Subgroups — C₅×D₃×#484 #14431740

Order 1920.

920 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×D₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#484	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5044	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4970	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4884	C₂	1	2	yes	maximal, complemented
7	C₅×D₃×#107	C₂	1	2	yes	maximal, complemented
8	C₅×#4811	C₂	1	2	yes	maximal, complemented
9	C₅×D₃×#103	C₂	1	2	yes	maximal, complemented
10	C₅×D₃×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
11	C₅×#4722	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#484	—	3	1	no	maximal, Hall
13	C₂×C₅×D₃×Q₈	C₂²	1	1	yes	characteristic
14	C₂²×C₄×C₅×D₃	—	2	1	no	—
15	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
16	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₅×#946	C₂²	1	1	yes	characteristic
19	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
20	C₅×#924	C₂²	1	1	yes	characteristic
21	C₂×C₅×Dic₃⋊C₄	—	2	1	no	—
22	C₂×C₅×D₃×C₈	C₂²	1	2	yes	—
23	C₅×#897	C₂²	1	1	yes	characteristic
24	C₅×#896	—	2	1	no	—
25	C₅×D₃×C₄⋊C₄	—	2	1	no	—
26	C₅×D₃×C₄⋊C₄	—	2	1	no	—
27	C₅×D₃×C₄⋊C₄	—	2	1	no	—
28	C₅×D₃×C₄⋊C₄	C₂²	1	2	yes	—
29	C₅×D₃×C₄⋊C₄	C₂²	1	2	yes	—
30	C₅×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
31	C₅×D₃×C₂²⋊C₄	—	2	1	no	—
32	C₅×#878	—	2	1	no	—
33	C₃×C₅×#107	C₂²	1	2	yes	complemented
34	C₃×C₅×#103	C₂²	1	2	yes	complemented
35	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
36	C₅×#835	C₂²	1	2	yes	complemented
37	C₅×#830	C₂²	1	1	yes	characteristic
38	C₅×(C₂×D₃)⋊C₈	C₂²	1	2	yes	—
39	C₅×#818	C₂²	1	2	yes	complemented
40	C₅×#816	C₂²	1	2	yes	complemented
41	C₅×#810	C₂²	1	2	yes	complemented
42	C₅×#807	C₂²	1	2	yes	complemented
43	C₅×#807	C₂²	1	2	yes	complemented
44	D₃×#484	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
45	C₂×C₅×C₂²⋊Q₈	—	3	1	no	—
46	C₂²×C₅×C₄⋊C₄	—	3	1	no	—
47	C₅×#484	—	3	2	no	—
48	C₅×#484	—	3	2	no	—
49	C₅×#484	—	3	1	no	—
50	C₅×#484	—	3	1	no	—
51	C₅×#484	—	3	1	no	—
52	C₅×#484	D₃	1	1	yes	characteristic, direct product factor
53	C₂×C₅×#107	—	3	2	no	—
54	C₂×C₅×#103	—	3	2	no	—
55	C₂×C₅×C₂²⋊C₈	—	3	1	no	—
56	C₂³×C₅×D₃	D₄	1	1	yes	characteristic
57	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
58	C₂²×C₃×C₄×C₅	—	2	1	no	—
59	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
60	C₂²×C₅×Dic₃	—	2	1	no	—
61	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
62	C₅×D₃×Q₈	—	2	4	no	—
63	C₂×C₄×C₅×D₃	—	2	4	no	—
