Subgroups — C₅×#70170 #14300085

Order 1920.

724 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₄×Dic₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×#102	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#832	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×#817	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4984	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4550	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4529	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1864	—	3	1	no	maximal, Hall
9	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
10	C₂³×C₅×Dic₃	—	2	1	no	—
11	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
13	C₂×C₅×#217	—	2	1	no	—
14	C₅×D₄×Dic₃	—	2	2	no	—
15	C₅×D₄×Dic₃	—	2	2	no	—
16	C₂×C₅×C₄⋊Dic₃	—	2	1	no	—
17	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
18	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
20	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
21	C₃×C₅×#102	C₄	1	4	yes	complemented
22	C₅×#832	—	2	2	no	—
23	C₅×C₃⋊#95	—	2	1	no	—
24	C₅×#817	—	2	2	no	—
25	#70170	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
26	C₂×C₄×C₅×D₄	—	3	1	no	—
27	C₂×C₅×#106	—	3	1	no	—
28	C₂×C₅×#102	—	3	1	no	—
29	C₂×C₅×#102	D₃	1	1	yes	characteristic
30	C₅×#389	—	3	1	no	—
31	C₅×#340	—	3	1	no	—
32	C₅×#336	—	3	1	no	—
33	C₂⁴×C₃×C₅	—	2	1	no	—
34	C₂×C₃×C₅×D₄	—	2	1	no	—
35	C₂×C₃×C₅×D₄	—	2	1	no	—
36	C₂×C₃×C₅×D₄	—	2	1	no	—
37	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
38	C₂×C₃×C₅×D₄	D₄	1	2	yes	—
39	C₂×C₃×C₅×D₄	Q₈	1	2	yes	—
40	C₂²×C₃×C₄×C₅	—	2	1	no	—
41	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
42	C₂²×C₅×Dic₃	—	2	4	no	—
43	C₂²×C₅×Dic₃	—	2	1	no	—
44	C₂²×C₅×Dic₃	—	2	1	no	—
45	C₂²×C₅×Dic₃	—	4	2	no	—
46	C₂²×C₅×Dic₃	—	4	2	no	—
47	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
48	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
49	C₂×C₃×C₅×C₈	—	2	1	no	—
50	C₂×C₃×C₅×C₈	—	2	1	no	—
51	C₂×C₃×C₅×C₈	C₂×C₄	1	2	yes	complemented
52	C₃×C₅×C₄⋊C₄	—	2	1	no	—
53	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	complemented
54	C₅×#217	—	2	4	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	—	4	2	no	—
59	C₅×C₄⋊Dic₃	D₄	1	2	yes	—
60	C₄×C₅×Dic₃	—	2	1	no	—
61	C₄×C₅×Dic₃	—	2	1	no	—
62	C₂×C₅×C₃⋊C₈	—	2	1	no	—
63	C₂×C₅×C₃⋊C₈	—	2	1	no	—
64	C₂×C₅×C₃⋊C₈	—	2	1	no	—
65	C₂×D₄×Dic₃	C₂×C₅	1	1	yes	characteristic
66	C₂×C₃×#102	C₂×C₅	1	1	yes	characteristic
67	C₂×#832	C₂×C₅	1	1	yes	characteristic
68	C₂×#817	C₂×C₅	1	1	yes	characteristic, complemented
69	#4984	C₂×C₅	1	1	yes	characteristic, complemented
70	#4550	C₂×C₅	1	1	yes	characteristic, complemented
71	#4529	C₂×C₅	1	1	yes	characteristic, complemented
72	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
73	C₂³×C₄×C₅	—	6	1	no	—
74	C₂²×C₅×C₈	—	3	1	no	—
75	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
