Subgroups — C₅×#69818 #14304699

Order 1920.

568 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#97	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#821	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#821	C₂	1	1	yes	maximal, characteristic
4	C₅×#4939	C₂	1	1	yes	maximal, characteristic
5	C₅×#4928	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×#1936	—	3	1	no	maximal, Hall
9	C₂²×C₅×D₁₂	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×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
13	C₂×C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
14	C₂×C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
15	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
16	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
17	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
18	C₂×C₅×Dic₃⋊C₄	—	2	1	no	—
19	C₃×C₅×#97	—	2	2	no	—
20	C₅×C₃⋊#95	—	2	1	no	—
21	C₅×#821	—	2	2	no	—
22	C₅×#821	C₄	1	4	yes	complemented
23	#69818	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
24	C₂×C₅×#102	—	3	1	no	—
25	C₂×C₅×#102	—	3	1	no	—
26	C₂×C₅×#97	D₃	1	1	yes	characteristic, complemented
27	C₅×#390	—	3	1	no	—
28	C₅×#389	—	3	1	no	—
29	C₅×#340	—	3	1	no	—
30	C₅×#340	—	3	1	no	—
31	C₂³×C₅×D₃	—	2	1	no	—
32	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
33	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
34	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
35	C₂²×C₅×Dic₃	—	2	1	no	—
36	C₂²×C₅×Dic₃	—	2	1	no	—
37	C₂²×C₅×Dic₃	—	2	1	no	—
38	C₂×C₅×D₁₂	—	2	1	no	—
39	C₂×C₅×D₁₂	—	2	1	no	—
40	C₂×C₅×D₁₂	—	2	1	no	—
41	C₂×C₅×D₁₂	—	2	1	no	—
42	C₂×C₅×D₁₂	—	2	1	no	—
43	C₂×C₅×D₁₂	C₂×C₄	1	2	yes	—
44	C₂×C₃×C₅×C₈	—	2	1	no	—
45	C₂×C₃×C₅×C₈	—	2	1	no	—
46	C₂×C₃×C₅×C₈	—	2	1	no	—
47	C₂×C₃×C₅×C₈	—	2	1	no	—
48	C₂×C₃×C₅×C₈	C₂×C₄	1	2	yes	—
49	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
50	C₃×C₄²×C₅	—	2	1	no	—
51	C₃×C₄²×C₅	—	2	1	no	—
52	C₅×(C₂×D₃)⋊C₄	—	4	2	no	—
53	C₅×(C₂×D₃)⋊C₄	—	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	C₂×C₄	1	2	yes	—
60	C₅×Dic₃⋊C₄	—	4	2	no	—
61	C₂×C₃×#97	C₂×C₅	1	1	yes	characteristic, complemented
62	C₂×#821	C₂×C₅	1	1	yes	characteristic
63	C₂×#821	C₂×C₅	1	1	yes	characteristic
64	#4939	C₂×C₅	1	1	yes	characteristic
65	#4928	C₂×C₅	1	1	yes	characteristic, complemented
66	#4551	C₂×C₅	1	1	yes	characteristic, complemented
67	#4551	C₂×C₅	1	1	yes	characteristic, complemented
68	C₂²×C₅×D₄	—	3	1	no	—
69	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
70	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
71	C₂×C₅×C₄⋊C₄	—	3	1	no	—
72	C₂×C₅×C₄⋊C₄	—	3	1	no	—
73	C₂×C₅×C₄⋊C₄	—	3	1	no	—
74	C₂×C₅×C₄⋊C₄	—	6	1	no	—