64	C₂×C₄×C₅×D₃	—	2	1	no	—
65	C₂×C₄×C₅×D₃	—	2	1	no	—
66	C₂×C₄×C₅×D₃	—	2	2	no	—
67	C₂×C₄×C₅×D₃	—	2	2	no	—
68	C₂×C₄×C₅×D₃	—	4	4	no	—
69	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
70	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
71	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
72	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
73	C₂×C₅×Dic₆	—	2	1	no	—
74	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
75	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
76	C₃×C₅×C₄⋊C₄	—	2	1	no	—
77	C₃×C₅×C₄⋊C₄	—	2	1	no	—
78	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
79	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
80	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
81	C₅×#217	—	2	1	no	—
82	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
83	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
84	C₅×C₄⋊Dic₃	—	2	1	no	—
85	C₅×C₄⋊Dic₃	—	2	1	no	—
86	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
87	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
88	C₅×Dic₃⋊C₄	—	2	1	no	—
89	C₅×Dic₃⋊C₄	—	2	1	no	—
90	C₅×Dic₃⋊C₄	—	2	1	no	—
91	C₅×Dic₃⋊C₄	—	2	2	no	—
92	C₅×Dic₃⋊C₄	—	2	2	no	—
93	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
94	C₅×D₃×C₈	—	2	4	no	—
95	D₃×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic
96	C₂×D₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
97	C₃×#484	C₂×C₅	1	1	yes	characteristic, complemented
98	#5044	C₂×C₅	1	1	yes	characteristic, complemented
99	#4970	C₂×C₅	1	1	yes	characteristic, complemented
100	#4884	C₂×C₅	1	2	yes	complemented
101	D₃×#107	C₂×C₅	1	2	yes	complemented
102	#4811	C₂×C₅	1	2	yes	complemented
103	D₃×#103	C₂×C₅	1	2	yes	complemented
104	D₃×C₂²⋊C₈	C₂×C₅	1	1	yes	characteristic
105	#4722	C₂×C₅	1	1	yes	characteristic, complemented
106	C₂²×C₅×Q₈	—	3	1	no	—
107	C₂³×C₄×C₅	—	3	1	no	—
108	C₂³×C₄×C₅	—	6	1	no	—
109	C₂²×C₅×C₈	—	3	2	no	—
110	C₅×C₂²⋊Q₈	—	3	1	no	—
111	C₅×C₂²⋊Q₈	—	3	1	no	—
112	C₅×C₂²⋊Q₈	—	3	1	no	—
113	C₅×C₂²⋊Q₈	—	6	1	no	—
114	C₅×C₂²⋊Q₈	—	6	1	no	—
115	C₅×C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic
116	C₂×C₅×C₄⋊C₄	—	3	1	no	—
117	C₂×C₅×C₄⋊C₄	—	3	2	no	—
118	C₂×C₅×C₄⋊C₄	—	3	1	no	—
119	C₂×C₅×C₄⋊C₄	—	3	2	no	—
120	C₂×C₅×C₄⋊C₄	—	6	1	no	—
121	C₂×C₅×C₄⋊C₄	—	6	1	no	—
122	C₂×C₅×C₄⋊C₄	—	6	1	no	—
123	C₂×C₅×C₄⋊C₄	—	6	1	no	—
124	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
125	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
126	C₅×#107	—	3	2	no	—
127	C₅×#107	—	3	2	no	—
128	C₅×#107	—	3	2	no	—
