⋊C₄	D₄	1	2	yes	—
61	C₅×(C₂×D₃)⋊C₄	—	4	2	no	—
62	C₅×(C₂×D₃)⋊C₄	—	4	2	no	—
63	C₅×Dic₃⋊C₄	—	2	4	no	—
64	C₄×C₅×Dic₃	—	2	4	no	—
65	C₄×C₅×Dic₃	—	2	1	no	—
66	C₄×C₅×Dic₃	—	2	1	no	—
67	C₂×C₅×C₃⋊C₈	—	2	1	no	—
68	C₂×C₅×C₃⋊C₈	—	2	1	no	—
69	C₂×C₅×C₃⋊C₈	—	2	1	no	—
70	C₅×#204	—	2	8	no	—
71	C₂²×#204	C₂×C₅	1	1	yes	characteristic
72	C₂×#887	C₂×C₅	1	1	yes	characteristic, complemented
73	#4988	C₂×C₅	1	1	yes	characteristic
74	C₂×#810	C₂×C₅	1	1	yes	characteristic, complemented
75	C₂×#809	C₂×C₅	1	1	yes	characteristic
76	C₃×#340	C₂×C₅	1	1	yes	characteristic, complemented
77	#4550	C₂×C₅	1	1	yes	characteristic, complemented
78	C₂²×C₅×Q₈	—	3	1	no	—
79	C₂²×C₅×D₄	—	3	1	no	—
80	C₂×C₅×SD₁₆	—	3	4	no	—
81	C₂×C₅×SD₁₆	—	6	2	no	—
82	C₂×C₅×SD₁₆	—	6	2	no	—
83	C₂²×C₅×C₈	—	3	1	no	—
84	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
85	C₄×C₅×Q₈	—	6	2	no	—
86	C₄×C₅×Q₈	—	6	2	no	—
87	C₂×C₅×C₄⋊C₄	—	6	1	no	—
88	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
89	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
90	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
91	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
92	C₂×C₄²×C₅	—	3	1	no	—
93	C₂×C₄²×C₅	—	6	1	no	—
94	C₅×#103	—	6	2	no	—
95	C₅×#102	—	6	2	no	—
96	#1880	—	3	1	no	Sylow
97	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₅×D₃	—	2	2	no	—
99	C₂²×C₅×D₃	—	4	1	no	—
100	C₂²×C₅×D₃	—	4	1	no	—
101	C₂²×C₅×D₃	—	4	1	no	—
102	C₂²×C₅×D₃	—	4	1	no	—
103	C₂²×C₅×D₃	—	4	1	no	—
104	C₂²×C₅×D₃	—	4	1	no	—
105	C₂×C₃×C₄×C₅	—	2	2	no	—
106	C₂×C₃×C₄×C₅	—	4	1	no	—
107	C₂×C₃×C₄×C₅	—	4	1	no	—
108	C₂×C₃×C₄×C₅	—	4	1	no	—
109	C₂×C₃×C₄×C₅	—	4	1	no	—
110	C₂×C₃×C₄×C₅	—	4	1	no	—
111	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
113	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
114	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
115	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
116	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
117	C₂×C₅×Dic₃	—	2	2	no	—
118	C₂×C₅×Dic₃	—	2	1	no	—
119	C₂×C₅×Dic₃	—	2	2	no	—
120	C₂×C₅×Dic₃	—	2	2	no	—
121	C₂×C₅×Dic₃	—	2	1	no	—
122	C₂×C₅×Dic₃	—	2	1	no	—
123	C₂×C₅×Dic₃	—	2	1	no	—
124	C₂×C₅×Dic₃	—	2	1	no	—
125	C₂×C₅×Dic₃	SD₁₆	1	2	yes	complemented
126	C₅×D₁₂	—	2	2	no	—
127	C₅×D₁₂	—	2	2	no	—
128	C₅×D₁₂	—	4	1	no	—
129	C₅×D₁₂	—	4	1	no	—
130	C₅×Dic₆	—	2	2	no	—
131	C₅×Dic₆	—	2	2	no	—
132	C₅×Dic₆	—	2	2	no	—
133	C₅×Dic₆	C₂²⋊C₄	1	4	yes	complemented
134	C₃×C₅×C₈	—	2	2	no	—
135	C₅×C₃⋊C₈	—	4	1	no	—
136	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
137	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
138	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
