Subgroups — C₅×D₃×#476 #14429859

Order 1920.

960 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₅×D₃×D₄	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#476	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5084	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5008	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4870	C₂	1	2	yes	maximal, complemented
7	C₅×D₃×#106	C₂	1	2	yes	maximal, complemented
8	C₅×#4842	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×D₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×D₃×#102	C₂	1	2	yes	maximal
11	C₅×#4761	C₂	1	2	yes	maximal, complemented
12	C₂×C₅×#476	—	3	1	no	maximal, Hall
13	C₂×C₅×D₃×Q₈	—	2	1	no	—
14	C₂×C₅×D₃×D₄	C₂²	1	1	yes	characteristic
15	C₂²×C₄×C₅×D₃	—	2	1	no	—
16	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
17	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
18	C₅×#944	—	2	1	no	—
19	C₅×D₄×Dic₃	C₂²	1	1	yes	characteristic
20	C₄×C₅×#67	—	2	1	no	—
21	C₂×C₅×D₃×C₈	C₂²	1	2	yes	—
22	C₅×#893	C₂²	1	1	yes	characteristic
23	C₅×D₃×C₄⋊C₄	—	2	1	no	—
24	C₅×D₃×C₄⋊C₄	C₂²	1	2	yes	—
25	C₅×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₅×#888	—	2	1	no	—
27	C₅×#888	C₂²	1	2	yes	complemented
28	C₅×#67⋊C₄	—	2	1	no	—
29	C₅×D₃×C₂²⋊C₄	—	2	1	no	—
30	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
31	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
32	C₅×#869	C₂²	1	1	yes	characteristic, complemented
33	C₃×C₅×#106	C₂²	1	2	yes	complemented
34	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
35	C₃×C₅×#102	C₂²	1	2	yes	—
36	C₅×#832	C₂²	1	2	yes	—
37	C₅×#821	C₂²	1	2	yes	—
38	C₅×#817	C₂²	1	2	yes	complemented
39	C₅×Dic₃⋊C₈	C₂²	1	2	yes	complemented
40	C₅×#809	C₂²	1	2	yes	—
41	C₅×#808	C₂²	1	2	yes	complemented
42	C₅×#808	C₂²	1	2	yes	complemented
43	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
44	D₃×#476	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
45	C₂×C₅×C₄⋊Q₈	—	3	1	no	—
46	C₂×C₄×C₅×D₄	—	3	1	no	—
47	C₅×#476	—	3	2	no	—
48	C₅×#476	—	3	1	no	—
49	C₅×#476	—	3	2	no	—
50	C₅×#476	—	3	1	no	—
51	C₅×#476	—	3	1	no	—
52	C₅×#476	D₃	1	1	yes	characteristic, direct product factor
53	C₂×C₅×#106	—	3	2	no	—
54	C₂×C₅×C₄⋊C₈	—	3	1	no	—
55	C₂×C₅×#102	—	3	2	no	—
56	C₂³×C₅×D₃	—	2	1	no	—
57	C₂×C₃×C₅×Q₈	—	2	1	no	—
58	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
59	C₂²×C₃×C₄×C₅	—	2	1	no	—
60	C₂×C₅×#67	—	2	1	no	—
61	C₂²×C₅×Dic₃	—	2	1	no	—
62	C₅×D₃×Q₈	—	4	4	no	—
63	C₅×D₃×D₄	—	2	2	no	—
64	C₅×D₃×D₄	Q₈	1	4	yes	complemented
65	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
66	C₂×C₄×C₅×D₃	—	2	1	no	—
67	C₂×C₄×C₅×D₃	—	2	2	no	—
68	C₂×C₄×C₅×D₃	—	2	1	no	—
69	C₂×C₄×C₅×D₃	—	2	1	no	—