129	C₅×#107	C₂×D₃	1	2	yes	complemented
130	C₅×#103	—	3	2	no	—
131	C₅×#103	—	3	2	no	—
132	C₅×#103	—	3	2	no	—
133	C₅×#103	C₂×D₃	1	2	yes	complemented
134	C₅×C₂²⋊C₈	—	3	1	no	—
135	C₅×C₂²⋊C₈	—	3	2	no	—
136	C₅×C₂²⋊C₈	C₂×D₃	1	1	yes	characteristic
137	C₂×#484	—	3	1	no	Sylow
138	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₅×D₃	—	2	2	no	—
140	C₂²×C₅×D₃	—	2	2	no	—
141	C₂²×C₅×D₃	Q₁₆	1	4	yes	—
142	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
144	C₃×C₅×Q₈	—	2	2	no	—
145	C₂×C₃×C₄×C₅	—	2	2	no	—
146	C₂×C₃×C₄×C₅	—	2	2	no	—
147	C₂×C₃×C₄×C₅	—	2	1	no	—
148	C₂×C₃×C₄×C₅	—	2	1	no	—
149	C₂×C₃×C₄×C₅	—	4	2	no	—
150	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
151	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
152	C₂×C₅×Dic₃	—	2	2	no	—
153	C₂×C₅×Dic₃	—	2	1	no	—
154	C₂×C₅×Dic₃	—	2	2	no	—
155	C₂×C₅×Dic₃	—	2	1	no	—
156	C₂×C₅×Dic₃	—	4	2	no	—
157	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
158	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
159	C₄×C₅×D₃	—	2	2	no	—
160	C₄×C₅×D₃	—	2	2	no	—
161	C₄×C₅×D₃	—	2	2	no	—
162	C₄×C₅×D₃	—	4	4	no	—
163	C₄×C₅×D₃	—	4	2	no	—
164	C₄×C₅×D₃	—	4	2	no	—
165	C₄×C₅×D₃	—	4	4	no	—
166	C₄×C₅×D₃	#41	1	4	yes	—
167	C₅×Dic₆	—	2	2	no	—
168	C₅×Dic₆	—	4	2	no	—
169	C₃×C₅×C₈	—	2	2	no	—
170	C₅×C₃⋊C₈	—	2	2	no	—
171	C₂×D₃×Q₈	C₂²×C₅	1	1	yes	characteristic
172	C₂²×C₄×D₃	—	2	1	no	—
173	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
174	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
175	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
176	#946	C₂²×C₅	1	1	yes	characteristic
177	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
178	#924	C₂²×C₅	1	1	yes	characteristic
179	C₂×Dic₃⋊C₄	—	2	1	no	—
180	C₂×D₃×C₈	C₂²×C₅	1	2	yes	—
181	#897	C₂²×C₅	1	1	yes	characteristic
182	#896	—	2	1	no	—
183	D₃×C₄⋊C₄	—	2	1	no	—
184	D₃×C₄⋊C₄	—	2	1	no	—
185	D₃×C₄⋊C₄	—	2	1	no	—
186	D₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
187	D₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
188	D₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
189	D₃×C₂²⋊C₄	—	2	1	no	—
190	#878	—	2	1	no	—
191	C₃×#107	C₂²×C₅	1	2	yes	complemented
192	C₃×#103	C₂²×C₅	1	2	yes	complemented
193	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
194	#835	C₂²×C₅	1	2	yes	complemented
195	#830	C₂²×C₅	1	1	yes	characteristic
196	(C₂×D₃)⋊C₈	C₂²×C₅	1	2	yes	—
197	#818	C₂²×C₅	1	2	yes	complemented
198	#816	C₂²×C₅	1	2	yes	complemented
199	#810	C₂²×C₅	1	2	yes	complemented
200	#807	C₂²×C₅	1	2	yes	complemented
