Subgroups — C₅×D₃×#400 #14332022

Order 1920.

1208 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×D₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#400	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4986	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4985	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×D₃×#95	C₂	1	1	yes	maximal, characteristic
7	C₅×D₃×#95	C₂	1	2	yes	maximal
8	C₅×D₃×#95	C₂	1	2	yes	maximal
9	C₅×#4660	C₂	1	2	yes	maximal, complemented
10	C₅×#4659	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4658	C₂	1	2	yes	maximal, complemented
12	C₂×C₅×#400	—	3	1	no	maximal, Hall
13	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
14	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
15	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
16	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
17	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
21	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
22	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
23	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
24	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
25	C₅×D₃×C₄⋊C₄	—	2	4	no	—
26	C₅×D₃×C₄⋊C₄	—	2	4	no	—
27	C₃×C₅×#95	C₂²	1	2	yes	—
28	C₃×C₅×#95	C₂²	1	1	yes	characteristic
29	C₃×C₅×#95	C₂²	1	2	yes	—
30	C₅×C₃⋊#95	C₂²	1	2	yes	—
31	C₅×C₃⋊#95	C₂²	1	2	yes	—
32	C₅×C₃⋊#95	C₂²	1	2	yes	—
33	C₅×C₃⋊#95	C₂²	1	2	yes	—
34	C₅×C₃⋊#95	C₂²	1	2	yes	—
35	C₅×C₃⋊#95	C₂²	1	2	yes	—
36	C₅×C₃⋊#95	C₂²	1	2	yes	—
37	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
38	D₃×#400	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
39	C₂²×C₅×C₄⋊C₄	—	3	1	no	—
40	C₂²×C₅×C₄⋊C₄	—	3	1	no	—
41	C₅×#400	—	3	2	no	—
42	C₅×#400	—	3	1	no	—
43	C₅×#400	—	3	2	no	—
44	C₅×#400	—	3	1	no	—
45	C₅×#400	—	3	1	no	—
46	C₅×#400	D₃	1	1	yes	characteristic, direct product factor
47	C₂×C₅×#95	—	3	2	no	—
48	C₂×C₅×#95	—	3	1	no	—
49	C₂×C₅×#95	—	3	2	no	—
50	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
51	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
52	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
53	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
54	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
55	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
56	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
57	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
58	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
59	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