70	C₂×C₄×C₅×D₃	—	4	4	no	—
71	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
72	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
73	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
74	C₂×C₅×Dic₆	—	2	1	no	—
75	C₂×C₅×Dic₆	—	2	2	no	—
76	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
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	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
82	C₅×#217	—	2	1	no	—
83	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
84	C₅×(C₂×D₃)⋊C₄	—	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	2	no	—
90	C₅×Dic₃⋊C₄	—	2	2	no	—
91	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
92	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
93	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
94	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
95	C₅×D₃×C₈	—	2	4	no	—
96	D₃×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
97	C₄×D₃×D₄	C₂×C₅	1	1	yes	characteristic
98	C₃×#476	C₂×C₅	1	1	yes	characteristic, complemented
99	#5084	C₂×C₅	1	1	yes	characteristic, complemented
100	#5008	C₂×C₅	1	1	yes	characteristic, complemented
101	#4870	C₂×C₅	1	2	yes	complemented
102	D₃×#106	C₂×C₅	1	2	yes	complemented
103	#4842	C₂×C₅	1	1	yes	characteristic, complemented
104	D₃×C₄⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
105	D₃×#102	C₂×C₅	1	2	yes	—
106	#4761	C₂×C₅	1	2	yes	complemented
107	C₂²×C₅×Q₈	—	6	1	no	—
108	C₂²×C₅×D₄	—	3	1	no	—
109	C₂³×C₄×C₅	—	6	1	no	—
110	C₂²×C₅×C₈	—	3	2	no	—
111	C₅×C₄⋊Q₈	—	3	2	no	—
112	C₅×C₄⋊Q₈	—	3	1	no	—
113	C₅×C₄⋊Q₈	—	6	1	no	—
114	C₅×C₄⋊Q₈	—	6	1	no	—
115	C₅×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
116	C₄×C₅×D₄	—	3	1	no	—
117	C₄×C₅×D₄	—	3	1	no	—
118	C₄×C₅×D₄	—	3	1	no	—
119	C₄×C₅×D₄	—	6	1	no	—
120	C₄×C₅×D₄	—	6	1	no	—
121	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
122	C₂×C₅×C₄⋊C₄	—	3	2	no	—
123	C₂×C₅×C₄⋊C₄	—	3	1	no	—
124	C₂×C₅×C₄⋊C₄	—	6	1	no	—
125	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
126	C₂×C₄²×C₅	—	3	1	no	—
127	C₅×#106	—	3	2	no	—
128	C₅×#106	—	3	2	no	—
129	C₅×#106	—	3	2	no	—
130	C₅×#106	C₂×D₃	1	2	yes	complemented
131	C₅×C₄⋊C₈	—	3	2	no	—
132	C₅×C₄⋊C₈	—	3	1	no	—
133	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic, complemented
134	C₅×#102	—	3	2	no	—
135	C₅×#102	—	3	2	no	—
136	C₅×#102	—	3	2	no	—
137	C₅×#102	C₂×D₃	1	2	yes	—
138	C₂×#476	—	3	1	no	Sylow
139	C₂³×C₃×C₅	—	2	1	no	—
140	C₂²×C₅×D₃	—	2	1	no	—
141	C₂²×C₅×D₃	—	2	4	no	—
142	C₂²×C₅×D₃	—	4	2	no	—
143	C₂²×C₅×D₃	—	4	2	no	—
144	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
145	C₃×C₅×Q₈	—	4	2	no	—
146	C₃×C₅×D₄	—	2	1	no	—
147	C₃×C₅×D₄	C₂×Q₈	1	2	yes	complemented
