Subgroups — C₅×#69929 #14299451

Order 1920.

632 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#926	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₅×#5212	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×#818	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#817	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4551	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4551	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1854	—	3	1	no	maximal, Hall
9	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
10	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₂×C₅×#217	—	2	1	no	—
13	C₂×C₅×#217	—	2	1	no	—
14	C₅×#926	—	2	2	no	—
15	C₅×#926	—	2	2	no	—
16	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
17	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
18	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
19	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₅×Dic₃	—	2	1	no	—
21	C₃×C₅×C₂²⋊C₈	C₄	1	4	yes	complemented
22	C₅×C₃⋊#95	—	2	1	no	—
23	C₅×#818	—	2	2	no	—
24	C₅×#817	—	2	2	no	—
25	#69929	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
26	C₂×C₅×#117	—	3	1	no	—
27	C₂×C₅×#107	—	3	1	no	—
28	C₂×C₅×#106	—	3	1	no	—
29	C₂×C₅×C₂²⋊C₈	D₃	1	1	yes	characteristic
30	C₅×#380	—	3	1	no	—
31	C₅×#340	—	3	1	no	—
32	C₅×#340	—	3	1	no	—
33	C₂⁴×C₃×C₅	D₄	1	1	yes	characteristic
34	C₂²×C₃×C₄×C₅	—	2	1	no	—
35	C₂²×C₃×C₄×C₅	—	2	1	no	—
36	C₂²×C₃×C₄×C₅	—	2	1	no	—
37	C₂²×C₃×C₄×C₅	—	2	1	no	—
38	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
39	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
40	C₂²×C₃×C₄×C₅	Q₈	1	2	yes	—
41	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
42	C₂²×C₅×Dic₃	—	2	1	no	—
43	C₂²×C₅×Dic₃	—	2	1	no	—
44	C₂²×C₅×Dic₃	—	2	1	no	—
45	C₂²×C₅×Dic₃	—	2	1	no	—
46	C₂×C₃×C₅×C₈	—	2	1	no	—
47	C₂×C₃×C₅×C₈	—	2	1	no	—
48	C₂×C₃×C₅×C₈	—	2	1	no	—
49	C₂×C₃×C₅×C₈	—	2	1	no	—
50	C₂×C₃×C₅×C₈	C₂×C₄	1	2	yes	—
51	C₂×C₃×C₅×C₈	C₂×C₄	1	2	yes	—
52	C₅×#217	—	2	4	no	—
53	C₅×#217	—	4	2	no	—
54	C₅×C₄⋊Dic₃	—	2	1	no	—
55	C₅×C₄⋊Dic₃	—	2	1	no	—
56	C₅×C₄⋊Dic₃	—	2	1	no	—
57	C₅×C₄⋊Dic₃	—	2	1	no	—
58	C₅×C₄⋊Dic₃	—	2	1	no	—
59	C₅×C₄⋊Dic₃	—	2	1	no	—
60	C₅×C₄⋊Dic₃	D₄	1	2	yes	—
61	C₅×C₄⋊Dic₃	D₄	1	2	yes	—
62	C₄×C₅×Dic₃	—	2	4	no	—
63	C₂×#926	C₂×C₅	1	1	yes	characteristic
64	C₂×C₃×C₂²⋊C₈	C₂×C₅	1	1	yes	characteristic
65	#5212	C₂×C₅	1	1	yes	characteristic