75	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
76	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
77	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
78	C₅×#102	—	3	4	no	—
79	C₅×#102	—	6	2	no	—
80	C₅×#97	—	2	2	no	—
81	C₅×#95	—	6	1	no	—
82	#1936	—	3	1	no	Sylow
83	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₅×D₃	—	2	2	no	—
85	C₂²×C₅×D₃	—	4	1	no	—
86	C₂²×C₅×D₃	—	4	1	no	—
87	C₂²×C₅×D₃	—	4	1	no	—
88	C₂²×C₅×D₃	—	4	1	no	—
89	C₂²×C₅×D₃	—	4	1	no	—
90	C₂²×C₅×D₃	—	4	1	no	—
91	C₂×C₃×C₄×C₅	—	2	1	no	—
92	C₂×C₃×C₄×C₅	—	2	1	no	—
93	C₂×C₃×C₄×C₅	—	2	1	no	—
94	C₂×C₃×C₄×C₅	—	2	1	no	—
95	C₂×C₃×C₄×C₅	—	2	1	no	—
96	C₂×C₃×C₄×C₅	—	2	1	no	—
97	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
99	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
100	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
101	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
102	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
103	C₂×C₅×Dic₃	—	2	2	no	—
104	C₂×C₅×Dic₃	—	4	1	no	—
105	C₂×C₅×Dic₃	—	4	1	no	—
106	C₂×C₅×Dic₃	—	4	1	no	—
107	C₂×C₅×Dic₃	—	4	1	no	—
108	C₂×C₅×Dic₃	—	4	1	no	—
109	C₂×C₅×Dic₃	—	4	1	no	—
110	C₂×C₅×Dic₃	—	4	1	no	—
111	C₂×C₅×Dic₃	—	4	1	no	—
112	C₅×D₁₂	—	2	2	no	—
113	C₅×D₁₂	—	2	2	no	—
114	C₅×D₁₂	—	4	1	no	—
115	C₅×D₁₂	—	4	1	no	—
116	C₃×C₅×C₈	—	2	2	no	—
117	C₃×C₅×C₈	—	2	2	no	—
118	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
119	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
120	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
121	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
122	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
123	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
124	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
125	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
126	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
127	C₂×Dic₃⋊C₄	—	2	1	no	—
128	C₃×#97	—	2	2	no	—
129	C₃⋊#95	—	2	1	no	—
130	#821	—	2	2	no	—
131	#821	C₄×C₅	1	4	yes	complemented
132	C₂⁴×C₅	—	6	1	no	—
133	C₂×C₅×D₄	—	3	2	no	—
134	C₂×C₅×D₄	—	6	1	no	—
135	C₂×C₅×D₄	—	6	1	no	—
136	C₂×C₅×D₄	—	6	1	no	—
137	C₂×C₅×D₄	—	6	1	no	—
138	C₂×C₅×D₄	—	6	1	no	—
139	C₂²×C₄×C₅	—	6	1	no	—
140	C₂²×C₄×C₅	—	6	1	no	—
141	C₂²×C₄×C₅	—	6	1	no	—
142	C₂²×C₄×C₅	D₁₂	1	1	yes	characteristic
143	C₂²×C₄×C₅	D₁₂	1	1	yes	characteristic
144	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
145	C₂×C₅×C₈	—	2	1	no	—
146	C₂×C₅×C₈	—	2	1	no	—
147	C₂×C₅×C₈	—	2	1	no	—
148	C₂×C₅×C₈	—	2	1	no	—
149	C₂×C₅×C₈	C₄×D₃	1	2	yes	—
150	C₂×C₅×C₈	#67	1	2	yes	—
151	C₅×C₄⋊C₄	—	3	2	no	—
152	C₅×C₄⋊C₄	—	6	1	no	—
153	C₅×C₄⋊C₄	—	6	1	no	—