148	C₂×C₃×C₄×C₅	—	2	2	no	—
149	C₂×C₃×C₄×C₅	—	2	1	no	—
150	C₂×C₃×C₄×C₅	—	4	2	no	—
151	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
152	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
153	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
154	C₅×#67	—	2	4	no	—
155	C₂×C₅×Dic₃	—	2	2	no	—
156	C₂×C₅×Dic₃	—	2	1	no	—
157	C₂×C₅×Dic₃	—	4	2	no	—
158	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
159	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
160	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
161	C₅×D₁₂	—	2	1	no	—
162	C₅×D₁₂	C₂×Q₈	1	2	yes	complemented
163	C₄×C₅×D₃	—	2	2	no	—
164	C₄×C₅×D₃	—	4	2	no	—
165	C₄×C₅×D₃	—	4	4	no	—
166	C₄×C₅×D₃	—	4	2	no	—
167	C₄×C₅×D₃	—	4	2	no	—
168	C₄×C₅×D₃	SD₁₆	1	4	yes	—
169	C₄×C₅×D₃	C₂×Q₈	1	2	yes	—
170	C₄×C₅×D₃	#41	1	2	yes	—
171	C₅×Dic₆	—	4	4	no	—
172	C₅×Dic₆	—	4	2	no	—
173	C₃×C₅×C₈	—	2	2	no	—
174	C₅×C₃⋊C₈	—	2	2	no	—
175	C₂×D₃×Q₈	—	2	1	no	—
176	C₂×D₃×D₄	C₂²×C₅	1	1	yes	characteristic
177	C₂²×C₄×D₃	—	2	1	no	—
178	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
179	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
180	#944	—	2	1	no	—
181	D₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
182	C₄×#67	—	2	1	no	—
183	C₂×D₃×C₈	C₂²×C₅	1	2	yes	—
184	#893	C₂²×C₅	1	1	yes	characteristic
185	D₃×C₄⋊C₄	—	2	1	no	—
186	D₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
187	D₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
188	#888	—	2	1	no	—
189	#888	C₂²×C₅	1	2	yes	complemented
190	#67⋊C₄	—	2	1	no	—
191	D₃×C₂²⋊C₄	—	2	1	no	—
192	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
193	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
194	#869	C₂²×C₅	1	1	yes	characteristic, complemented
195	C₃×#106	C₂²×C₅	1	2	yes	complemented
196	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
197	C₃×#102	C₂²×C₅	1	2	yes	—
198	#832	C₂²×C₅	1	2	yes	—
199	#821	C₂²×C₅	1	2	yes	—
200	#817	C₂²×C₅	1	2	yes	complemented
201	Dic₃⋊C₈	C₂²×C₅	1	2	yes	complemented
202	#809	C₂²×C₅	1	2	yes	—
203	#808	C₂²×C₅	1	2	yes	complemented
204	#808	C₂²×C₅	1	2	yes	complemented
205	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic, complemented
206	C₂⁴×C₅	—	6	1	no	—
207	C₂×C₅×Q₈	—	2	1	no	—
208	C₂×C₅×Q₈	—	6	2	no	—
209	C₂×C₅×Q₈	—	6	1	no	—
210	C₂×C₅×Q₈	—	12	4	no	—
211	C₂×C₅×D₄	—	3	4	no	—
212	C₂×C₅×D₄	—	3	1	no	—
213	C₂×C₅×D₄	—	6	2	no	—
214	C₂×C₅×D₄	—	6	1	no	—
215	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
216	C₂²×C₄×C₅	—	2	1	no	—
217	C₂²×C₄×C₅	—	3	1	no	—
218	C₂²×C₄×C₅	—	3	1	no	—
219	C₂²×C₄×C₅	—	3	1	no	—
220	C₂²×C₄×C₅	—	6	1	no	—
221	C₂²×C₄×C₅	—	6	1	no	—
222	C₂²×C₄×C₅	—	6	2	no	—
223	C₂²×C₄×C₅	—	6	1	no	—