66	C₂×#818	C₂×C₅	1	1	yes	characteristic, complemented
67	C₂×#817	C₂×C₅	1	1	yes	characteristic, complemented
68	#4551	C₂×C₅	1	1	yes	characteristic, complemented
69	#4551	C₂×C₅	1	1	yes	characteristic, complemented
70	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
71	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
72	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
73	C₅×#117	—	6	2	no	—
74	C₅×#117	—	6	2	no	—
75	C₂×C₅×C₄⋊C₄	—	3	1	no	—
76	C₂×C₅×C₄⋊C₄	—	3	1	no	—
77	C₂×C₅×C₄⋊C₄	—	3	1	no	—
78	C₂×C₅×C₄⋊C₄	—	3	1	no	—
79	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
80	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
81	C₂×C₄²×C₅	—	6	1	no	—
82	C₅×#107	—	6	2	no	—
83	C₅×#106	—	6	2	no	—
84	C₅×C₂²⋊C₈	Dic₃	1	4	yes	complemented
85	C₅×#95	—	6	1	no	—
86	#1854	—	3	1	no	Sylow
87	C₂³×C₃×C₅	—	2	1	no	—
88	C₂³×C₃×C₅	—	2	1	no	—
89	C₂³×C₃×C₅	—	2	1	no	—
90	C₂³×C₃×C₅	—	2	1	no	—
91	C₂³×C₃×C₅	—	2	1	no	—
92	C₂³×C₃×C₅	—	2	1	no	—
93	C₂³×C₃×C₅	C₄⋊C₄	1	2	yes	—
94	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
95	C₂×C₃×C₄×C₅	—	2	1	no	—
96	C₂×C₃×C₄×C₅	—	2	1	no	—
97	C₂×C₃×C₄×C₅	—	2	2	no	—
98	C₂×C₃×C₄×C₅	—	2	2	no	—
99	C₂×C₃×C₄×C₅	—	2	2	no	—
100	C₂×C₃×C₄×C₅	—	2	2	no	—
101	C₂×C₃×C₄×C₅	C₄⋊C₄	1	2	yes	—
102	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
104	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
105	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
106	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
107	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
108	C₂×C₅×Dic₃	—	2	2	no	—
109	C₂×C₅×Dic₃	—	2	2	no	—
110	C₂×C₅×Dic₃	—	4	1	no	—
111	C₂×C₅×Dic₃	—	4	1	no	—
112	C₂×C₅×Dic₃	—	4	1	no	—
113	C₂×C₅×Dic₃	—	4	1	no	—
114	C₂×C₅×Dic₃	—	4	1	no	—
115	C₂×C₅×Dic₃	—	4	1	no	—
116	C₂×C₅×Dic₃	—	4	1	no	—
117	C₂×C₅×Dic₃	—	4	1	no	—
118	C₂×C₅×Dic₃	—	4	1	no	—
119	C₂×C₅×Dic₃	—	4	1	no	—
120	C₃×C₅×C₈	—	2	2	no	—
121	C₃×C₅×C₈	—	2	2	no	—
122	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
123	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
124	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
125	C₂×#217	—	2	1	no	—
126	C₂×#217	—	2	1	no	—
127	#926	—	2	2	no	—
128	#926	—	2	2	no	—
129	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
130	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
131	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
132	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