154	C₅×C₄⋊C₄	—	6	1	no	—
155	C₅×C₄⋊C₄	—	6	1	no	—
156	C₅×C₄⋊C₄	—	6	1	no	—
157	C₅×C₄⋊C₄	—	12	2	no	—
158	C₅×C₂²⋊C₄	—	12	2	no	—
159	C₅×C₂²⋊C₄	—	12	2	no	—
160	C₄²×C₅	—	2	1	no	—
161	C₄²×C₅	—	2	1	no	—
162	C₂×#102	—	3	1	no	—
163	C₂×#102	—	3	1	no	—
164	C₂×#97	C₅×D₃	1	1	yes	characteristic, complemented
165	#390	—	3	1	no	—
166	#389	—	3	1	no	—
167	#340	—	3	1	no	—
168	#340	—	3	1	no	—
169	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
170	C₂²×C₃×C₅	#121	1	1	yes	characteristic
171	C₂²×C₃×C₅	#124	1	1	yes	characteristic
172	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
173	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
174	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
175	C₂²×C₃×C₅	#137	1	1	yes	characteristic
176	C₂×C₅×D₃	—	4	2	no	—
177	C₂×C₅×D₃	—	4	2	no	—
178	C₂×C₅×D₃	—	4	2	no	—
179	C₂×C₅×D₃	—	8	1	no	—
180	C₂×C₅×D₃	—	8	1	no	—
181	C₂×C₅×D₃	—	8	1	no	—
182	C₂×C₅×D₃	—	8	1	no	—
183	C₃×C₄×C₅	—	4	1	no	—
184	C₃×C₄×C₅	—	4	1	no	—
185	C₃×C₄×C₅	#117	1	1	yes	characteristic
186	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
187	C₃×C₄×C₅	#123	1	1	yes	characteristic
188	C₃×C₄×C₅	#126	1	1	yes	characteristic
189	C₅×Dic₃	—	4	2	no	—
190	C₅×Dic₃	—	8	1	no	—
191	C₅×Dic₃	—	8	1	no	—
192	C₂³×D₃	—	2	1	no	—
193	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
194	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
195	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
196	C₂²×Dic₃	—	2	1	no	—
197	C₂²×Dic₃	—	2	1	no	—
198	C₂²×Dic₃	—	2	1	no	—
199	C₂×D₁₂	—	2	1	no	—
200	C₂×D₁₂	—	2	1	no	—
201	C₂×D₁₂	—	2	1	no	—
202	C₂×D₁₂	—	2	1	no	—
203	C₂×D₁₂	—	2	1	no	—
204	C₂×D₁₂	C₂×C₄×C₅	1	2	yes	—
205	C₂×C₃×C₈	—	2	1	no	—
206	C₂×C₃×C₈	—	2	1	no	—
207	C₂×C₃×C₈	—	2	1	no	—
208	C₂×C₃×C₈	—	2	1	no	—
209	C₂×C₃×C₈	C₂×C₄×C₅	1	2	yes	—
210	C₂×C₃×C₈	C₅×D₄	1	2	yes	—
211	C₃×C₄²	—	2	1	no	—
212	C₃×C₄²	—	2	1	no	—
213	(C₂×D₃)⋊C₄	—	4	2	no	—
214	(C₂×D₃)⋊C₄	—	4	2	no	—
215	C₄⋊Dic₃	—	2	1	no	—
216	C₄⋊Dic₃	—	2	1	no	—
217	C₄⋊Dic₃	—	2	1	no	—
218	C₄⋊Dic₃	—	2	1	no	—
219	C₄⋊Dic₃	—	2	1	no	—
220	C₄⋊Dic₃	C₂×C₄×C₅	1	2	yes	—
221	Dic₃⋊C₄	—	4	2	no	—
222	C₂³×C₅	—	6	2	no	—
223	C₂³×C₅	—	12	1	no	—
224	C₂³×C₅	—	12	1	no	—
225	C₂³×C₅	—	12	1	no	—
226	C₂³×C₅	—	12	1	no	—
227	C₂³×C₅	—	12	1	no	—
228	C₂³×C₅	—	12	1	no	—
229	C₂³×C₅	C₂×D₁₂	1	1	yes	characteristic
230	C₅×D₄	—	6	2	no	—
231	C₅×D₄	—	6	2	no	—
232	C₅×D₄	—	12	1	no	—
233	C₅×D₄	—	12	1	no	—
234	C₂×C₄×C₅	—	2	1	no	—
235	C₂×C₄×C₅	—	2	1	no	—
236	C₂×C₄×C₅	—	2	1	no	—
237	C₂×C₄×C₅	—	2	1	no	—
238	C₂×C₄×C₅	—	2	1	no	—
239	C₂×C₄×C₅	—	2	1	no	—
240	C₂×C₄×C₅	—	6	2	no	—
241	C₂×C₄×C₅	—	12	1	no	—
242	C₂×C₄×C₅	—	12	1	no	—