224	C₂²×C₄×C₅	—	6	1	no	—
225	C₂²×C₄×C₅	—	12	4	no	—
226	C₂×C₅×C₈	—	3	2	no	—
227	C₂×C₅×C₈	—	6	4	no	—
228	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
229	C₅×C₄⋊C₄	—	2	1	no	—
230	C₅×C₄⋊C₄	—	3	1	no	—
231	C₅×C₄⋊C₄	—	3	2	no	—
232	C₅×C₄⋊C₄	—	6	1	no	—
233	C₅×C₄⋊C₄	—	6	2	no	—
234	C₅×C₄⋊C₄	—	6	2	no	—
235	C₅×C₄⋊C₄	—	6	1	no	—
236	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
237	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
238	C₅×C₂²⋊C₄	—	2	1	no	—
239	C₅×C₂²⋊C₄	—	6	1	no	—
240	C₅×C₂²⋊C₄	—	6	1	no	—
241	C₅×C₂²⋊C₄	—	6	1	no	—
242	C₄²×C₅	—	3	1	no	—
243	C₄²×C₅	—	3	1	no	—
244	C₄²×C₅	—	3	1	no	—
245	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
246	C₂×C₄⋊Q₈	—	3	1	no	—
247	C₂×C₄×D₄	—	3	1	no	—
248	#476	—	3	1	no	—
249	#476	—	3	1	no	—
250	#476	—	3	2	no	—
251	#476	—	3	1	no	—
252	#476	—	3	2	no	—
253	#476	C₅×D₃	1	1	yes	characteristic, direct product factor
254	C₂×#106	—	3	2	no	—
255	C₂×C₄⋊C₈	—	3	1	no	—
256	C₂×#102	—	3	2	no	—
257	C₂²×C₃×C₅	—	2	2	no	—
258	C₂²×C₃×C₅	—	4	1	no	—
259	C₂²×C₃×C₅	—	4	1	no	—
260	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
261	C₂×C₅×D₃	—	2	2	no	—
262	C₂×C₅×D₃	—	4	1	no	—
263	C₂×C₅×D₃	—	4	1	no	—
264	C₂×C₅×D₃	—	4	8	no	—
265	C₂×C₅×D₃	C₂²⋊Q₈	1	2	yes	—
266	C₂×C₅×D₃	C₂×SD₁₆	1	2	yes	—
267	C₂×C₅×D₃	AGL(1,ℤ/8)	1	2	yes	—
268	C₃×C₄×C₅	—	2	1	no	—
269	C₃×C₄×C₅	—	4	1	no	—
270	C₃×C₄×C₅	—	4	2	no	—
271	C₃×C₄×C₅	C₂×SD₁₆	1	2	yes	—
272	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
273	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
274	C₅×Dic₃	—	2	1	no	—
275	C₅×Dic₃	—	4	1	no	—
276	C₅×Dic₃	—	4	2	no	—
277	C₅×Dic₃	C₂²⋊Q₈	1	2	yes	—
278	C₅×Dic₃	C₂×SD₁₆	1	2	yes	—
279	C₂³×D₃	—	2	1	no	—
280	C₂×C₃×Q₈	—	2	1	no	—
281	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
282	C₂²×C₃×C₄	—	2	1	no	—
283	C₂×#67	—	2	1	no	—
284	C₂²×Dic₃	—	2	1	no	—
285	D₃×Q₈	—	4	4	no	—
286	D₃×D₄	—	2	2	no	—
287	D₃×D₄	C₅×Q₈	1	4	yes	complemented
288	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
289	C₂×C₄×D₃	—	2	1	no	—
290	C₂×C₄×D₃	—	2	2	no	—
291	C₂×C₄×D₃	—	2	1	no	—
292	C₂×C₄×D₃	—	2	1	no	—
293	C₂×C₄×D₃	—	4	4	no	—
294	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
295	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
296	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
297	C₂×Dic₆	—	2	1	no	—
298	C₂×Dic₆	—	2	2	no	—
299	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
300	C₃×C₄⋊C₄	—	2	1	no	—
301	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
302	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
303	C₃×C₂²⋊C₄	—	2	1	no	—
304	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
305	#217	—	2	1	no	—
306	(C₂×D₃)⋊C₄	—	2	1	no	—