133	C₂×C₄×Dic₃	—	2	1	no	—
134	C₃×C₂²⋊C₈	C₄×C₅	1	4	yes	complemented
135	C₃⋊#95	—	2	1	no	—
136	#818	—	2	2	no	—
137	#817	—	2	2	no	—
138	C₂⁴×C₅	D₁₂	1	1	yes	characteristic
139	C₂²×C₄×C₅	—	2	1	no	—
140	C₂²×C₄×C₅	—	2	1	no	—
141	C₂²×C₄×C₅	—	2	1	no	—
142	C₂²×C₄×C₅	—	2	1	no	—
143	C₂²×C₄×C₅	—	6	1	no	—
144	C₂²×C₄×C₅	—	6	1	no	—
145	C₂²×C₄×C₅	—	6	1	no	—
146	C₂²×C₄×C₅	—	6	1	no	—
147	C₂²×C₄×C₅	Dic₆	1	2	yes	—
148	C₂²×C₄×C₅	D₁₂	1	1	yes	characteristic
149	C₂²×C₄×C₅	C₂×Dic₃	1	2	yes	—
150	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
151	C₂×C₅×C₈	—	2	1	no	—
152	C₂×C₅×C₈	—	2	1	no	—
153	C₂×C₅×C₈	—	2	1	no	—
154	C₂×C₅×C₈	—	2	1	no	—
155	C₂×C₅×C₈	C₂×Dic₃	1	2	yes	—
156	C₂×C₅×C₈	C₂×Dic₃	1	2	yes	—
157	C₅×C₄⋊C₄	—	3	2	no	—
158	C₅×C₄⋊C₄	—	3	2	no	—
159	C₅×C₄⋊C₄	—	6	1	no	—
160	C₅×C₄⋊C₄	—	6	1	no	—
161	C₅×C₄⋊C₄	—	6	1	no	—
162	C₅×C₄⋊C₄	—	6	1	no	—
163	C₅×C₄⋊C₄	—	6	1	no	—
164	C₅×C₄⋊C₄	—	6	1	no	—
165	C₅×C₂²⋊C₄	—	6	4	no	—
166	C₅×C₂²⋊C₄	—	12	2	no	—
167	C₄²×C₅	—	6	4	no	—
168	C₂×#117	—	3	1	no	—
169	C₂×#107	—	3	1	no	—
170	C₂×#106	—	3	1	no	—
171	C₂×C₂²⋊C₈	C₅×D₃	1	1	yes	characteristic
172	#380	—	3	1	no	—
173	#340	—	3	1	no	—
174	#340	—	3	1	no	—
175	C₂²×C₃×C₅	—	2	2	no	—
176	C₂²×C₃×C₅	—	2	2	no	—
177	C₂²×C₃×C₅	—	2	2	no	—
178	C₂²×C₃×C₅	—	4	1	no	—
179	C₂²×C₃×C₅	—	4	1	no	—
180	C₂²×C₃×C₅	—	4	1	no	—
181	C₂²×C₃×C₅	—	4	1	no	—
182	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
183	C₂²×C₃×C₅	#120	1	1	yes	characteristic
184	C₂²×C₃×C₅	#123	1	1	yes	characteristic
185	C₂²×C₃×C₅	#135	1	1	yes	characteristic
186	C₂²×C₃×C₅	#135	1	1	yes	characteristic
187	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
188	C₂²×C₃×C₅	#137	1	1	yes	characteristic
189	C₃×C₄×C₅	—	2	2	no	—
190	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
191	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
192	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
193	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
194	C₅×Dic₃	—	4	2	no	—
195	C₅×Dic₃	—	4	2	no	—
196	C₅×Dic₃	—	8	1	no	—
197	C₅×Dic₃	—	8	1	no	—
198	C₂⁴×C₃	C₅×D₄	1	1	yes	characteristic
199	C₂²×C₃×C₄	—	2	1	no	—
200	C₂²×C₃×C₄	—	2	1	no	—
201	C₂²×C₃×C₄	—	2	1	no	—
202	C₂²×C₃×C₄	—	2	1	no	—
203	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
204	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
205	C₂²×C₃×C₄	C₅×Q₈	1	2	yes	—
206	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