243	C₂×C₄×C₅	—	12	1	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	C₂×C₄×D₃	1	1	yes	characteristic
250	C₂×C₄×C₅	#235	1	1	yes	characteristic
251	C₂×C₄×C₅	#235	1	1	yes	characteristic
252	C₂×C₄×C₅	#235	1	1	yes	characteristic
253	C₂×C₄×C₅	#235	1	1	yes	characteristic
254	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
255	C₅×C₈	—	2	2	no	—
256	C₅×C₈	—	2	2	no	—
257	C₂²×D₄	—	3	1	no	—
258	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
259	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
260	C₂×C₄⋊C₄	—	3	1	no	—
261	C₂×C₄⋊C₄	—	3	1	no	—
262	C₂×C₄⋊C₄	—	3	1	no	—
263	C₂×C₄⋊C₄	—	6	1	no	—
264	C₂×C₂²⋊C₄	—	6	1	no	—
265	C₂×C₂²⋊C₄	—	6	1	no	—
266	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
267	#102	—	3	4	no	—
268	#102	—	6	2	no	—
269	#97	—	2	2	no	—
270	#95	—	6	1	no	—
271	C₂×C₃×C₅	#388	1	1	yes	characteristic
272	C₂×C₃×C₅	#440	1	1	yes	characteristic
273	C₂×C₃×C₅	#442	1	1	yes	characteristic
274	C₂×C₃×C₅	#468	1	1	yes	characteristic
275	C₂×C₃×C₅	#469	1	1	yes	characteristic
276	C₂×C₃×C₅	#489	1	1	yes	characteristic
277	C₂×C₃×C₅	#490	1	1	yes	characteristic
278	C₅×D₃	—	8	2	no	—
279	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
280	C₂²×D₃	—	2	2	no	—
281	C₂²×D₃	—	4	1	no	—
282	C₂²×D₃	—	4	1	no	—
283	C₂²×D₃	—	4	1	no	—
284	C₂²×D₃	—	4	1	no	—
285	C₂²×D₃	—	4	1	no	—
286	C₂²×D₃	—	4	1	no	—
287	C₂×C₃×C₄	—	2	1	no	—
288	C₂×C₃×C₄	—	2	1	no	—
289	C₂×C₃×C₄	—	2	1	no	—
290	C₂×C₃×C₄	—	2	1	no	—
291	C₂×C₃×C₄	—	2	1	no	—
292	C₂×C₃×C₄	—	2	1	no	—
293	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
294	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
295	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
296	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
297	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
298	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
299	C₂×Dic₃	—	2	2	no	—
300	C₂×Dic₃	—	4	1	no	—
301	C₂×Dic₃	—	4	1	no	—
302	C₂×Dic₃	—	4	1	no	—
303	C₂×Dic₃	—	4	1	no	—
304	C₂×Dic₃	—	4	1	no	—
305	C₂×Dic₃	—	4	1	no	—
306	C₂×Dic₃	—	4	1	no	—
307	C₂×Dic₃	—	4	1	no	—
308	D₁₂	—	2	2	no	—
309	D₁₂	—	2	2	no	—
310	D₁₂	—	4	1	no	—
311	D₁₂	—	4	1	no	—
312	C₃×C₈	—	2	2	no	—
313	C₃×C₈	—	2	2	no	—
314	C₂²×C₅	—	12	2	no	—
315	C₂²×C₅	—	12	2	no	—
316	C₂²×C₅	—	12	2	no	—
317	C₂²×C₅	—	24	1	no	—
318	C₂²×C₅	—	24	1	no	—
319	C₂²×C₅	—	24	1	no	—
320	C₂²×C₅	—	24	1	no	—
321	C₂²×C₅	C₄×D₁₂	1	1	yes	characteristic
322	C₂²×C₅	#875	1	1	yes	characteristic
323	C₂²×C₅	#908	1	1	yes	characteristic
324	C₂²×C₅	#908	1	1	yes	characteristic
325	C₂²×C₅	#908	1	1	yes	characteristic
326	C₂²×C₅	#909	1	1	yes	characteristic
327	C₂²×C₅	#930	1	1	yes	characteristic
328	C₄×C₅	—	4	1	no	—
329	C₄×C₅	—	4	1	no	—