60	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
61	C₂×C₄×C₅×D₃	—	2	2	no	—
62	C₂×C₄×C₅×D₃	—	2	2	no	—
63	C₂×C₄×C₅×D₃	—	2	4	no	—
64	C₂×C₄×C₅×D₃	—	2	2	no	—
65	C₂×C₄×C₅×D₃	—	2	4	no	—
66	C₂×C₄×C₅×D₃	—	2	4	no	—
67	C₂×C₄×C₅×D₃	—	2	8	no	—
68	C₂×C₄×C₅×D₃	—	2	4	no	—
69	C₂×C₄×C₅×D₃	—	2	4	no	—
70	C₂×C₄×C₅×D₃	—	2	4	no	—
71	C₂×C₄×C₅×D₃	D₄	1	4	yes	—
72	C₂×C₄×C₅×D₃	Q₈	1	4	yes	—
73	C₃×C₅×C₄⋊C₄	—	2	2	no	—
74	C₃×C₅×C₄⋊C₄	—	2	2	no	—
75	C₅×C₄⋊Dic₃	—	2	2	no	—
76	C₅×C₄⋊Dic₃	—	2	2	no	—
77	C₅×Dic₃⋊C₄	—	2	2	no	—
78	C₅×Dic₃⋊C₄	—	2	2	no	—
79	C₅×Dic₃⋊C₄	—	2	4	no	—
80	C₂×D₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
81	C₂×D₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
82	C₃×#400	C₂×C₅	1	1	yes	characteristic, complemented
83	#4986	C₂×C₅	1	1	yes	characteristic, complemented
84	#4985	C₂×C₅	1	1	yes	characteristic, complemented
85	D₃×#95	C₂×C₅	1	2	yes	—
86	D₃×#95	C₂×C₅	1	1	yes	characteristic
87	D₃×#95	C₂×C₅	1	2	yes	—
88	#4660	C₂×C₅	1	2	yes	complemented
89	#4659	C₂×C₅	1	1	yes	characteristic, complemented
90	#4658	C₂×C₅	1	2	yes	complemented
91	C₂³×C₄×C₅	—	3	1	no	—
92	C₂³×C₄×C₅	—	3	1	no	—
93	C₂³×C₄×C₅	—	3	2	no	—
94	C₂³×C₄×C₅	—	3	2	no	—
95	C₂³×C₄×C₅	—	3	1	no	—
96	C₂×C₅×C₄⋊C₄	—	3	1	no	—
97	C₂×C₅×C₄⋊C₄	—	3	2	no	—
98	C₂×C₅×C₄⋊C₄	—	3	1	no	—
99	C₂×C₅×C₄⋊C₄	—	3	1	no	—
100	C₂×C₅×C₄⋊C₄	—	3	1	no	—
101	C₂×C₅×C₄⋊C₄	—	6	4	no	—
102	C₂×C₅×C₄⋊C₄	—	6	4	no	—
103	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
104	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
105	C₅×#95	—	3	2	no	—
106	C₅×#95	—	3	2	no	—
107	C₅×#95	—	3	2	no	—
108	C₅×#95	—	3	2	no	—
109	C₅×#95	—	3	2	no	—
110	C₅×#95	—	3	2	no	—
111	C₅×#95	—	3	2	no	—
112	C₅×#95	—	3	1	no	—
113	C₅×#95	C₂×D₃	1	2	yes	—
114	C₅×#95	C₂×D₃	1	2	yes	—
115	C₅×#95	C₂×D₃	1	1	yes	characteristic
116	C₂×#400	—	3	1	no	Sylow
117	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
118	C₂²×C₅×D₃	C₂×D₄	1	2	yes	—
119	C₂²×C₅×D₃	C₂×Q₈	1	2	yes	—
120	C₂²×C₅×D₃	#41	1	2	yes	—
121	C₂²×C₅×D₃	#41	1	4	yes	—
122	C₂²×C₅×D₃	#41	1	4	yes	—
123	C₂×C₃×C₄×C₅	—	2	1	no	—
124	C₂×C₃×C₄×C₅	—	2	1	no	—
125	C₂×C₃×C₄×C₅	—	2	2	no	—
126	C₂×C₃×C₄×C₅	—	2	1	no	—
127	C₂×C₃×C₄×C₅	—	2	2	no	—
128	C₂×C₃×C₄×C₅	—	2	2	no	—
129	C₂×C₃×C₄×C₅	—	2	4	no	—
130	C₂×C₃×C₄×C₅	—	2	2	no	—
131	C₂×C₃×C₄×C₅	—	2	2	no	—
132	C₂×C₃×C₄×C₅	—	2	2	no	—
133	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
134	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
135	C₂×C₅×Dic₃	—	2	1	no	—
136	C₂×C₅×Dic₃	—	2	1	no	—
137	C₂×C₅×Dic₃	—	2	2	no	—
138	C₂×C₅×Dic₃	—	2	1	no	—