201	#807	C₂²×C₅	1	2	yes	complemented
202	C₂⁴×C₅	—	3	1	no	—
203	C₂×C₅×Q₈	—	3	1	no	—
204	C₂×C₅×Q₈	—	6	1	no	—
205	C₂×C₅×Q₈	—	6	4	no	—
206	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
207	C₂²×C₄×C₅	—	2	1	no	—
208	C₂²×C₄×C₅	—	3	1	no	—
209	C₂²×C₄×C₅	—	3	1	no	—
210	C₂²×C₄×C₅	—	3	1	no	—
211	C₂²×C₄×C₅	—	3	1	no	—
212	C₂²×C₄×C₅	—	3	1	no	—
213	C₂²×C₄×C₅	—	6	4	no	—
214	C₂²×C₄×C₅	—	6	1	no	—
215	C₂²×C₄×C₅	—	6	1	no	—
216	C₂²×C₄×C₅	—	6	2	no	—
217	C₂²×C₄×C₅	—	6	2	no	—
218	C₂²×C₄×C₅	—	6	1	no	—
219	C₂²×C₄×C₅	—	12	4	no	—
220	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
221	C₂×C₅×C₈	—	3	2	no	—
222	C₂×C₅×C₈	—	6	4	no	—
223	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
224	C₅×C₄⋊C₄	—	2	1	no	—
225	C₅×C₄⋊C₄	—	2	1	no	—
226	C₅×C₄⋊C₄	—	3	2	no	—
227	C₅×C₄⋊C₄	—	3	1	no	—
228	C₅×C₄⋊C₄	—	6	2	no	—
229	C₅×C₄⋊C₄	—	6	2	no	—
230	C₅×C₄⋊C₄	—	6	1	no	—
231	C₅×C₄⋊C₄	—	6	1	no	—
232	C₅×C₄⋊C₄	—	6	1	no	—
233	C₅×C₄⋊C₄	—	6	1	no	—
234	C₅×C₄⋊C₄	—	6	1	no	—
235	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
236	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
237	C₅×C₂²⋊C₄	—	2	1	no	—
238	C₅×C₂²⋊C₄	—	6	1	no	—
239	C₅×C₂²⋊C₄	—	6	1	no	—
240	C₅×C₂²⋊C₄	—	6	1	no	—
241	C₂×C₂²⋊Q₈	—	3	1	no	—
242	C₂²×C₄⋊C₄	—	3	1	no	—
243	#484	—	3	1	no	—
244	#484	—	3	1	no	—
245	#484	—	3	2	no	—
246	#484	—	3	2	no	—
247	#484	—	3	1	no	—
248	#484	C₅×D₃	1	1	yes	characteristic, direct product factor
249	C₂×#107	—	3	2	no	—
250	C₂×#103	—	3	2	no	—
251	C₂×C₂²⋊C₈	—	3	1	no	—
252	C₂²×C₃×C₅	—	2	1	no	—
253	C₂²×C₃×C₅	—	2	1	no	—
254	C₂²×C₃×C₅	C₂×Q₁₆	1	2	yes	—
255	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
256	C₂×C₅×D₃	—	2	1	no	—
257	C₂×C₅×D₃	—	2	1	no	—
258	C₂×C₅×D₃	—	2	8	no	—
259	C₂×C₅×D₃	#123	1	2	yes	—
260	C₂×C₅×D₃	C₂×Q₁₆	1	2	yes	—
261	C₂×C₅×D₃	C₂×Q₁₆	1	2	yes	—
262	C₂×C₅×D₃	AGL(1,ℤ/8)	1	2	yes	—
263	C₃×C₄×C₅	—	2	1	no	—
264	C₃×C₄×C₅	—	4	1	no	—
265	C₃×C₄×C₅	—	4	2	no	—
266	C₃×C₄×C₅	—	4	1	no	—
267	C₃×C₄×C₅	C₂×#41	1	2	yes	—
268	C₅×Dic₃	—	2	1	no	—
269	C₅×Dic₃	—	4	1	no	—
270	C₅×Dic₃	—	4	2	no	—
271	C₅×Dic₃	—	4	1	no	—
272	C₅×Dic₃	#123	1	2	yes	—
273	C₂³×D₃	C₅×D₄	1	1	yes	characteristic
274	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
275	C₂²×C₃×C₄	—	2	1	no	—
276	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
277	C₂²×Dic₃	—	2	1	no	—
278	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
279	D₃×Q₈	—	2	4	no	—
280	C₂×C₄×D₃	—	2	4	no	—
281	C₂×C₄×D₃	—	2	1	no	—
282	C₂×C₄×D₃	—	2	1	no	—
283	C₂×C₄×D₃	—	2	2	no	—
284	C₂×C₄×D₃	—	2	2	no	—
285	C₂×C₄×D₃	—	4	4	no	—