330	C₄×C₅	—	12	2	no	—
331	C₄×C₅	—	24	1	no	—
332	C₄×C₅	—	24	1	no	—
333	C₄×C₅	#872	1	1	yes	characteristic
334	C₄×C₅	#876	1	1	yes	characteristic
335	C₄×C₅	C₄×#67	1	1	yes	characteristic
336	C₄×C₅	#929	1	1	yes	characteristic
337	C₂⁴	—	6	1	no	—
338	C₂×D₄	—	3	2	no	—
339	C₂×D₄	—	6	1	no	—
340	C₂×D₄	—	6	1	no	—
341	C₂×D₄	—	6	1	no	—
342	C₂×D₄	—	6	1	no	—
343	C₂×D₄	—	6	1	no	—
344	C₂²×C₄	—	6	1	no	—
345	C₂²×C₄	—	6	1	no	—
346	C₂²×C₄	—	6	1	no	—
347	C₂²×C₄	C₅×D₁₂	1	1	yes	characteristic
348	C₂²×C₄	C₅×D₁₂	1	1	yes	characteristic
349	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	C₄×C₅×D₃	1	2	yes	—
355	C₂×C₈	C₅×#67	1	2	yes	—
356	C₄⋊C₄	—	3	2	no	—
357	C₄⋊C₄	—	6	1	no	—
358	C₄⋊C₄	—	6	1	no	—
359	C₄⋊C₄	—	6	1	no	—
360	C₄⋊C₄	—	6	1	no	—
361	C₄⋊C₄	—	6	1	no	—
362	C₄⋊C₄	—	12	2	no	—
363	C₂²⋊C₄	—	12	2	no	—
364	C₂²⋊C₄	—	12	2	no	—
365	C₄²	—	2	1	no	—
366	C₄²	—	2	1	no	—
367	C₃×C₅	#1936	1	1	yes	characteristic, complemented, Hall
368	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
369	C₂²×C₃	C₅×#121	1	1	yes	characteristic
370	C₂²×C₃	C₅×#124	1	1	yes	characteristic
371	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
372	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
373	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
374	C₂²×C₃	C₅×#137	1	1	yes	characteristic
375	C₂×D₃	—	4	2	no	—
376	C₂×D₃	—	4	2	no	—
377	C₂×D₃	—	4	2	no	—
378	C₂×D₃	—	8	1	no	—
379	C₂×D₃	—	8	1	no	—
380	C₂×D₃	—	8	1	no	—
381	C₂×D₃	—	8	1	no	—
382	C₃×C₄	—	4	1	no	—
383	C₃×C₄	—	4	1	no	—
384	C₃×C₄	C₅×#117	1	1	yes	characteristic
385	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
386	C₃×C₄	C₅×#123	1	1	yes	characteristic
387	C₃×C₄	C₅×#126	1	1	yes	characteristic
388	Dic₃	—	4	2	no	—
389	Dic₃	—	8	1	no	—
390	Dic₃	—	8	1	no	—
391	C₂×C₅	—	24	2	no	—
392	C₂×C₅	#4710	1	1	yes	characteristic
393	C₂×C₅	#4711	1	1	yes	characteristic
394	C₂×C₅	#4713	1	1	yes	characteristic
395	C₂×C₅	#4714	1	1	yes	characteristic
396	C₂×C₅	#4940	1	1	yes	characteristic
397	C₂×C₅	#5134	1	1	yes	characteristic
398	C₂×C₅	#5135	1	1	yes	characteristic
399	C₂³	—	6	2	no	—
400	C₂³	—	12	1	no	—
401	C₂³	—	12	1	no	—
402	C₂³	—	12	1	no	—
403	C₂³	—	12	1	no	—
404	C₂³	—	12	1	no	—
405	C₂³	—	12	1	no	—
406	C₂³	C₂×C₅×D₁₂	1	1	yes	characteristic
407	D₄	—	6	2	no	—
408	D₄	—	6	2	no	—
409	D₄	—	12	1	no	—
410	D₄	—	12	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	6	2	no	—
418	C₂×C₄	—	12	1	no	—
419	C₂×C₄	—	12	1	no	—
420	C₂×C₄	—	12	1	no	—
421	C₂×C₄	—	12	1	no	—
422	C₂×C₄	—	12	1	no	—
423	C₂×C₄	—	12	1	no	—
424	C₂×C₄	—	12	1	no	—
425	C₂×C₄	—	12	1	no	—
426	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
427	C₂×C₄	C₅×#235	1	1	yes	characteristic