207	C₂²×Dic₃	—	2	1	no	—
208	C₂²×Dic₃	—	2	1	no	—
209	C₂²×Dic₃	—	2	1	no	—
210	C₂²×Dic₃	—	2	1	no	—
211	C₂×C₃×C₈	—	2	1	no	—
212	C₂×C₃×C₈	—	2	1	no	—
213	C₂×C₃×C₈	—	2	1	no	—
214	C₂×C₃×C₈	—	2	1	no	—
215	C₂×C₃×C₈	C₂×C₄×C₅	1	2	yes	—
216	C₂×C₃×C₈	C₂×C₄×C₅	1	2	yes	—
217	#217	—	2	4	no	—
218	#217	—	4	2	no	—
219	C₄⋊Dic₃	—	2	1	no	—
220	C₄⋊Dic₃	—	2	1	no	—
221	C₄⋊Dic₃	—	2	1	no	—
222	C₄⋊Dic₃	—	2	1	no	—
223	C₄⋊Dic₃	—	2	1	no	—
224	C₄⋊Dic₃	—	2	1	no	—
225	C₄⋊Dic₃	C₅×D₄	1	2	yes	—
226	C₄⋊Dic₃	C₅×D₄	1	2	yes	—
227	C₄×Dic₃	—	2	4	no	—
228	C₂³×C₅	—	2	1	no	—
229	C₂³×C₅	—	2	1	no	—
230	C₂³×C₅	—	2	1	no	—
231	C₂³×C₅	—	2	1	no	—
232	C₂³×C₅	—	2	1	no	—
233	C₂³×C₅	—	2	1	no	—
234	C₂³×C₅	C₄⋊Dic₃	1	2	yes	—
235	C₂³×C₅	C₂×D₁₂	1	1	yes	characteristic
236	C₂×C₄×C₅	—	2	1	no	—
237	C₂×C₄×C₅	—	2	1	no	—
238	C₂×C₄×C₅	—	2	2	no	—
239	C₂×C₄×C₅	—	2	2	no	—
240	C₂×C₄×C₅	—	2	2	no	—
241	C₂×C₄×C₅	—	2	2	no	—
242	C₂×C₄×C₅	—	6	2	no	—
243	C₂×C₄×C₅	—	6	2	no	—
244	C₂×C₄×C₅	—	12	1	no	—
245	C₂×C₄×C₅	—	12	1	no	—
246	C₂×C₄×C₅	—	12	1	no	—
247	C₂×C₄×C₅	—	12	1	no	—
248	C₂×C₄×C₅	—	12	1	no	—
249	C₂×C₄×C₅	—	12	1	no	—
250	C₂×C₄×C₅	—	12	1	no	—
251	C₂×C₄×C₅	—	12	1	no	—
252	C₂×C₄×C₅	—	12	1	no	—
253	C₂×C₄×C₅	—	12	1	no	—
254	C₂×C₄×C₅	C₄⋊Dic₃	1	2	yes	—
255	C₂×C₄×C₅	C₂×Dic₆	1	1	yes	characteristic
256	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
257	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
258	C₂×C₄×C₅	#237	1	1	yes	characteristic
259	C₂×C₄×C₅	#237	1	1	yes	characteristic
260	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
261	C₅×C₈	—	2	2	no	—
262	C₅×C₈	—	2	2	no	—
263	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
264	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
265	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
266	#117	—	6	2	no	—
267	#117	—	6	2	no	—
268	C₂×C₄⋊C₄	—	3	1	no	—
269	C₂×C₄⋊C₄	—	3	1	no	—
270	C₂×C₄⋊C₄	—	3	1	no	—
271	C₂×C₄⋊C₄	—	3	1	no	—
272	C₂×C₂²⋊C₄	—	6	1	no	—
273	C₂×C₂²⋊C₄	—	6	1	no	—
274	C₂×C₄²	—	6	1	no	—
275	#107	—	6	2	no	—
276	#106	—	6	2	no	—
277	C₂²⋊C₈	C₅×Dic₃	1	4	yes	complemented
278	#95	—	6	1	no	—
279	C₂×C₃×C₅	—	4	2	no	—
280	C₂×C₃×C₅	#385	1	1	yes	characteristic
281	C₂×C₃×C₅	#427	1	1	yes	characteristic
282	C₂×C₃×C₅	#428	1	1	yes	characteristic
283	C₂×C₃×C₅	#449	1	1	yes	characteristic
284	C₂×C₃×C₅	#452	1	1	yes	characteristic
285	C₂×C₃×C₅	#482	1	1	yes	characteristic