139	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
140	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
141	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
142	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
143	C₂×Dic₃⋊C₄	—	2	1	no	—
144	C₂×C₄×Dic₃	—	2	1	no	—
145	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
146	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
147	C₂×#204	—	2	2	no	—
148	C₂×#204	—	2	2	no	—
149	C₂×#204	C₄×C₅	1	4	yes	complemented
150	#887	—	2	2	no	—
151	#887	—	2	2	no	—
152	#810	—	2	2	no	—
153	#809	—	2	2	no	—
154	C₂⁴×C₅	—	6	1	no	—
155	C₂×C₅×Q₈	—	3	2	no	—
156	C₂×C₅×Q₈	—	3	2	no	—
157	C₂×C₅×Q₈	—	3	2	no	—
158	C₂×C₅×Q₈	—	6	1	no	—
159	C₂×C₅×Q₈	—	6	1	no	—
160	C₂×C₅×Q₈	—	6	1	no	—
161	C₂×C₅×D₄	—	3	2	no	—
162	C₂×C₅×D₄	—	6	1	no	—
163	C₂×C₅×D₄	—	6	1	no	—
164	C₂×C₅×D₄	—	6	1	no	—
165	C₂×C₅×D₄	—	6	1	no	—
166	C₂×C₅×D₄	—	6	1	no	—
167	C₂²×C₄×C₅	—	2	1	no	—
168	C₂²×C₄×C₅	—	2	1	no	—
169	C₂²×C₄×C₅	—	3	1	no	—
170	C₂²×C₄×C₅	—	3	1	no	—
171	C₂²×C₄×C₅	—	6	1	no	—
172	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
173	C₅×SD₁₆	—	6	8	no	—
174	C₂×C₅×C₈	—	2	1	no	—
175	C₂×C₅×C₈	—	2	1	no	—
176	C₂×C₅×C₈	—	6	1	no	—
177	C₂×C₅×C₈	—	6	1	no	—
178	C₂×C₅×C₈	—	6	1	no	—
179	C₂×C₅×C₈	C₄×D₃	1	2	yes	—
180	C₅×C₄⋊C₄	—	2	1	no	—
181	C₅×C₄⋊C₄	—	2	1	no	—
182	C₅×C₄⋊C₄	—	2	1	no	—
183	C₅×C₄⋊C₄	—	6	4	no	—
184	C₅×C₄⋊C₄	D₁₂	1	2	yes	—
185	C₅×C₂²⋊C₄	—	12	2	no	—
186	C₅×C₂²⋊C₄	—	12	2	no	—
187	C₄²×C₅	—	6	4	no	—
188	C₄²×C₅	—	6	1	no	—
189	C₄²×C₅	—	6	1	no	—
190	C₂²×SD₁₆	—	3	1	no	—
191	C₂×C₄×Q₈	—	3	1	no	—
192	C₂×#103	—	3	1	no	—
193	C₂×#102	—	3	1	no	—
194	#390	—	3	1	no	—
195	#340	C₅×D₃	1	1	yes	characteristic, complemented
196	#336	—	3	1	no	—
197	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
198	C₂²×C₃×C₅	#120	1	1	yes	characteristic
199	C₂²×C₃×C₅	#121	1	1	yes	characteristic
200	C₂²×C₃×C₅	C₂×SD₁₆	1	1	yes	characteristic
201	C₂²×C₃×C₅	#135	1	1	yes	characteristic
202	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
203	C₂²×C₃×C₅	#137	1	1	yes	characteristic
204	C₂×C₅×D₃	—	4	2	no	—
205	C₂×C₅×D₃	—	4	2	no	—
206	C₂×C₅×D₃	—	4	2	no	—
207	C₂×C₅×D₃	—	8	1	no	—
208	C₂×C₅×D₃	—	8	1	no	—
209	C₂×C₅×D₃	—	8	1	no	—
210	C₂×C₅×D₃	—	8	1	no	—
211	C₃×C₄×C₅	—	4	2	no	—
212	C₃×C₄×C₅	—	8	1	no	—
213	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
214	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
215	C₃×C₄×C₅	#121	1	1	yes	characteristic
216	C₃×C₄×C₅	#123	1	1	yes	characteristic
217	C₅×Dic₃	—	2	4	no	—
218	C₅×Dic₃	—	2	2	no	—
219	C₅×Dic₃	—	4	1	no	—
220	C₂³×D₃	—	2	1	no	—
221	C₂²×C₃×C₄	—	2	1	no	—
222	C₂²×C₃×C₄	—	2	1	no	—