286	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
287	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
288	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
289	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
290	C₂×Dic₆	—	2	1	no	—
291	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
292	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
293	C₃×C₄⋊C₄	—	2	1	no	—
294	C₃×C₄⋊C₄	—	2	1	no	—
295	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
296	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
297	C₃×C₂²⋊C₄	—	2	1	no	—
298	#217	—	2	1	no	—
299	(C₂×D₃)⋊C₄	—	2	1	no	—
300	(C₂×D₃)⋊C₄	—	2	1	no	—
301	C₄⋊Dic₃	—	2	1	no	—
302	C₄⋊Dic₃	—	2	1	no	—
303	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
304	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
305	Dic₃⋊C₄	—	2	1	no	—
306	Dic₃⋊C₄	—	2	1	no	—
307	Dic₃⋊C₄	—	2	1	no	—
308	Dic₃⋊C₄	—	2	2	no	—
309	Dic₃⋊C₄	—	2	2	no	—
310	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
311	D₃×C₈	—	2	4	no	—
312	C₂³×C₅	—	3	1	no	—
313	C₂³×C₅	—	3	4	no	—
314	C₂³×C₅	—	3	1	no	—
315	C₂³×C₅	—	6	2	no	—
316	C₂³×C₅	—	6	2	no	—
317	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
318	C₅×Q₈	—	2	2	no	—
319	C₅×Q₈	—	6	2	no	—
320	C₅×Q₈	—	12	2	no	—
321	C₂×C₄×C₅	—	2	2	no	—
322	C₂×C₄×C₅	—	2	1	no	—
323	C₂×C₄×C₅	—	2	1	no	—
324	C₂×C₄×C₅	—	2	2	no	—
325	C₂×C₄×C₅	—	3	1	no	—
326	C₂×C₄×C₅	—	3	4	no	—
327	C₂×C₄×C₅	—	3	1	no	—
328	C₂×C₄×C₅	—	4	2	no	—
329	C₂×C₄×C₅	—	6	2	no	—
330	C₂×C₄×C₅	—	6	2	no	—
331	C₂×C₄×C₅	—	6	2	no	—
332	C₂×C₄×C₅	—	6	2	no	—
333	C₂×C₄×C₅	—	6	1	no	—
334	C₂×C₄×C₅	—	6	1	no	—
335	C₂×C₄×C₅	—	6	2	no	—
336	C₂×C₄×C₅	—	12	2	no	—
337	C₂×C₄×C₅	—	12	4	no	—
338	C₂×C₄×C₅	—	12	2	no	—
339	C₂×C₄×C₅	—	12	4	no	—
340	C₂×C₄×C₅	—	12	2	no	—
341	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
342	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
343	C₅×C₈	—	2	2	no	—
344	C₅×C₈	—	6	2	no	—
345	C₂²×Q₈	—	3	1	no	—
346	C₂³×C₄	—	3	1	no	—
347	C₂³×C₄	—	6	1	no	—
348	C₂²×C₈	—	3	2	no	—
349	C₂²⋊Q₈	—	3	1	no	—
350	C₂²⋊Q₈	—	3	1	no	—
351	C₂²⋊Q₈	—	3	1	no	—
352	C₂²⋊Q₈	—	6	1	no	—
353	C₂²⋊Q₈	—	6	1	no	—
354	C₂²⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic
355	C₂×C₄⋊C₄	—	3	1	no	—
356	C₂×C₄⋊C₄	—	3	2	no	—
357	C₂×C₄⋊C₄	—	3	2	no	—
358	C₂×C₄⋊C₄	—	3	1	no	—
359	C₂×C₄⋊C₄	—	6	1	no	—
360	C₂×C₄⋊C₄	—	6	1	no	—
361	C₂×C₄⋊C₄	—	6	1	no	—
362	C₂×C₄⋊C₄	—	6	1	no	—
363	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
364	C₂×C₂²⋊C₄	—	6	1	no	—
365	#107	—	3	2	no	—
366	#107	—	3	2	no	—