286	C₂×C₃×C₅	#485	1	1	yes	characteristic
287	C₂³×C₃	—	2	1	no	—
288	C₂³×C₃	—	2	1	no	—
289	C₂³×C₃	—	2	1	no	—
290	C₂³×C₃	—	2	1	no	—
291	C₂³×C₃	—	2	1	no	—
292	C₂³×C₃	—	2	1	no	—
293	C₂³×C₃	C₅×C₄⋊C₄	1	2	yes	—
294	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
295	C₂×C₃×C₄	—	2	1	no	—
296	C₂×C₃×C₄	—	2	1	no	—
297	C₂×C₃×C₄	—	2	2	no	—
298	C₂×C₃×C₄	—	2	2	no	—
299	C₂×C₃×C₄	—	2	2	no	—
300	C₂×C₃×C₄	—	2	2	no	—
301	C₂×C₃×C₄	C₅×C₄⋊C₄	1	2	yes	—
302	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
303	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
304	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
305	C₂×C₃×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
306	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
307	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
308	C₂×Dic₃	—	2	2	no	—
309	C₂×Dic₃	—	2	2	no	—
310	C₂×Dic₃	—	4	1	no	—
311	C₂×Dic₃	—	4	1	no	—
312	C₂×Dic₃	—	4	1	no	—
313	C₂×Dic₃	—	4	1	no	—
314	C₂×Dic₃	—	4	1	no	—
315	C₂×Dic₃	—	4	1	no	—
316	C₂×Dic₃	—	4	1	no	—
317	C₂×Dic₃	—	4	1	no	—
318	C₂×Dic₃	—	4	1	no	—
319	C₂×Dic₃	—	4	1	no	—
320	C₃×C₈	—	2	2	no	—
321	C₃×C₈	—	2	2	no	—
322	C₂²×C₅	—	2	2	no	—
323	C₂²×C₅	—	2	2	no	—
324	C₂²×C₅	—	2	2	no	—
325	C₂²×C₅	—	4	1	no	—
326	C₂²×C₅	—	4	1	no	—
327	C₂²×C₅	—	4	1	no	—
328	C₂²×C₅	—	4	1	no	—
329	C₂²×C₅	#882	1	1	yes	characteristic
330	C₂²×C₅	#886	1	1	yes	characteristic
331	C₂²×C₅	#904	1	1	yes	characteristic
332	C₂²×C₅	#904	1	1	yes	characteristic
333	C₂²×C₅	#908	1	1	yes	characteristic
334	C₂²×C₅	#909	1	1	yes	characteristic
335	C₂²×C₅	C₂×C₄⋊Dic₃	1	1	yes	characteristic
336	C₄×C₅	—	2	2	no	—
337	C₄×C₅	—	12	2	no	—
338	C₄×C₅	—	12	2	no	—
339	C₄×C₅	—	24	1	no	—
340	C₄×C₅	—	24	1	no	—
341	C₄×C₅	#878	1	1	yes	characteristic
342	C₄×C₅	#878	1	1	yes	characteristic
343	C₄×C₅	D₄×Dic₃	1	1	yes	characteristic
344	C₄×C₅	D₄×Dic₃	1	1	yes	characteristic
345	C₂⁴	C₅×D₁₂	1	1	yes	characteristic
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	6	1	no	—
351	C₂²×C₄	—	6	1	no	—
352	C₂²×C₄	—	6	1	no	—
353	C₂²×C₄	—	6	1	no	—
354	C₂²×C₄	C₅×Dic₆	1	2	yes	—
355	C₂²×C₄	C₅×D₁₂	1	1	yes	characteristic
356	C₂²×C₄	C₂×C₅×Dic₃	1	2	yes	—
357	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	2	1	no	—
362	C₂×C₈	C₂×C₅×Dic₃	1	2	yes	—
363	C₂×C₈	C₂×C₅×Dic₃	1	2	yes	—
364	C₄⋊C₄	—	3	2	no	—
365	C₄⋊C₄	—	3	2	no	—
366	C₄⋊C₄	—	6	1	no	—
367	C₄⋊C₄	—	6	1	no	—
368	C₄⋊C₄	—	6	1	no	—
369	C₄⋊C₄	—	6	1	no	—