307	(C₂×D₃)⋊C₄	—	2	1	no	—
308	C₄⋊Dic₃	—	2	1	no	—
309	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
310	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
311	Dic₃⋊C₄	—	2	1	no	—
312	Dic₃⋊C₄	—	2	2	no	—
313	Dic₃⋊C₄	—	2	2	no	—
314	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
315	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
316	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
317	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
318	D₃×C₈	—	2	4	no	—
319	C₂³×C₅	—	2	1	no	—
320	C₂³×C₅	—	3	1	no	—
321	C₂³×C₅	—	6	4	no	—
322	C₂³×C₅	—	6	1	no	—
323	C₂³×C₅	—	12	2	no	—
324	C₂³×C₅	—	12	2	no	—
325	C₅×Q₈	—	4	2	no	—
326	C₅×Q₈	—	12	2	no	—
327	C₅×Q₈	—	12	4	no	—
328	C₅×D₄	—	2	1	no	—
329	C₅×D₄	—	3	2	no	—
330	C₅×D₄	—	6	4	no	—
331	C₅×D₄	—	6	1	no	—
332	C₅×D₄	D₃×Q₈	1	2	yes	complemented
333	C₂×C₄×C₅	—	2	1	no	—
334	C₂×C₄×C₅	—	2	2	no	—
335	C₂×C₄×C₅	—	3	1	no	—
336	C₂×C₄×C₅	—	3	1	no	—
337	C₂×C₄×C₅	—	3	4	no	—
338	C₂×C₄×C₅	—	3	2	no	—
339	C₂×C₄×C₅	—	3	2	no	—
340	C₂×C₄×C₅	—	3	1	no	—
341	C₂×C₄×C₅	—	4	2	no	—
342	C₂×C₄×C₅	—	6	2	no	—
343	C₂×C₄×C₅	—	6	1	no	—
344	C₂×C₄×C₅	—	6	2	no	—
345	C₂×C₄×C₅	—	12	2	no	—
346	C₂×C₄×C₅	—	12	2	no	—
347	C₂×C₄×C₅	—	12	2	no	—
348	C₂×C₄×C₅	—	12	4	no	—
349	C₂×C₄×C₅	—	12	2	no	—
350	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
351	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
352	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
353	C₅×C₈	—	2	2	no	—
354	C₅×C₈	—	6	2	no	—
355	C₂²×Q₈	—	6	1	no	—
356	C₂²×D₄	—	3	1	no	—
357	C₂³×C₄	—	6	1	no	—
358	C₂²×C₈	—	3	2	no	—
359	C₄⋊Q₈	—	3	2	no	—
360	C₄⋊Q₈	—	3	1	no	—
361	C₄⋊Q₈	—	6	1	no	—
362	C₄⋊Q₈	—	6	1	no	—
363	C₄⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
364	C₄×D₄	—	3	1	no	—
365	C₄×D₄	—	3	1	no	—
366	C₄×D₄	—	3	1	no	—
367	C₄×D₄	—	6	1	no	—
368	C₄×D₄	—	6	1	no	—
369	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
370	C₂×C₄⋊C₄	—	3	1	no	—
371	C₂×C₄⋊C₄	—	3	2	no	—
372	C₂×C₄⋊C₄	—	6	1	no	—
373	C₂×C₂²⋊C₄	—	6	1	no	—
374	C₂×C₄²	—	3	1	no	—
375	#106	—	3	2	no	—
376	#106	—	3	2	no	—
377	#106	—	3	2	no	—
378	#106	C₂×C₅×D₃	1	2	yes	complemented
379	C₄⋊C₈	—	3	2	no	—
380	C₄⋊C₈	—	3	1	no	—
381	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
382	#102	—	3	2	no	—
383	#102	—	3	2	no	—
384	#102	—	3	2	no	—
385	#102	C₂×C₅×D₃	1	2	yes	—
386	C₂×C₃×C₅	—	4	2	no	—
387	C₂×C₃×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
388	C₂×C₃×C₅	C₂²×SD₁₆	1	1	yes	characteristic
389	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
390	C₅×D₃	—	4	2	no	—
391	C₅×D₃	#476	1	4	yes	direct product factor
392	C₂³×C₃	—	2	1	no	—
393	C₂²×D₃	—	2	1	no	—
394	C₂²×D₃	—	2	4	no	—
395	C₂²×D₃	—	4	2	no	—