367	#107	—	3	2	no	—
368	#107	C₂×C₅×D₃	1	2	yes	complemented
369	#103	—	3	2	no	—
370	#103	—	3	2	no	—
371	#103	—	3	2	no	—
372	#103	C₂×C₅×D₃	1	2	yes	complemented
373	C₂²⋊C₈	—	3	1	no	—
374	C₂²⋊C₈	—	3	2	no	—
375	C₂²⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
376	C₂×C₃×C₅	—	2	2	no	—
377	C₂×C₃×C₅	C₂×#123	1	1	yes	characteristic
378	C₂×C₃×C₅	C₂²×Q₁₆	1	1	yes	characteristic
379	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
380	C₅×D₃	—	2	2	no	—
381	C₅×D₃	#484	1	4	yes	direct product factor
382	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
383	C₂²×D₃	—	2	2	no	—
384	C₂²×D₃	—	2	2	no	—
385	C₂²×D₃	C₅×Q₁₆	1	4	yes	—
386	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
387	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
388	C₃×Q₈	—	2	2	no	—
389	C₂×C₃×C₄	—	2	2	no	—
390	C₂×C₃×C₄	—	2	2	no	—
391	C₂×C₃×C₄	—	2	1	no	—
392	C₂×C₃×C₄	—	2	1	no	—
393	C₂×C₃×C₄	—	4	2	no	—
394	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
395	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
396	C₂×Dic₃	—	2	2	no	—
397	C₂×Dic₃	—	2	1	no	—
398	C₂×Dic₃	—	2	2	no	—
399	C₂×Dic₃	—	2	1	no	—
400	C₂×Dic₃	—	4	2	no	—
401	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
402	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
403	C₄×D₃	—	2	2	no	—
404	C₄×D₃	—	2	2	no	—
405	C₄×D₃	—	2	2	no	—
406	C₄×D₃	—	4	4	no	—
407	C₄×D₃	—	4	2	no	—
408	C₄×D₃	—	4	2	no	—
409	C₄×D₃	—	4	4	no	—
410	C₄×D₃	C₅×#41	1	4	yes	—
411	Dic₆	—	2	2	no	—
412	Dic₆	—	4	2	no	—
413	C₃×C₈	—	2	2	no	—
414	C₃⋊C₈	—	2	2	no	—
415	C₂²×C₅	—	2	1	no	—
416	C₂²×C₅	—	2	1	no	—
417	C₂²×C₅	—	3	2	no	—
418	C₂²×C₅	—	3	2	no	—
419	C₂²×C₅	—	3	2	no	—
420	C₂²×C₅	—	3	2	no	—
421	C₂²×C₅	—	6	8	no	—
422	C₂²×C₅	—	6	1	no	—
423	C₂²×C₅	—	6	1	no	—
424	C₂²×C₅	D₃×Q₁₆	1	2	yes	—
425	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
426	C₄×C₅	—	2	1	no	—
427	C₄×C₅	—	3	2	no	—
428	C₄×C₅	—	4	1	no	—
429	C₄×C₅	—	4	2	no	—
430	C₄×C₅	—	4	1	no	—
431	C₄×C₅	—	6	1	no	—
432	C₄×C₅	—	12	1	no	—
433	C₄×C₅	—	12	1	no	—
434	C₄×C₅	—	12	2	no	—
435	C₄×C₅	D₃×#41	1	2	yes	—
436	C₂⁴	—	3	1	no	—
437	C₂×Q₈	—	3	1	no	—
438	C₂×Q₈	—	6	1	no	—
439	C₂×Q₈	—	6	4	no	—
440	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	3	1	no	—
443	C₂²×C₄	—	3	1	no	—
444	C₂²×C₄	—	3	1	no	—
445	C₂²×C₄	—	3	1	no	—
446	C₂²×C₄	—	3	1	no	—
447	C₂²×C₄	—	6	4	no	—
448	C₂²×C₄	—	6	1	no	—
449	C₂²×C₄	—	6	1	no	—
450	C₂²×C₄	—	6	2	no	—
451	C₂²×C₄	—	6	2	no	—
452	C₂²×C₄	—	6	1	no	—
453	C₂²×C₄	—	12	4	no	—
454	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
455	C₂×C₈	—	3	2	no	—