370	C₄⋊C₄	—	6	1	no	—
371	C₄⋊C₄	—	6	1	no	—
372	C₂²⋊C₄	—	6	4	no	—
373	C₂²⋊C₄	—	12	2	no	—
374	C₄²	—	6	4	no	—
375	C₃×C₅	#1854	1	1	yes	characteristic, complemented, Hall
376	C₂²×C₃	—	2	2	no	—
377	C₂²×C₃	—	2	2	no	—
378	C₂²×C₃	—	2	2	no	—
379	C₂²×C₃	—	4	1	no	—
380	C₂²×C₃	—	4	1	no	—
381	C₂²×C₃	—	4	1	no	—
382	C₂²×C₃	—	4	1	no	—
383	C₂²×C₃	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
384	C₂²×C₃	C₅×#120	1	1	yes	characteristic
385	C₂²×C₃	C₅×#123	1	1	yes	characteristic
386	C₂²×C₃	C₅×#135	1	1	yes	characteristic
387	C₂²×C₃	C₅×#135	1	1	yes	characteristic
388	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
389	C₂²×C₃	C₅×#137	1	1	yes	characteristic
390	C₃×C₄	—	2	2	no	—
391	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
392	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
393	C₃×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
394	C₃×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
395	Dic₃	—	4	2	no	—
396	Dic₃	—	4	2	no	—
397	Dic₃	—	8	1	no	—
398	Dic₃	—	8	1	no	—
399	C₂×C₅	—	4	2	no	—
400	C₂×C₅	#4723	1	1	yes	characteristic
401	C₂×C₅	#4733	1	1	yes	characteristic
402	C₂×C₅	#4734	1	1	yes	characteristic
403	C₂×C₅	#4737	1	1	yes	characteristic
404	C₂×C₅	#4950	1	1	yes	characteristic
405	C₂×C₅	#5106	1	1	yes	characteristic
406	C₂×C₅	#5121	1	1	yes	characteristic
407	C₂³	—	2	1	no	—
408	C₂³	—	2	1	no	—
409	C₂³	—	2	1	no	—
410	C₂³	—	2	1	no	—
411	C₂³	—	2	1	no	—
412	C₂³	—	2	1	no	—
413	C₂³	C₅×C₄⋊Dic₃	1	2	yes	—
414	C₂³	C₂×C₅×D₁₂	1	1	yes	characteristic
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	6	2	no	—
422	C₂×C₄	—	6	2	no	—
423	C₂×C₄	—	12	1	no	—
424	C₂×C₄	—	12	1	no	—
425	C₂×C₄	—	12	1	no	—
426	C₂×C₄	—	12	1	no	—
427	C₂×C₄	—	12	1	no	—
428	C₂×C₄	—	12	1	no	—
429	C₂×C₄	—	12	1	no	—
430	C₂×C₄	—	12	1	no	—
431	C₂×C₄	—	12	1	no	—
432	C₂×C₄	—	12	1	no	—
433	C₂×C₄	C₅×C₄⋊Dic₃	1	2	yes	—
434	C₂×C₄	C₂×C₅×Dic₆	1	1	yes	characteristic
435	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
436	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
437	C₂×C₄	C₅×#237	1	1	yes	characteristic
438	C₂×C₄	C₅×#237	1	1	yes	characteristic
439	C₂×C₄	C₂²×C₅×Dic₃	1	1	yes	characteristic
440	C₈	—	2	2	no	—
441	C₈	—	2	2	no	—
442	C₂×C₃	—	4	2	no	—
443	C₂×C₃	C₅×#385	1	1	yes	characteristic
444	C₂×C₃	C₅×#427	1	1	yes	characteristic
445	C₂×C₃	C₅×#428	1	1	yes	characteristic
446	C₂×C₃	C₅×#449	1	1	yes	characteristic