139	C₂×C₅×Dic₃	—	2	2	no	—
140	C₂×C₅×Dic₃	—	2	2	no	—
141	C₂×C₅×Dic₃	—	2	4	no	—
142	C₂×C₅×Dic₃	—	2	2	no	—
143	C₂×C₅×Dic₃	—	2	2	no	—
144	C₂×C₅×Dic₃	—	2	2	no	—
145	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
146	C₂×C₅×Dic₃	C₂×Q₈	1	2	yes	—
147	C₄×C₅×D₃	—	2	8	no	—
148	C₄×C₅×D₃	—	2	8	no	—
149	C₄×C₅×D₃	—	4	4	no	—
150	C₄×C₅×D₃	—	4	8	no	—
151	C₄×C₅×D₃	—	4	8	no	—
152	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
153	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
154	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
155	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
156	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
157	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
158	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
159	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
160	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
161	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
162	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
163	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
164	D₃×C₄⋊C₄	—	2	4	no	—
165	D₃×C₄⋊C₄	—	2	4	no	—
166	C₃×#95	C₂²×C₅	1	2	yes	—
167	C₃×#95	C₂²×C₅	1	1	yes	characteristic
168	C₃×#95	C₂²×C₅	1	2	yes	—
169	C₃⋊#95	C₂²×C₅	1	2	yes	—
170	C₃⋊#95	C₂²×C₅	1	2	yes	—
171	C₃⋊#95	C₂²×C₅	1	2	yes	—
172	C₃⋊#95	C₂²×C₅	1	2	yes	—
173	C₃⋊#95	C₂²×C₅	1	2	yes	—
174	C₃⋊#95	C₂²×C₅	1	2	yes	—
175	C₃⋊#95	C₂²×C₅	1	2	yes	—
176	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
177	C₂⁴×C₅	—	3	1	no	—
178	C₂²×C₄×C₅	—	3	1	no	—
179	C₂²×C₄×C₅	—	3	1	no	—
180	C₂²×C₄×C₅	—	3	4	no	—
181	C₂²×C₄×C₅	—	3	4	no	—
182	C₂²×C₄×C₅	—	3	1	no	—
183	C₂²×C₄×C₅	—	3	2	no	—
184	C₂²×C₄×C₅	—	3	2	no	—
185	C₂²×C₄×C₅	—	6	2	no	—
186	C₂²×C₄×C₅	—	6	2	no	—
187	C₂²×C₄×C₅	—	6	4	no	—
188	C₂²×C₄×C₅	—	6	2	no	—
189	C₂²×C₄×C₅	—	6	4	no	—
190	C₂²×C₄×C₅	—	6	4	no	—
191	C₂²×C₄×C₅	—	6	4	no	—
192	C₂²×C₄×C₅	—	6	4	no	—
193	C₂²×C₄×C₅	—	6	4	no	—
194	C₂²×C₄×C₅	—	6	8	no	—
195	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
196	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
197	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
198	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
199	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
200	C₅×C₄⋊C₄	—	2	2	no	—
201	C₅×C₄⋊C₄	—	2	2	no	—
202	C₅×C₄⋊C₄	—	6	2	no	—
203	C₅×C₄⋊C₄	—	6	4	no	—
204	C₅×C₄⋊C₄	—	6	2	no	—
205	C₅×C₄⋊C₄	—	6	2	no	—
206	C₅×C₄⋊C₄	—	6	2	no	—
207	C₂²×C₄⋊C₄	—	3	1	no	—
208	C₂²×C₄⋊C₄	—	3	1	no	—
209	#400	—	3	1	no	—
210	#400	—	3	1	no	—