223	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
224	C₂²×Dic₃	—	2	1	no	—
225	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
226	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
227	C₂×D₁₂	—	2	1	no	—
228	C₂×D₁₂	—	2	1	no	—
229	C₂×D₁₂	—	2	1	no	—
230	C₂×D₁₂	—	2	1	no	—
231	C₂×D₁₂	—	2	1	no	—
232	C₂×D₁₂	C₂×C₄×C₅	1	2	yes	—
233	C₂×Dic₆	—	2	1	no	—
234	C₂×Dic₆	—	2	1	no	—
235	C₂×Dic₆	—	2	1	no	—
236	C₂×Dic₆	C₂×C₄×C₅	1	2	yes	—
237	C₂×Dic₆	C₅×D₄	1	2	yes	—
238	C₂×Dic₆	C₅×D₄	1	2	yes	—
239	C₂×C₃×C₈	—	2	1	no	—
240	C₂×C₃×C₈	—	2	1	no	—
241	C₂×C₃×C₈	C₂×C₄×C₅	1	2	yes	—
242	C₃×C₄⋊C₄	—	2	1	no	—
243	C₃×C₄⋊C₄	—	2	1	no	—
244	C₃×C₄⋊C₄	—	2	1	no	—
245	C₃×C₄⋊C₄	C₅×D₄	1	2	yes	—
246	(C₂×D₃)⋊C₄	—	4	2	no	—
247	(C₂×D₃)⋊C₄	—	4	2	no	—
248	Dic₃⋊C₄	—	2	4	no	—
249	C₄×Dic₃	—	2	4	no	—
250	C₄×Dic₃	—	2	1	no	—
251	C₄×Dic₃	—	2	1	no	—
252	C₂×C₃⋊C₈	—	2	1	no	—
253	C₂×C₃⋊C₈	—	2	1	no	—
254	C₂×C₃⋊C₈	—	2	1	no	—
255	#204	—	2	8	no	—
256	C₂³×C₅	—	6	2	no	—
257	C₂³×C₅	—	12	1	no	—
258	C₂³×C₅	—	12	1	no	—
259	C₂³×C₅	—	12	1	no	—
260	C₂³×C₅	—	12	1	no	—
261	C₂³×C₅	—	12	1	no	—
262	C₂³×C₅	—	12	1	no	—
263	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
264	C₅×Q₈	—	3	4	no	—
265	C₅×Q₈	—	6	2	no	—
266	C₅×Q₈	—	6	2	no	—
267	C₅×Q₈	—	6	2	no	—
268	C₅×D₄	—	6	2	no	—
269	C₅×D₄	—	6	2	no	—
270	C₅×D₄	—	12	1	no	—
271	C₅×D₄	—	12	1	no	—
272	C₂×C₄×C₅	—	2	2	no	—
273	C₂×C₄×C₅	—	3	2	no	—
274	C₂×C₄×C₅	—	4	1	no	—
275	C₂×C₄×C₅	—	4	1	no	—
276	C₂×C₄×C₅	—	4	1	no	—
277	C₂×C₄×C₅	—	4	1	no	—
278	C₂×C₄×C₅	—	4	1	no	—
279	C₂×C₄×C₅	—	6	1	no	—
280	C₂×C₄×C₅	—	6	2	no	—
281	C₂×C₄×C₅	—	6	2	no	—
282	C₂×C₄×C₅	—	6	2	no	—
283	C₂×C₄×C₅	—	6	1	no	—
284	C₂×C₄×C₅	—	6	1	no	—
285	C₂×C₄×C₅	—	6	1	no	—
286	C₂×C₄×C₅	—	6	1	no	—
287	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
288	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
289	C₂×C₄×C₅	#235	1	1	yes	characteristic
290	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
291	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
292	C₂×C₄×C₅	#239	1	1	yes	characteristic
293	C₅×C₈	—	2	2	no	—
294	C₅×C₈	—	12	1	no	—
295	C₂²×Q₈	—	3	1	no	—
296	C₂²×D₄	—	3	1	no	—
297	C₂×SD₁₆	—	3	4	no	—
298	C₂×SD₁₆	—	6	2	no	—
299	C₂×SD₁₆	—	6	2	no	—
300	C₂²×C₈	—	3	1	no	—
301	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
302	C₄×Q₈	—	6	2	no	—
303	C₄×Q₈	—	6	2	no	—
304	C₂×C₄⋊C₄	—	6	1	no	—
305	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
306	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
307	C₂×C₂²⋊C₄	—	6	1	no	—
308	C₂×C₂²⋊C₄	—	6	1	no	—
309	C₂×C₄²	—	3	1	no	—
310	C₂×C₄²	—	6	1	no	—
311	#103	—	6	2	no	—
312	#102	—	6	2	no	—
313	C₂×C₃×C₅	#386	1	1	yes	characteristic
314	C₂×C₃×C₅	C₄×SD₁₆	1	1	yes	characteristic