396	C₂²×D₃	—	4	2	no	—
397	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
398	C₃×Q₈	—	4	2	no	—
399	C₃×D₄	—	2	1	no	—
400	C₃×D₄	C₂×C₅×Q₈	1	2	yes	complemented
401	C₂×C₃×C₄	—	2	2	no	—
402	C₂×C₃×C₄	—	2	1	no	—
403	C₂×C₃×C₄	—	4	2	no	—
404	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
405	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
406	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
407	#67	—	2	4	no	—
408	C₂×Dic₃	—	2	2	no	—
409	C₂×Dic₃	—	2	1	no	—
410	C₂×Dic₃	—	4	2	no	—
411	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
412	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
413	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
414	D₁₂	—	2	1	no	—
415	D₁₂	C₂×C₅×Q₈	1	2	yes	complemented
416	C₄×D₃	—	2	2	no	—
417	C₄×D₃	—	4	2	no	—
418	C₄×D₃	—	4	4	no	—
419	C₄×D₃	—	4	2	no	—
420	C₄×D₃	—	4	2	no	—
421	C₄×D₃	C₅×SD₁₆	1	4	yes	—
422	C₄×D₃	C₂×C₅×Q₈	1	2	yes	—
423	C₄×D₃	C₅×#41	1	2	yes	—
424	Dic₆	—	4	4	no	—
425	Dic₆	—	4	2	no	—
426	C₃×C₈	—	2	2	no	—
427	C₃⋊C₈	—	2	2	no	—
428	C₂²×C₅	—	2	2	no	—
429	C₂²×C₅	—	3	2	no	—
430	C₂²×C₅	—	3	2	no	—
431	C₂²×C₅	—	3	2	no	—
432	C₂²×C₅	—	4	1	no	—
433	C₂²×C₅	—	4	1	no	—
434	C₂²×C₅	—	6	2	no	—
435	C₂²×C₅	—	12	8	no	—
436	C₂²×C₅	—	12	1	no	—
437	C₂²×C₅	—	12	1	no	—
438	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
439	C₄×C₅	—	2	1	no	—
440	C₄×C₅	—	3	2	no	—
441	C₄×C₅	—	3	2	no	—
442	C₄×C₅	—	4	1	no	—
443	C₄×C₅	—	4	2	no	—
444	C₄×C₅	—	6	1	no	—
445	C₄×C₅	—	12	1	no	—
446	C₄×C₅	—	12	2	no	—
447	C₄×C₅	D₃×SD₁₆	1	2	yes	—
448	C₄×C₅	C₂×D₃×Q₈	1	1	yes	characteristic
449	C₄×C₅	D₃×#41	1	1	yes	characteristic
450	C₂⁴	—	6	1	no	—
451	C₂×Q₈	—	2	1	no	—
452	C₂×Q₈	—	6	2	no	—
453	C₂×Q₈	—	6	1	no	—
454	C₂×Q₈	—	12	4	no	—
455	C₂×D₄	—	3	4	no	—
456	C₂×D₄	—	3	1	no	—
457	C₂×D₄	—	6	2	no	—
458	C₂×D₄	—	6	1	no	—
459	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	3	1	no	—
462	C₂²×C₄	—	3	1	no	—
463	C₂²×C₄	—	3	1	no	—
464	C₂²×C₄	—	6	1	no	—
465	C₂²×C₄	—	6	1	no	—
466	C₂²×C₄	—	6	2	no	—
467	C₂²×C₄	—	6	1	no	—
468	C₂²×C₄	—	6	1	no	—
469	C₂²×C₄	—	12	4	no	—
470	C₂×C₈	—	3	2	no	—
471	C₂×C₈	—	6	4	no	—
472	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	3	2	no	—
475	C₄⋊C₄	—	3	1	no	—
476	C₄⋊C₄	—	6	1	no	—
477	C₄⋊C₄	—	6	2	no	—
478	C₄⋊C₄	—	6	2	no	—
479	C₄⋊C₄	—	6	1	no	—
480	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
481	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
482	C₂²⋊C₄	—	2	1	no	—
483	C₂²⋊C₄	—	6	1	no	—
484	C₂²⋊C₄	—	6	1	no	—
485	C₂²⋊C₄	—	6	1	no	—
486	C₄²	—	3	1	no	—
487	C₄²	—	3	1	no	—
488	C₄²	—	3	1	no	—
489	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
490	C₃×C₅	C₂×#476	1	1	yes	characteristic, complemented, Hall