76	C₄×C₅×D₄	—	6	2	no	—
77	C₄×C₅×D₄	—	6	2	no	—
78	C₂×C₅×C₄⋊C₄	—	3	1	no	—
79	C₂×C₅×C₄⋊C₄	—	3	1	no	—
80	C₂×C₅×C₄⋊C₄	—	6	1	no	—
81	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
82	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
83	C₂×C₄²×C₅	—	3	1	no	—
84	C₅×#106	—	6	2	no	—
85	C₅×#102	—	6	2	no	—
86	C₅×#102	Dic₃	1	4	yes	complemented
87	C₅×#95	—	6	1	no	—
88	#1864	—	3	1	no	Sylow
89	C₂³×C₃×C₅	—	2	2	no	—
90	C₂³×C₃×C₅	—	2	2	no	—
91	C₂³×C₃×C₅	—	2	2	no	—
92	C₂³×C₃×C₅	—	4	1	no	—
93	C₂³×C₃×C₅	—	4	1	no	—
94	C₂³×C₃×C₅	—	4	1	no	—
95	C₂³×C₃×C₅	—	4	1	no	—
96	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
97	C₃×C₅×D₄	—	2	2	no	—
98	C₃×C₅×D₄	—	2	2	no	—
99	C₃×C₅×D₄	—	2	2	no	—
100	C₃×C₅×D₄	C₄⋊C₄	1	4	yes	complemented
101	C₂×C₃×C₄×C₅	—	2	2	no	—
102	C₂×C₃×C₄×C₅	—	4	1	no	—
103	C₂×C₃×C₄×C₅	—	4	1	no	—
104	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
106	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
107	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
108	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
109	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
110	C₂×C₅×Dic₃	—	2	1	no	—
111	C₂×C₅×Dic₃	—	2	1	no	—
112	C₂×C₅×Dic₃	—	2	1	no	—
113	C₂×C₅×Dic₃	—	2	2	no	—
114	C₂×C₅×Dic₃	—	2	1	no	—
115	C₂×C₅×Dic₃	—	2	1	no	—
116	C₂×C₅×Dic₃	—	4	8	no	—
117	C₂×C₅×Dic₃	—	4	1	no	—
118	C₂×C₅×Dic₃	—	4	1	no	—
119	C₂×C₅×Dic₃	—	4	1	no	—
120	C₂×C₅×Dic₃	—	4	1	no	—
121	C₂×C₅×Dic₃	—	4	1	no	—
122	C₂×C₅×Dic₃	SD₁₆	1	2	yes	—
123	C₃×C₅×C₈	—	2	2	no	—
124	C₅×C₃⋊C₈	—	4	1	no	—
125	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
126	C₂³×Dic₃	—	2	1	no	—
127	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
128	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
129	C₂×#217	—	2	1	no	—
130	D₄×Dic₃	—	2	2	no	—
131	D₄×Dic₃	—	2	2	no	—
132	C₂×C₄⋊Dic₃	—	2	1	no	—
133	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
134	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
135	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
136	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
137	C₃×#102	C₄×C₅	1	4	yes	complemented
138	#832	—	2	2	no	—
139	C₃⋊#95	—	2	1	no	—
140	#817	—	2	2	no	—
141	C₂⁴×C₅	—	2	1	no	—
142	C₂×C₅×D₄	—	2	1	no	—
143	C₂×C₅×D₄	—	2	1	no	—
144	C₂×C₅×D₄	—	2	1	no	—
145	C₂×C₅×D₄	Dic₆	1	2	yes	—
146	C₂×C₅×D₄	D₁₂	1	2	yes	—
147	C₂×C₅×D₄	C₂×Dic₃	1	2	yes	—
148	C₂²×C₄×C₅	—	2	1	no	—
149	C₂²×C₄×C₅	—	3	1	no	—
150	C₂²×C₄×C₅	—	3	1	no	—
151	C₂²×C₄×C₅	—	6	4	no	—
152	C₂²×C₄×C₅	—	6	1	no	—
153	C₂²×C₄×C₅	—	6	1	no	—
154	C₂²×C₄×C₅	—	12	2	no	—
155	C₂²×C₄×C₅	—	12	2	no	—
156	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
157	C₂×C₅×C₈	—	2	1	no	—
158	C₂×C₅×C₈	—	2	1	no	—
159	C₂×C₅×C₈	—	6	1	no	—
160	C₂×C₅×C₈	—	6	1	no	—
161	C₂×C₅×C₈	—	6	1	no	—
162	C₂×C₅×C₈	C₂×Dic₃	1	2	yes	complemented
163	C₅×C₄⋊C₄	—	2	1	no	—
164	C₅×C₄⋊C₄	—	3	2	no	—
165	C₅×C₄⋊C₄	—	6	1	no	—