315	C₂×C₃×C₅	#440	1	1	yes	characteristic
316	C₂×C₃×C₅	#448	1	1	yes	characteristic
317	C₂×C₃×C₅	#449	1	1	yes	characteristic
318	C₂×C₃×C₅	#460	1	1	yes	characteristic
319	C₂×C₃×C₅	#464	1	1	yes	characteristic
320	C₅×D₃	—	8	2	no	—
321	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
322	C₂²×D₃	—	2	2	no	—
323	C₂²×D₃	—	4	1	no	—
324	C₂²×D₃	—	4	1	no	—
325	C₂²×D₃	—	4	1	no	—
326	C₂²×D₃	—	4	1	no	—
327	C₂²×D₃	—	4	1	no	—
328	C₂²×D₃	—	4	1	no	—
329	C₂×C₃×C₄	—	2	2	no	—
330	C₂×C₃×C₄	—	4	1	no	—
331	C₂×C₃×C₄	—	4	1	no	—
332	C₂×C₃×C₄	—	4	1	no	—
333	C₂×C₃×C₄	—	4	1	no	—
334	C₂×C₃×C₄	—	4	1	no	—
335	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
336	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
337	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
338	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
339	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
340	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
341	C₂×Dic₃	—	2	2	no	—
342	C₂×Dic₃	—	2	1	no	—
343	C₂×Dic₃	—	2	2	no	—
344	C₂×Dic₃	—	2	2	no	—
345	C₂×Dic₃	—	2	1	no	—
346	C₂×Dic₃	—	2	1	no	—
347	C₂×Dic₃	—	2	1	no	—
348	C₂×Dic₃	—	2	1	no	—
349	C₂×Dic₃	C₅×SD₁₆	1	2	yes	complemented
350	D₁₂	—	2	2	no	—
351	D₁₂	—	2	2	no	—
352	D₁₂	—	4	1	no	—
353	D₁₂	—	4	1	no	—
354	Dic₆	—	2	2	no	—
355	Dic₆	—	2	2	no	—
356	Dic₆	—	2	2	no	—
357	Dic₆	C₅×C₂²⋊C₄	1	4	yes	complemented
358	C₃×C₈	—	2	2	no	—
359	C₃⋊C₈	—	4	1	no	—
360	C₂²×C₅	—	12	2	no	—
361	C₂²×C₅	—	12	2	no	—
362	C₂²×C₅	—	12	2	no	—
363	C₂²×C₅	—	24	1	no	—
364	C₂²×C₅	—	24	1	no	—
365	C₂²×C₅	—	24	1	no	—
366	C₂²×C₅	—	24	1	no	—
367	C₂²×C₅	#882	1	1	yes	characteristic
368	C₂²×C₅	#884	1	1	yes	characteristic
369	C₂²×C₅	#893	1	1	yes	characteristic
370	C₂²×C₅	#911	1	1	yes	characteristic
371	C₂²×C₅	D₃×SD₁₆	1	1	yes	characteristic
372	C₂²×C₅	#916	1	1	yes	characteristic
373	C₂²×C₅	#918	1	1	yes	characteristic
374	C₄×C₅	—	4	2	no	—
375	C₄×C₅	—	6	4	no	—
376	C₄×C₅	—	6	2	no	—
377	C₄×C₅	—	8	1	no	—
378	C₄×C₅	—	12	1	no	—
379	C₄×C₅	C₄×D₁₂	1	1	yes	characteristic
380	C₄×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
381	C₄×C₅	#894	1	1	yes	characteristic
382	C₄×C₅	#895	1	1	yes	characteristic
383	C₂⁴	—	6	1	no	—
384	C₂×Q₈	—	3	2	no	—
385	C₂×Q₈	—	3	2	no	—
386	C₂×Q₈	—	3	2	no	—
387	C₂×Q₈	—	6	1	no	—
388	C₂×Q₈	—	6	1	no	—
389	C₂×Q₈	—	6	1	no	—
390	C₂×D₄	—	3	2	no	—
391	C₂×D₄	—	6	1	no	—
392	C₂×D₄	—	6	1	no	—
393	C₂×D₄	—	6	1	no	—
394	C₂×D₄	—	6	1	no	—
395	C₂×D₄	—	6	1	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	3	1	no	—
399	C₂²×C₄	—	3	1	no	—
400	C₂²×C₄	—	6	1	no	—
401	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
402	SD₁₆	—	6	8	no	—