491	C₂²×C₃	—	2	2	no	—
492	C₂²×C₃	—	4	1	no	—
493	C₂²×C₃	—	4	1	no	—
494	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
495	C₂×D₃	—	2	2	no	—
496	C₂×D₃	—	4	1	no	—
497	C₂×D₃	—	4	1	no	—
498	C₂×D₃	—	4	8	no	—
499	C₂×D₃	C₅×C₂²⋊Q₈	1	2	yes	—
500	C₂×D₃	C₂×C₅×SD₁₆	1	2	yes	—
501	C₂×D₃	C₅×AGL(1,ℤ/8)	1	2	yes	—
502	C₃×C₄	—	2	1	no	—
503	C₃×C₄	—	4	1	no	—
504	C₃×C₄	—	4	2	no	—
505	C₃×C₄	C₂×C₅×SD₁₆	1	2	yes	—
506	C₃×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
507	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
508	Dic₃	—	2	1	no	—
509	Dic₃	—	4	1	no	—
510	Dic₃	—	4	2	no	—
511	Dic₃	C₅×C₂²⋊Q₈	1	2	yes	—
512	Dic₃	C₂×C₅×SD₁₆	1	2	yes	—
513	C₂×C₅	—	3	4	no	—
514	C₂×C₅	—	4	2	no	—
515	C₂×C₅	—	12	2	no	—
516	C₂×C₅	D₃×C₂²⋊Q₈	1	1	yes	characteristic
517	C₂×C₅	C₂×D₃×SD₁₆	1	1	yes	characteristic
518	C₂×C₅	D₃×AGL(1,ℤ/8)	1	1	yes	characteristic
519	C₂³	—	2	1	no	—
520	C₂³	—	3	1	no	—
521	C₂³	—	6	4	no	—
522	C₂³	—	6	1	no	—
523	C₂³	—	12	2	no	—
524	C₂³	—	12	2	no	—
525	Q₈	—	4	2	no	—
526	Q₈	—	12	2	no	—
527	Q₈	—	12	4	no	—
528	D₄	—	2	1	no	—
529	D₄	—	3	2	no	—
530	D₄	—	6	4	no	—
531	D₄	—	6	1	no	—
532	D₄	C₅×D₃×Q₈	1	2	yes	complemented
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	3	1	no	—
536	C₂×C₄	—	3	1	no	—
537	C₂×C₄	—	3	4	no	—
538	C₂×C₄	—	3	2	no	—
539	C₂×C₄	—	3	2	no	—
540	C₂×C₄	—	3	1	no	—
541	C₂×C₄	—	4	2	no	—
542	C₂×C₄	—	6	2	no	—
543	C₂×C₄	—	6	1	no	—
544	C₂×C₄	—	6	2	no	—
545	C₂×C₄	—	12	2	no	—
546	C₂×C₄	—	12	2	no	—
547	C₂×C₄	—	12	2	no	—
548	C₂×C₄	—	12	4	no	—
549	C₂×C₄	—	12	2	no	—
550	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
551	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
552	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
553	C₈	—	2	2	no	—
554	C₈	—	6	2	no	—
555	C₂×C₃	—	4	2	no	—
556	C₂×C₃	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
557	C₂×C₃	C₂²×C₅×SD₁₆	1	1	yes	characteristic
558	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
559	D₃	—	4	2	no	—
560	D₃	C₅×#476	1	4	yes	direct product factor
561	C₅	D₃×#476	1	1	yes	characteristic, direct product factor, Sylow
562	C₂²	—	2	2	no	—
563	C₂²	—	3	2	no	—
564	C₂²	—	3	2	no	—
565	C₂²	—	3	2	no	—
566	C₂²	—	4	1	no	—
567	C₂²	—	4	1	no	—
568	C₂²	—	6	2	no	—
569	C₂²	—	12	8	no	—
570	C₂²	—	12	1	no	—
571	C₂²	—	12	1	no	—
572	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
573	C₄	—	2	1	no	—
574	C₄	—	3	2	no	—
575	C₄	—	3	2	no	—
576	C₄	—	4	1	no	—
577	C₄	—	4	2	no	—
578	C₄	—	6	1	no	—
579	C₄	—	12	1	no	—
580	C₄	—	12	2	no	—
581	C₄	C₅×D₃×SD₁₆	1	2	yes	—
582	C₄	C₂×C₅×D₃×Q₈	1	1	yes	characteristic
583	C₄	C₅×D₃×#41	1	1	yes	characteristic
584	C₃	C₂×C₅×#476	1	1	yes	characteristic, complemented, Sylow
585	C₂	—	3	4	no	—