211	#400	—	3	2	no	—
212	#400	—	3	1	no	—
213	#400	—	3	2	no	—
214	#400	C₅×D₃	1	1	yes	characteristic, direct product factor
215	C₂×#95	—	3	1	no	—
216	C₂×#95	—	3	2	no	—
217	C₂×#95	—	3	2	no	—
218	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
219	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
220	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
221	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
222	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
223	C₂×C₅×D₃	C₂²⋊Q₈	1	4	yes	—
224	C₂×C₅×D₃	#123	1	4	yes	—
225	C₂×C₅×D₃	#124	1	4	yes	—
226	C₂×C₅×D₃	#125	1	8	yes	—
227	C₂×C₅×D₃	#126	1	8	yes	—
228	C₃×C₄×C₅	—	2	2	no	—
229	C₃×C₄×C₅	—	2	2	no	—
230	C₃×C₄×C₅	—	4	1	no	—
231	C₃×C₄×C₅	—	4	2	no	—
232	C₃×C₄×C₅	—	4	2	no	—
233	C₅×Dic₃	—	2	2	no	—
234	C₅×Dic₃	—	2	2	no	—
235	C₅×Dic₃	—	4	1	no	—
236	C₅×Dic₃	—	4	2	no	—
237	C₅×Dic₃	—	4	2	no	—
238	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
239	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
240	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
241	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
242	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
243	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
244	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
245	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
246	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
247	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
248	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
249	C₂×C₄×D₃	—	2	2	no	—
250	C₂×C₄×D₃	—	2	2	no	—
251	C₂×C₄×D₃	—	2	4	no	—
252	C₂×C₄×D₃	—	2	2	no	—
253	C₂×C₄×D₃	—	2	4	no	—
254	C₂×C₄×D₃	—	2	4	no	—
255	C₂×C₄×D₃	—	2	8	no	—
256	C₂×C₄×D₃	—	2	4	no	—
257	C₂×C₄×D₃	—	2	4	no	—
258	C₂×C₄×D₃	—	2	4	no	—
259	C₂×C₄×D₃	C₅×D₄	1	4	yes	—
260	C₂×C₄×D₃	C₅×Q₈	1	4	yes	—
261	C₃×C₄⋊C₄	—	2	2	no	—
262	C₃×C₄⋊C₄	—	2	2	no	—
263	C₄⋊Dic₃	—	2	2	no	—
264	C₄⋊Dic₃	—	2	2	no	—
265	Dic₃⋊C₄	—	2	2	no	—
266	Dic₃⋊C₄	—	2	2	no	—
267	Dic₃⋊C₄	—	2	4	no	—
268	C₂³×C₅	—	3	2	no	—
269	C₂³×C₅	—	3	2	no	—
270	C₂³×C₅	—	3	4	no	—
271	C₂³×C₅	—	3	4	no	—
272	C₂³×C₅	—	3	2	no	—
273	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
274	C₂×C₄×C₅	—	2	1	no	—
275	C₂×C₄×C₅	—	2	2	no	—
276	C₂×C₄×C₅	—	2	1	no	—
277	C₂×C₄×C₅	—	2	1	no	—
278	C₂×C₄×C₅	—	2	2	no	—
279	C₂×C₄×C₅	—	2	2	no	—
280	C₂×C₄×C₅	—	2	4	no	—
281	C₂×C₄×C₅	—	2	2	no	—
282	C₂×C₄×C₅	—	2	2	no	—
283	C₂×C₄×C₅	—	2	2	no	—
284	C₂×C₄×C₅	—	3	2	no	—
285	C₂×C₄×C₅	—	3	2	no	—
286	C₂×C₄×C₅	—	6	8	no	—
287	C₂×C₄×C₅	—	6	8	no	—