403	C₂×C₈	—	2	1	no	—
404	C₂×C₈	—	2	1	no	—
405	C₂×C₈	—	6	1	no	—
406	C₂×C₈	—	6	1	no	—
407	C₂×C₈	—	6	1	no	—
408	C₂×C₈	C₄×C₅×D₃	1	2	yes	—
409	C₄⋊C₄	—	2	1	no	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	—	2	1	no	—
412	C₄⋊C₄	—	6	4	no	—
413	C₄⋊C₄	C₅×D₁₂	1	2	yes	—
414	C₂²⋊C₄	—	12	2	no	—
415	C₂²⋊C₄	—	12	2	no	—
416	C₄²	—	6	4	no	—
417	C₄²	—	6	1	no	—
418	C₄²	—	6	1	no	—
419	C₃×C₅	#1880	1	1	yes	characteristic, complemented, Hall
420	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
421	C₂²×C₃	C₅×#120	1	1	yes	characteristic
422	C₂²×C₃	C₅×#121	1	1	yes	characteristic
423	C₂²×C₃	C₂×C₅×SD₁₆	1	1	yes	characteristic
424	C₂²×C₃	C₅×#135	1	1	yes	characteristic
425	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
426	C₂²×C₃	C₅×#137	1	1	yes	characteristic
427	C₂×D₃	—	4	2	no	—
428	C₂×D₃	—	4	2	no	—
429	C₂×D₃	—	4	2	no	—
430	C₂×D₃	—	8	1	no	—
431	C₂×D₃	—	8	1	no	—
432	C₂×D₃	—	8	1	no	—
433	C₂×D₃	—	8	1	no	—
434	C₃×C₄	—	4	2	no	—
435	C₃×C₄	—	8	1	no	—
436	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
437	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
438	C₃×C₄	C₅×#121	1	1	yes	characteristic
439	C₃×C₄	C₅×#123	1	1	yes	characteristic
440	Dic₃	—	2	4	no	—
441	Dic₃	—	2	2	no	—
442	Dic₃	—	4	1	no	—
443	C₂×C₅	—	24	2	no	—
444	C₂×C₅	#4665	1	1	yes	characteristic
445	C₂×C₅	#4762	1	1	yes	characteristic
446	C₂×C₅	#4781	1	1	yes	characteristic
447	C₂×C₅	#4798	1	1	yes	characteristic
448	C₂×C₅	#4806	1	1	yes	characteristic
449	C₂×C₅	#4852	1	1	yes	characteristic
450	C₂×C₅	#4889	1	1	yes	characteristic
451	C₂³	—	6	2	no	—
452	C₂³	—	12	1	no	—
453	C₂³	—	12	1	no	—
454	C₂³	—	12	1	no	—
455	C₂³	—	12	1	no	—
456	C₂³	—	12	1	no	—
457	C₂³	—	12	1	no	—
458	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
459	Q₈	—	3	4	no	—
460	Q₈	—	6	2	no	—
461	Q₈	—	6	2	no	—
462	Q₈	—	6	2	no	—
463	D₄	—	6	2	no	—
464	D₄	—	6	2	no	—
465	D₄	—	12	1	no	—
466	D₄	—	12	1	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	3	2	no	—
469	C₂×C₄	—	4	1	no	—
470	C₂×C₄	—	4	1	no	—
471	C₂×C₄	—	4	1	no	—
472	C₂×C₄	—	4	1	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	6	1	no	—
475	C₂×C₄	—	6	2	no	—
476	C₂×C₄	—	6	2	no	—
477	C₂×C₄	—	6	2	no	—
478	C₂×C₄	—	6	1	no	—
479	C₂×C₄	—	6	1	no	—
480	C₂×C₄	—	6	1	no	—
481	C₂×C₄	—	6	1	no	—
482	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
483	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
484	C₂×C₄	C₅×#235	1	1	yes	characteristic
485	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
486	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
487	C₂×C₄	C₅×#239	1	1	yes	characteristic
488	C₈	—	2	2	no	—
489	C₈	—	12	1	no	—
490	C₂×C₃	C₅×#386	1	1	yes	characteristic