586	C₂	—	4	2	no	—
587	C₂	—	12	2	no	—
588	C₂	C₅×D₃×C₂²⋊Q₈	1	1	yes	characteristic
589	C₂	C₂×C₅×D₃×SD₁₆	1	1	yes	characteristic
590	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×#476	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₅×D₃×D₄	C₂²
hypercenter	C₅×#476	D₃
hypocenter	C₃	C₂×C₅×#476
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#476

Complements

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

N	H ≅ G/N	type
1. C₅×D₃×C₄⋊Q₈	C₂	semidirect
3. C₃×C₅×#476	C₂	semidirect
4. C₅×#5084	C₂	semidirect
5. C₅×#5008	C₂	semidirect
6. C₅×#4870	C₂	semidirect
7. C₅×D₃×#106	C₂	semidirect
8. C₅×#4842	C₂	semidirect
9. C₅×D₃×C₄⋊C₈	C₂	semidirect
11. C₅×#4761	C₂	semidirect
16. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
27. C₅×#888	C₂²	semidirect
32. C₅×#869	C₂²	semidirect
33. C₃×C₅×#106	C₂²	semidirect
34. C₃×C₅×C₄⋊C₈	C₂²	semidirect
38. C₅×#817	C₂²	semidirect
39. C₅×Dic₃⋊C₈	C₂²	semidirect
41. C₅×#808	C₂²	semidirect
42. C₅×#808	C₂²	semidirect
43. C₅×C₄⋊(C₃⋊C₈)	C₂²	semidirect
44. D₃×#476	C₅	direct (N × H)
52. C₅×#476	D₃	direct (N × H)
64. C₅×D₃×D₄	Q₈	semidirect
96. D₃×C₄⋊Q₈	C₂×C₅	semidirect
98. C₃×#476	C₂×C₅	semidirect
99. #5084	C₂×C₅	semidirect
100. #5008	C₂×C₅	semidirect
101. #4870	C₂×C₅	semidirect
102. D₃×#106	C₂×C₅	semidirect
103. #4842	C₂×C₅	semidirect
104. D₃×C₄⋊C₈	C₂×C₅	semidirect
106. #4761	C₂×C₅	semidirect
115. C₅×C₄⋊Q₈	C₂×D₃	semidirect
130. C₅×#106	C₂×D₃	semidirect
133. C₅×C₄⋊C₈	C₂×D₃	semidirect
147. C₃×C₅×D₄	C₂×Q₈	semidirect
162. C₅×D₁₂	C₂×Q₈	semidirect
178. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
189. #888	C₂²×C₅	semidirect
194. #869	C₂²×C₅	semidirect
195. C₃×#106	C₂²×C₅	semidirect
196. C₃×C₄⋊C₈	C₂²×C₅	semidirect
200. #817	C₂²×C₅	semidirect
201. Dic₃⋊C₈	C₂²×C₅	semidirect
203. #808	C₂²×C₅	semidirect
204. #808	C₂²×C₅	semidirect
205. C₄⋊(C₃⋊C₈)	C₂²×C₅	semidirect
253. #476	C₅×D₃	direct (N × H)
287. D₃×D₄	C₅×Q₈	semidirect
332. C₅×D₄	D₃×Q₈	semidirect
363. C₄⋊Q₈	C₂×C₅×D₃	semidirect
378. #106	C₂×C₅×D₃	semidirect
381. C₄⋊C₈	C₂×C₅×D₃	semidirect
391. C₅×D₃	#476	direct (N × H)
400. C₃×D₄	C₂×C₅×Q₈	semidirect
415. D₁₂	C₂×C₅×Q₈	semidirect
490. C₃×C₅	C₂×#476	semidirect
532. D₄	C₅×D₃×Q₈	semidirect
560. D₃	C₅×#476	direct (N × H)
561. C₅	D₃×#476	direct (N × H)
584. C₃	C₂×C₅×#476	semidirect

Maximal subgroups

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

subgroup	index
C₅×D₃×C₄⋊Q₈	2
C₄×C₅×D₃×D₄	2
C₃×C₅×#476	2
C₅×#5084	2
C₅×#5008	2
C₅×#4870	2
C₅×D₃×#106	2
C₅×#4842	2
C₅×D₃×C₄⋊C₈	2
C₅×D₃×#102	2
C₅×#4761	2
C₂×C₅×#476	3
D₃×#476	5

Subgroups — C5×D3×#476 #14429859

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×#476 #14429859