288	C₂×C₄×C₅	—	6	1	no	—
289	C₂×C₄×C₅	—	6	2	no	—
290	C₂×C₄×C₅	—	6	1	no	—
291	C₂×C₄×C₅	—	6	1	no	—
292	C₂×C₄×C₅	—	6	2	no	—
293	C₂×C₄×C₅	—	6	2	no	—
294	C₂×C₄×C₅	—	6	4	no	—
295	C₂×C₄×C₅	—	6	2	no	—
296	C₂×C₄×C₅	—	6	2	no	—
297	C₂×C₄×C₅	—	6	2	no	—
298	C₂×C₄×C₅	—	12	4	no	—
299	C₂×C₄×C₅	—	12	8	no	—
300	C₂×C₄×C₅	—	12	8	no	—
301	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
302	C₂×C₄×C₅	D₃×Q₈	1	2	yes	—
303	C₂³×C₄	—	3	1	no	—
304	C₂³×C₄	—	3	1	no	—
305	C₂³×C₄	—	3	1	no	—
306	C₂³×C₄	—	3	2	no	—
307	C₂³×C₄	—	3	2	no	—
308	C₂×C₄⋊C₄	—	3	1	no	—
309	C₂×C₄⋊C₄	—	3	2	no	—
310	C₂×C₄⋊C₄	—	3	1	no	—
311	C₂×C₄⋊C₄	—	3	1	no	—
312	C₂×C₄⋊C₄	—	3	1	no	—
313	C₂×C₄⋊C₄	—	6	4	no	—
314	C₂×C₄⋊C₄	—	6	4	no	—
315	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
316	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
317	#95	—	3	2	no	—
318	#95	—	3	2	no	—
319	#95	—	3	2	no	—
320	#95	—	3	1	no	—
321	#95	—	3	2	no	—
322	#95	—	3	2	no	—
323	#95	—	3	2	no	—
324	#95	—	3	2	no	—
325	#95	C₂×C₅×D₃	1	1	yes	characteristic
326	#95	C₂×C₅×D₃	1	2	yes	—
327	#95	C₂×C₅×D₃	1	2	yes	—
328	C₂×C₃×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
329	C₂×C₃×C₅	C₂×#123	1	1	yes	characteristic
330	C₂×C₃×C₅	C₂×#124	1	1	yes	characteristic
331	C₂×C₃×C₅	C₂×#125	1	2	yes	—
332	C₂×C₃×C₅	C₂×#126	1	2	yes	—
333	C₅×D₃	#400	1	8	yes	direct product factor
334	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
335	C₂²×D₃	C₂×C₅×D₄	1	2	yes	—
336	C₂²×D₃	C₂×C₅×Q₈	1	2	yes	—
337	C₂²×D₃	C₅×#41	1	2	yes	—
338	C₂²×D₃	C₅×#41	1	4	yes	—
339	C₂²×D₃	C₅×#41	1	4	yes	—
340	C₂×C₃×C₄	—	2	1	no	—
341	C₂×C₃×C₄	—	2	1	no	—
342	C₂×C₃×C₄	—	2	2	no	—
343	C₂×C₃×C₄	—	2	1	no	—
344	C₂×C₃×C₄	—	2	2	no	—
345	C₂×C₃×C₄	—	2	2	no	—
346	C₂×C₃×C₄	—	2	4	no	—
347	C₂×C₃×C₄	—	2	2	no	—
348	C₂×C₃×C₄	—	2	2	no	—
349	C₂×C₃×C₄	—	2	2	no	—
350	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
351	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
352	C₂×Dic₃	—	2	1	no	—
353	C₂×Dic₃	—	2	1	no	—
354	C₂×Dic₃	—	2	2	no	—
355	C₂×Dic₃	—	2	1	no	—
356	C₂×Dic₃	—	2	2	no	—
357	C₂×Dic₃	—	2	2	no	—
358	C₂×Dic₃	—	2	4	no	—
359	C₂×Dic₃	—	2	2	no	—
360	C₂×Dic₃	—	2	2	no	—
361	C₂×Dic₃	—	2	2	no	—
362	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
363	C₂×Dic₃	C₂×C₅×Q₈	1	2	yes	—
364	C₄×D₃	—	2	8	no	—
365	C₄×D₃	—	2	8	no	—
366	C₄×D₃	—	4	4	no	—
367	C₄×D₃	—	4	8	no	—
368	C₄×D₃	—	4	8	no	—
369	C₂²×C₅	—	3	4	no	—
370	C₂²×C₅	—	3	4	no	—
371	C₂²×C₅	—	3	8	no	—
372	C₂²×C₅	—	3	8	no	—
373	C₂²×C₅	—	3	4	no	—
374	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