491	C₂×C₃	C₄×C₅×SD₁₆	1	1	yes	characteristic
492	C₂×C₃	C₅×#440	1	1	yes	characteristic
493	C₂×C₃	C₅×#448	1	1	yes	characteristic
494	C₂×C₃	C₅×#449	1	1	yes	characteristic
495	C₂×C₃	C₅×#460	1	1	yes	characteristic
496	C₂×C₃	C₅×#464	1	1	yes	characteristic
497	D₃	—	8	2	no	—
498	C₅	#68909	1	1	yes	characteristic, direct product factor, Sylow
499	C₂²	—	12	2	no	—
500	C₂²	—	12	2	no	—
501	C₂²	—	12	2	no	—
502	C₂²	—	24	1	no	—
503	C₂²	—	24	1	no	—
504	C₂²	—	24	1	no	—
505	C₂²	—	24	1	no	—
506	C₂²	C₅×#882	1	1	yes	characteristic
507	C₂²	C₅×#884	1	1	yes	characteristic
508	C₂²	C₅×#893	1	1	yes	characteristic
509	C₂²	C₅×#911	1	1	yes	characteristic
510	C₂²	C₅×D₃×SD₁₆	1	1	yes	characteristic
511	C₂²	C₅×#916	1	1	yes	characteristic
512	C₂²	C₅×#918	1	1	yes	characteristic
513	C₄	—	4	2	no	—
514	C₄	—	6	4	no	—
515	C₄	—	6	2	no	—
516	C₄	—	8	1	no	—
517	C₄	—	12	1	no	—
518	C₄	C₄×C₅×D₁₂	1	1	yes	characteristic
519	C₄	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
520	C₄	C₅×#894	1	1	yes	characteristic
521	C₄	C₅×#895	1	1	yes	characteristic
522	C₃	C₅×#1880	1	1	yes	characteristic, complemented, Sylow
523	C₂	—	24	2	no	—
524	C₂	C₅×#4665	1	1	yes	characteristic
525	C₂	C₅×#4762	1	1	yes	characteristic
526	C₂	C₅×#4781	1	1	yes	characteristic
527	C₂	C₅×#4798	1	1	yes	characteristic
528	C₂	C₅×#4806	1	1	yes	characteristic
529	C₂	C₅×#4852	1	1	yes	characteristic
530	C₂	C₅×#4889	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	D₃×D₄
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₃×C₅×#340	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂²×C₅×D₁₂	C₂²
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₅×#340	D₃
hypocenter	C₃	C₅×#1880
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#340

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#887	C₂	semidirect
4. C₂×C₅×#810	C₂	semidirect
6. C₃×C₅×#340	C₂	semidirect
7. C₅×#4550	C₂	semidirect
22. C₂×C₅×#204	C₄	semidirect
27. #68909	C₅	direct (N × H)
33. C₅×#340	D₃	semidirect
72. C₂×#887	C₂×C₅	semidirect
74. C₂×#810	C₂×C₅	semidirect
76. C₃×#340	C₂×C₅	semidirect
77. #4550	C₂×C₅	semidirect
125. C₂×C₅×Dic₃	SD₁₆	semidirect
133. C₅×Dic₆	C₂²⋊C₄	semidirect
149. C₂×#204	C₄×C₅	semidirect
195. #340	C₅×D₃	semidirect
349. C₂×Dic₃	C₅×SD₁₆	semidirect
357. Dic₆	C₅×C₂²⋊C₄	semidirect
419. C₃×C₅	#1880	semidirect
498. C₅	#68909	direct (N × H)
522. C₃	C₅×#1880	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₅×#204	2
C₂×C₅×#887	2
C₅×#4988	2
C₂×C₅×#810	2
C₂×C₅×#809	2
C₃×C₅×#340	2
C₅×#4550	2
C₅×#1880	3
#68909	5

Subgroups — C5×#68909 #14301086

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#68909 #14301086