456	C₂×C₈	—	6	4	no	—
457	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	3	2	no	—
461	C₄⋊C₄	—	3	1	no	—
462	C₄⋊C₄	—	6	2	no	—
463	C₄⋊C₄	—	6	2	no	—
464	C₄⋊C₄	—	6	1	no	—
465	C₄⋊C₄	—	6	1	no	—
466	C₄⋊C₄	—	6	1	no	—
467	C₄⋊C₄	—	6	1	no	—
468	C₄⋊C₄	—	6	1	no	—
469	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
470	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
471	C₂²⋊C₄	—	2	1	no	—
472	C₂²⋊C₄	—	6	1	no	—
473	C₂²⋊C₄	—	6	1	no	—
474	C₂²⋊C₄	—	6	1	no	—
475	C₃×C₅	C₂×#484	1	1	yes	characteristic, complemented, Hall
476	C₂²×C₃	—	2	1	no	—
477	C₂²×C₃	—	2	1	no	—
478	C₂²×C₃	C₂×C₅×Q₁₆	1	2	yes	—
479	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
480	C₂×D₃	—	2	1	no	—
481	C₂×D₃	—	2	1	no	—
482	C₂×D₃	—	2	8	no	—
483	C₂×D₃	C₅×#123	1	2	yes	—
484	C₂×D₃	C₂×C₅×Q₁₆	1	2	yes	—
485	C₂×D₃	C₂×C₅×Q₁₆	1	2	yes	—
486	C₂×D₃	C₅×AGL(1,ℤ/8)	1	2	yes	—
487	C₃×C₄	—	2	1	no	—
488	C₃×C₄	—	4	1	no	—
489	C₃×C₄	—	4	2	no	—
490	C₃×C₄	—	4	1	no	—
491	C₃×C₄	C₂×C₅×#41	1	2	yes	—
492	Dic₃	—	2	1	no	—
493	Dic₃	—	4	1	no	—
494	Dic₃	—	4	2	no	—
495	Dic₃	—	4	1	no	—
496	Dic₃	C₅×#123	1	2	yes	—
497	C₂×C₅	—	2	2	no	—
498	C₂×C₅	—	3	4	no	—
499	C₂×C₅	—	6	2	no	—
500	C₂×C₅	D₃×#123	1	1	yes	characteristic
501	C₂×C₅	C₂×D₃×Q₁₆	1	1	yes	characteristic
502	C₂×C₅	D₃×AGL(1,ℤ/8)	1	1	yes	characteristic
503	C₂³	—	3	1	no	—
504	C₂³	—	3	4	no	—
505	C₂³	—	3	1	no	—
506	C₂³	—	6	2	no	—
507	C₂³	—	6	2	no	—
508	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
509	Q₈	—	2	2	no	—
510	Q₈	—	6	2	no	—
511	Q₈	—	12	2	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	3	1	no	—
517	C₂×C₄	—	3	4	no	—
518	C₂×C₄	—	3	1	no	—
519	C₂×C₄	—	4	2	no	—
520	C₂×C₄	—	6	2	no	—
521	C₂×C₄	—	6	2	no	—
522	C₂×C₄	—	6	2	no	—
523	C₂×C₄	—	6	2	no	—
524	C₂×C₄	—	6	1	no	—
525	C₂×C₄	—	6	1	no	—
526	C₂×C₄	—	6	2	no	—
527	C₂×C₄	—	12	4	no	—
528	C₂×C₄	—	12	2	no	—
529	C₂×C₄	—	12	2	no	—
530	C₂×C₄	—	12	4	no	—
531	C₂×C₄	—	12	2	no	—
532	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
533	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
534	C₈	—	2	2	no	—
535	C₈	—	6	2	no	—
536	C₂×C₃	—	2	2	no	—
537	C₂×C₃	C₂×C₅×#123	1	1	yes	characteristic
538	C₂×C₃	C₂²×C₅×Q₁₆	1	1	yes	characteristic
539	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
540	D₃	—	2	2	no	—
541	D₃	C₅×#484	1	4	yes	direct product factor
542	C₅	D₃×#484	1	1	yes	characteristic, direct product factor, Sylow
543	C₂²	—	2	1	no	—
544	C₂²	—	2	1	no	—
545	C₂²	—	3	2	no	—
546	C₂²	—	3	2	no	—
547	C₂²	—	3	2	no	—
548	C₂²	—	3	2	no	—
549	C₂²	—	6	8	no	—
550	C₂²	—	6	1	no	—