375	C₂²×C₅	C₂×D₃×Q₈	1	1	yes	characteristic
376	C₂²×C₅	D₃×#41	1	2	yes	—
377	C₂²×C₅	D₃×#41	1	2	yes	—
378	C₂²×C₅	D₃×#41	1	1	yes	characteristic
379	C₄×C₅	—	2	2	no	—
380	C₄×C₅	—	2	2	no	—
381	C₄×C₅	—	4	1	no	—
382	C₄×C₅	—	4	2	no	—
383	C₄×C₅	—	4	2	no	—
384	C₄×C₅	—	6	2	no	—
385	C₄×C₅	—	6	2	no	—
386	C₄×C₅	—	12	1	no	—
387	C₄×C₅	—	12	2	no	—
388	C₄×C₅	—	12	2	no	—
389	C₂⁴	—	3	1	no	—
390	C₂²×C₄	—	3	1	no	—
391	C₂²×C₄	—	3	1	no	—
392	C₂²×C₄	—	3	4	no	—
393	C₂²×C₄	—	3	4	no	—
394	C₂²×C₄	—	3	2	no	—
395	C₂²×C₄	—	3	1	no	—
396	C₂²×C₄	—	3	2	no	—
397	C₂²×C₄	—	6	2	no	—
398	C₂²×C₄	—	6	4	no	—
399	C₂²×C₄	—	6	2	no	—
400	C₂²×C₄	—	6	2	no	—
401	C₂²×C₄	—	6	4	no	—
402	C₂²×C₄	—	6	4	no	—
403	C₂²×C₄	—	6	8	no	—
404	C₂²×C₄	—	6	4	no	—
405	C₂²×C₄	—	6	4	no	—
406	C₂²×C₄	—	6	4	no	—
407	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
408	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
409	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
410	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
411	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	6	2	no	—
415	C₄⋊C₄	—	6	4	no	—
416	C₄⋊C₄	—	6	2	no	—
417	C₄⋊C₄	—	6	2	no	—
418	C₄⋊C₄	—	6	2	no	—
419	C₃×C₅	C₂×#400	1	1	yes	characteristic, complemented, Hall
420	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
421	C₂²×C₃	C₂²×C₅×Q₈	1	1	yes	characteristic
422	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
423	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
424	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
425	C₂×D₃	C₅×C₂²⋊Q₈	1	4	yes	—
426	C₂×D₃	C₅×#123	1	4	yes	—
427	C₂×D₃	C₅×#124	1	4	yes	—
428	C₂×D₃	C₅×#125	1	8	yes	—
429	C₂×D₃	C₅×#126	1	8	yes	—
430	C₃×C₄	—	2	2	no	—
431	C₃×C₄	—	2	2	no	—
432	C₃×C₄	—	4	1	no	—
433	C₃×C₄	—	4	2	no	—
434	C₃×C₄	—	4	2	no	—
435	Dic₃	—	2	2	no	—
436	Dic₃	—	2	2	no	—
437	Dic₃	—	4	1	no	—
438	Dic₃	—	4	2	no	—
439	Dic₃	—	4	2	no	—
440	C₂×C₅	—	3	8	no	—
441	C₂×C₅	D₃×C₂²⋊Q₈	1	1	yes	characteristic
442	C₂×C₅	D₃×#123	1	1	yes	characteristic
443	C₂×C₅	D₃×#124	1	1	yes	characteristic
444	C₂×C₅	D₃×#125	1	2	yes	—
445	C₂×C₅	D₃×#126	1	2	yes	—
446	C₂³	—	3	2	no	—
447	C₂³	—	3	2	no	—
448	C₂³	—	3	4	no	—
449	C₂³	—	3	4	no	—
450	C₂³	—	3	2	no	—
451	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	4	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	3	2	no	—
463	C₂×C₄	—	3	2	no	—
464	C₂×C₄	—	6	8	no	—
465	C₂×C₄	—	6	8	no	—
466	C₂×C₄	—	6	1	no	—
467	C₂×C₄	—	6	2	no	—
468	C₂×C₄	—	6	1	no	—
469	C₂×C₄	—	6	1	no	—
470	C₂×C₄	—	6	2	no	—
471	C₂×C₄	—	6	2	no	—
472	C₂×C₄	—	6	4	no	—