428	C₂×C₄	C₅×#235	1	1	yes	characteristic
429	C₂×C₄	C₅×#235	1	1	yes	characteristic
430	C₂×C₄	C₅×#235	1	1	yes	characteristic
431	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
432	C₈	—	2	2	no	—
433	C₈	—	2	2	no	—
434	C₂×C₃	C₅×#388	1	1	yes	characteristic
435	C₂×C₃	C₅×#440	1	1	yes	characteristic
436	C₂×C₃	C₅×#442	1	1	yes	characteristic
437	C₂×C₃	C₅×#468	1	1	yes	characteristic
438	C₂×C₃	C₅×#469	1	1	yes	characteristic
439	C₂×C₃	C₅×#489	1	1	yes	characteristic
440	C₂×C₃	C₅×#490	1	1	yes	characteristic
441	D₃	—	8	2	no	—
442	C₅	#69818	1	1	yes	characteristic, direct product factor, Sylow
443	C₂²	—	12	2	no	—
444	C₂²	—	12	2	no	—
445	C₂²	—	12	2	no	—
446	C₂²	—	24	1	no	—
447	C₂²	—	24	1	no	—
448	C₂²	—	24	1	no	—
449	C₂²	—	24	1	no	—
450	C₂²	C₄×C₅×D₁₂	1	1	yes	characteristic
451	C₂²	C₅×#875	1	1	yes	characteristic
452	C₂²	C₅×#908	1	1	yes	characteristic
453	C₂²	C₅×#908	1	1	yes	characteristic
454	C₂²	C₅×#908	1	1	yes	characteristic
455	C₂²	C₅×#909	1	1	yes	characteristic
456	C₂²	C₅×#930	1	1	yes	characteristic
457	C₄	—	4	1	no	—
458	C₄	—	4	1	no	—
459	C₄	—	12	2	no	—
460	C₄	—	24	1	no	—
461	C₄	—	24	1	no	—
462	C₄	C₅×#872	1	1	yes	characteristic
463	C₄	C₅×#876	1	1	yes	characteristic
464	C₄	C₄×C₅×#67	1	1	yes	characteristic
465	C₄	C₅×#929	1	1	yes	characteristic
466	C₃	C₅×#1936	1	1	yes	characteristic, complemented, Sylow
467	C₂	—	24	2	no	—
468	C₂	C₅×#4710	1	1	yes	characteristic
469	C₂	C₅×#4711	1	1	yes	characteristic
470	C₂	C₅×#4713	1	1	yes	characteristic
471	C₂	C₅×#4714	1	1	yes	characteristic
472	C₂	C₅×#4940	1	1	yes	characteristic
473	C₂	C₅×#5134	1	1	yes	characteristic
474	C₂	C₅×#5135	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×#97	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂²×C₅×D₁₂	C₂²
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₂×C₅×#97	D₃
hypocenter	C₃	C₅×#1936
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₄²×C₅ ◁ C₂×C₅×#97

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#97	C₂	semidirect
5. C₅×#4928	C₂	semidirect
6. C₅×#4551	C₂	semidirect
7. C₅×#4551	C₂	semidirect
22. C₅×#821	C₄	semidirect
23. #69818	C₅	direct (N × H)
26. C₂×C₅×#97	D₃	semidirect
61. C₂×C₃×#97	C₂×C₅	semidirect
65. #4928	C₂×C₅	semidirect
66. #4551	C₂×C₅	semidirect
67. #4551	C₂×C₅	semidirect
131. #821	C₄×C₅	semidirect
164. C₂×#97	C₅×D₃	semidirect
367. C₃×C₅	#1936	semidirect
442. C₅	#69818	direct (N × H)
466. C₃	C₅×#1936	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×#97	2
C₂×C₅×#821	2
C₅×#4939	2
C₅×#4928	2
C₅×#4551	2
C₅×#1936	3
#69818	5

Subgroups — C5×#69818 #14304699

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#69818 #14304699