447	C₂×C₃	C₅×#452	1	1	yes	characteristic
448	C₂×C₃	C₅×#482	1	1	yes	characteristic
449	C₂×C₃	C₅×#485	1	1	yes	characteristic
450	C₅	#69929	1	1	yes	characteristic, direct product factor, Sylow
451	C₂²	—	2	2	no	—
452	C₂²	—	2	2	no	—
453	C₂²	—	2	2	no	—
454	C₂²	—	4	1	no	—
455	C₂²	—	4	1	no	—
456	C₂²	—	4	1	no	—
457	C₂²	—	4	1	no	—
458	C₂²	C₅×#882	1	1	yes	characteristic
459	C₂²	C₅×#886	1	1	yes	characteristic
460	C₂²	C₅×#904	1	1	yes	characteristic
461	C₂²	C₅×#904	1	1	yes	characteristic
462	C₂²	C₅×#908	1	1	yes	characteristic
463	C₂²	C₅×#909	1	1	yes	characteristic
464	C₂²	C₂×C₅×C₄⋊Dic₃	1	1	yes	characteristic
465	C₄	—	2	2	no	—
466	C₄	—	12	2	no	—
467	C₄	—	12	2	no	—
468	C₄	—	24	1	no	—
469	C₄	—	24	1	no	—
470	C₄	C₅×#878	1	1	yes	characteristic
471	C₄	C₅×#878	1	1	yes	characteristic
472	C₄	C₅×D₄×Dic₃	1	1	yes	characteristic
473	C₄	C₅×D₄×Dic₃	1	1	yes	characteristic
474	C₃	C₅×#1854	1	1	yes	characteristic, complemented, Sylow
475	C₂	—	4	2	no	—
476	C₂	C₅×#4723	1	1	yes	characteristic
477	C₂	C₅×#4733	1	1	yes	characteristic
478	C₂	C₅×#4734	1	1	yes	characteristic
479	C₂	C₅×#4737	1	1	yes	characteristic
480	C₂	C₅×#4950	1	1	yes	characteristic
481	C₂	C₅×#5106	1	1	yes	characteristic
482	C₂	C₅×#5121	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂×D₁₂
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₂×C₃×C₅×C₂²⋊C₈	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂⁴×C₃×C₅	D₄
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₂×C₅×C₂²⋊C₈	D₃
hypocenter	C₃	C₅×#1854
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂³×C₄×C₅ ◁ C₂×C₅×C₂²⋊C₈

Complements

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

N	H ≅ G/N	type
4. C₂×C₅×#818	C₂	semidirect
5. C₂×C₅×#817	C₂	semidirect
6. C₅×#4551	C₂	semidirect
7. C₅×#4551	C₂	semidirect
21. C₃×C₅×C₂²⋊C₈	C₄	semidirect
25. #69929	C₅	direct (N × H)
66. C₂×#818	C₂×C₅	semidirect
67. C₂×#817	C₂×C₅	semidirect
68. #4551	C₂×C₅	semidirect
69. #4551	C₂×C₅	semidirect
84. C₅×C₂²⋊C₈	Dic₃	semidirect
134. C₃×C₂²⋊C₈	C₄×C₅	semidirect
277. C₂²⋊C₈	C₅×Dic₃	semidirect
375. C₃×C₅	#1854	semidirect
450. C₅	#69929	direct (N × H)
474. C₃	C₅×#1854	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#926	2
C₂×C₃×C₅×C₂²⋊C₈	2
C₅×#5212	2
C₂×C₅×#818	2
C₂×C₅×#817	2
C₅×#4551	2
C₅×#1854	3
#69929	5

Subgroups — C5×#69929 #14299451

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#69929 #14299451