473	C₂×C₄	—	6	2	no	—
474	C₂×C₄	—	6	2	no	—
475	C₂×C₄	—	6	2	no	—
476	C₂×C₄	—	12	4	no	—
477	C₂×C₄	—	12	8	no	—
478	C₂×C₄	—	12	8	no	—
479	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
480	C₂×C₄	C₅×D₃×Q₈	1	2	yes	—
481	C₂×C₃	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
482	C₂×C₃	C₂×C₅×#123	1	1	yes	characteristic
483	C₂×C₃	C₂×C₅×#124	1	1	yes	characteristic
484	C₂×C₃	C₂×C₅×#125	1	2	yes	—
485	C₂×C₃	C₂×C₅×#126	1	2	yes	—
486	D₃	C₅×#400	1	8	yes	direct product factor
487	C₅	D₃×#400	1	1	yes	characteristic, direct product factor, Sylow
488	C₂²	—	3	4	no	—
489	C₂²	—	3	4	no	—
490	C₂²	—	3	8	no	—
491	C₂²	—	3	8	no	—
492	C₂²	—	3	4	no	—
493	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
494	C₂²	C₂×C₅×D₃×Q₈	1	1	yes	characteristic
495	C₂²	C₅×D₃×#41	1	2	yes	—
496	C₂²	C₅×D₃×#41	1	2	yes	—
497	C₂²	C₅×D₃×#41	1	1	yes	characteristic
498	C₄	—	2	2	no	—
499	C₄	—	2	2	no	—
500	C₄	—	4	1	no	—
501	C₄	—	4	2	no	—
502	C₄	—	4	2	no	—
503	C₄	—	6	2	no	—
504	C₄	—	6	2	no	—
505	C₄	—	12	1	no	—
506	C₄	—	12	2	no	—
507	C₄	—	12	2	no	—
508	C₃	C₂×C₅×#400	1	1	yes	characteristic, complemented, Sylow
509	C₂	—	3	8	no	—
510	C₂	C₅×D₃×C₂²⋊Q₈	1	1	yes	characteristic
511	C₂	C₅×D₃×#123	1	1	yes	characteristic
512	C₂	C₅×D₃×#124	1	1	yes	characteristic
513	C₂	C₅×D₃×#125	1	2	yes	—
514	C₂	C₅×D₃×#126	1	2	yes	—

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator, cosocle	C₂³×C₃	C₂⁴×C₅
Frattini	C₂³	C₂³×C₅×D₃
Fitting	C₃×C₅×#400	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂³×C₅×D₃	C₂³
hypercenter	C₅×#400	D₃
hypocenter	C₃	C₂×C₅×#400
LCS	G ▷ C₂³×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₅×#400

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×#400	C₂	semidirect
4. C₅×#4986	C₂	semidirect
5. C₅×#4985	C₂	semidirect
9. C₅×#4660	C₂	semidirect
10. C₅×#4659	C₂	semidirect
11. C₅×#4658	C₂	semidirect
38. D₃×#400	C₅	direct (N × H)
46. C₅×#400	D₃	direct (N × H)
82. C₃×#400	C₂×C₅	semidirect
83. #4986	C₂×C₅	semidirect
84. #4985	C₂×C₅	semidirect
88. #4660	C₂×C₅	semidirect
89. #4659	C₂×C₅	semidirect
90. #4658	C₂×C₅	semidirect
214. #400	C₅×D₃	direct (N × H)
333. C₅×D₃	#400	direct (N × H)
419. C₃×C₅	C₂×#400	semidirect
486. D₃	C₅×#400	direct (N × H)
487. C₅	D₃×#400	direct (N × H)
508. C₃	C₂×C₅×#400	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×D₃×C₄⋊C₄	2
C₃×C₅×#400	2
C₅×#4986	2
C₅×#4985	2
C₅×D₃×#95	2
C₅×#4660	2
C₅×#4659	2
C₅×#4658	2
C₂×C₅×#400	3
D₃×#400	5

Subgroups — C5×D3×#400 #14332022

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×#400 #14332022