551	C₂²	—	6	1	no	—
552	C₂²	C₅×D₃×Q₁₆	1	2	yes	—
553	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
554	C₄	—	2	1	no	—
555	C₄	—	3	2	no	—
556	C₄	—	4	1	no	—
557	C₄	—	4	2	no	—
558	C₄	—	4	1	no	—
559	C₄	—	6	1	no	—
560	C₄	—	12	1	no	—
561	C₄	—	12	2	no	—
562	C₄	—	12	1	no	—
563	C₄	C₅×D₃×#41	1	2	yes	—
564	C₃	C₂×C₅×#484	1	1	yes	characteristic, complemented, Sylow
565	C₂	—	2	2	no	—
566	C₂	—	3	4	no	—
567	C₂	—	6	2	no	—
568	C₂	C₅×D₃×#123	1	1	yes	characteristic
569	C₂	C₂×C₅×D₃×Q₁₆	1	1	yes	characteristic
570	C₂	C₅×D₃×AGL(1,ℤ/8)	1	1	yes	characteristic

	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×#484	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂³×C₅×D₃	D₄
hypercenter	C₅×#484	D₃
hypocenter	C₃	C₂×C₅×#484
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#484

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×#484	C₂	semidirect
4. C₅×#5044	C₂	semidirect
5. C₅×#4970	C₂	semidirect
6. C₅×#4884	C₂	semidirect
7. C₅×D₃×#107	C₂	semidirect
8. C₅×#4811	C₂	semidirect
9. C₅×D₃×#103	C₂	semidirect
11. C₅×#4722	C₂	semidirect
33. C₃×C₅×#107	C₂²	semidirect
34. C₃×C₅×#103	C₂²	semidirect
36. C₅×#835	C₂²	semidirect
39. C₅×#818	C₂²	semidirect
40. C₅×#816	C₂²	semidirect
41. C₅×#810	C₂²	semidirect
42. C₅×#807	C₂²	semidirect
43. C₅×#807	C₂²	semidirect
44. D₃×#484	C₅	direct (N × H)
52. C₅×#484	D₃	direct (N × H)
97. C₃×#484	C₂×C₅	semidirect
98. #5044	C₂×C₅	semidirect
99. #4970	C₂×C₅	semidirect
100. #4884	C₂×C₅	semidirect
101. D₃×#107	C₂×C₅	semidirect
102. #4811	C₂×C₅	semidirect
103. D₃×#103	C₂×C₅	semidirect
105. #4722	C₂×C₅	semidirect
129. C₅×#107	C₂×D₃	semidirect
133. C₅×#103	C₂×D₃	semidirect
191. C₃×#107	C₂²×C₅	semidirect
192. C₃×#103	C₂²×C₅	semidirect
194. #835	C₂²×C₅	semidirect
197. #818	C₂²×C₅	semidirect
198. #816	C₂²×C₅	semidirect
199. #810	C₂²×C₅	semidirect
200. #807	C₂²×C₅	semidirect
201. #807	C₂²×C₅	semidirect
248. #484	C₅×D₃	direct (N × H)
368. #107	C₂×C₅×D₃	semidirect
372. #103	C₂×C₅×D₃	semidirect
381. C₅×D₃	#484	direct (N × H)
475. C₃×C₅	C₂×#484	semidirect
541. D₃	C₅×#484	direct (N × H)
542. C₅	D₃×#484	direct (N × H)
564. C₃	C₂×C₅×#484	semidirect

Maximal subgroups

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

subgroup	index
C₅×D₃×C₂²⋊Q₈	2
C₂×C₅×D₃×C₄⋊C₄	2
C₃×C₅×#484	2
C₅×#5044	2
C₅×#4970	2
C₅×#4884	2
C₅×D₃×#107	2
C₅×#4811	2
C₅×D₃×#103	2
C₅×D₃×C₂²⋊C₈	2
C₅×#4722	2
C₂×C₅×#484	3
D₃×#484	5

Subgroups — C5×D3×#484 #14431740

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×#484 #14431740