166	C₅×C₄⋊C₄	—	6	1	no	—
167	C₅×C₄⋊C₄	—	6	1	no	—
168	C₅×C₄⋊C₄	—	12	2	no	—
169	C₅×C₄⋊C₄	C₂×Dic₃	1	2	yes	complemented
170	C₅×C₂²⋊C₄	—	6	4	no	—
171	C₄²×C₅	—	6	1	no	—
172	C₄²×C₅	—	6	1	no	—
173	C₂×C₄×D₄	—	3	1	no	—
174	C₂×#106	—	3	1	no	—
175	C₂×#102	—	3	1	no	—
176	C₂×#102	C₅×D₃	1	1	yes	characteristic
177	#389	—	3	1	no	—
178	#340	—	3	1	no	—
179	#336	—	3	1	no	—
180	C₂²×C₃×C₅	—	2	4	no	—
181	C₂²×C₃×C₅	—	4	2	no	—
182	C₂²×C₃×C₅	—	4	2	no	—
183	C₂²×C₃×C₅	—	4	2	no	—
184	C₂²×C₃×C₅	—	4	2	no	—
185	C₂²×C₃×C₅	—	4	2	no	—
186	C₂²×C₃×C₅	—	4	2	no	—
187	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
188	C₂²×C₃×C₅	#120	1	1	yes	characteristic
189	C₂²×C₃×C₅	C₂²⋊Q₈	1	1	yes	characteristic
190	C₂²×C₃×C₅	C₂×SD₁₆	1	1	yes	characteristic
191	C₂²×C₃×C₅	#135	1	1	yes	characteristic
192	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
193	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
194	C₃×C₄×C₅	—	4	2	no	—
195	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
196	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
197	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
198	C₃×C₄×C₅	#123	1	1	yes	characteristic
199	C₅×Dic₃	—	2	2	no	—
200	C₅×Dic₃	—	4	1	no	—
201	C₅×Dic₃	—	4	2	no	—
202	C₅×Dic₃	—	8	1	no	—
203	C₂⁴×C₃	—	2	1	no	—
204	C₂×C₃×D₄	—	2	1	no	—
205	C₂×C₃×D₄	—	2	1	no	—
206	C₂×C₃×D₄	—	2	1	no	—
207	C₂×C₃×D₄	C₂×C₄×C₅	1	2	yes	—
208	C₂×C₃×D₄	C₅×D₄	1	2	yes	—
209	C₂×C₃×D₄	C₅×Q₈	1	2	yes	—
210	C₂²×C₃×C₄	—	2	1	no	—
211	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
212	C₂²×Dic₃	—	2	4	no	—
213	C₂²×Dic₃	—	2	1	no	—
214	C₂²×Dic₃	—	2	1	no	—
215	C₂²×Dic₃	—	4	2	no	—
216	C₂²×Dic₃	—	4	2	no	—
217	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
218	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
219	C₂×C₃×C₈	—	2	1	no	—
220	C₂×C₃×C₈	—	2	1	no	—
221	C₂×C₃×C₈	C₂×C₄×C₅	1	2	yes	complemented
222	C₃×C₄⋊C₄	—	2	1	no	—
223	C₃×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	complemented
224	#217	—	2	4	no	—
225	C₄⋊Dic₃	—	2	1	no	—
226	C₄⋊Dic₃	—	2	1	no	—
227	C₄⋊Dic₃	—	2	1	no	—
228	C₄⋊Dic₃	—	4	2	no	—
229	C₄⋊Dic₃	C₅×D₄	1	2	yes	—
230	C₄×Dic₃	—	2	1	no	—
231	C₄×Dic₃	—	2	1	no	—
232	C₂×C₃⋊C₈	—	2	1	no	—
233	C₂×C₃⋊C₈	—	2	1	no	—
234	C₂×C₃⋊C₈	—	2	1	no	—
235	C₂³×C₅	—	2	2	no	—
236	C₂³×C₅	—	2	2	no	—
237	C₂³×C₅	—	2	2	no	—
238	C₂³×C₅	—	4	1	no	—
239	C₂³×C₅	—	4	1	no	—
240	C₂³×C₅	—	4	1	no	—
241	C₂³×C₅	—	4	1	no	—
242	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
243	C₅×D₄	—	2	2	no	—
244	C₅×D₄	—	2	2	no	—
245	C₅×D₄	—	2	2	no	—
246	C₅×D₄	C₄⋊Dic₃	1	4	yes	complemented
247	C₂×C₄×C₅	—	2	2	no	—
248	C₂×C₄×C₅	—	3	2	no	—
249	C₂×C₄×C₅	—	4	1	no	—
250	C₂×C₄×C₅	—	4	1	no	—
251	C₂×C₄×C₅	—	6	1	no	—
252	C₂×C₄×C₅	—	6	1	no	—
253	C₂×C₄×C₅	—	6	1	no	—
254	C₂×C₄×C₅	—	6	2	no	—
255	C₂×C₄×C₅	—	6	1	no	—
256	C₂×C₄×C₅	—	6	1	no	—
257	C₂×C₄×C₅	—	12	8	no	—
258	C₂×C₄×C₅	—	12	1	no	—
259	C₂×C₄×C₅	—	12	1	no	—
260	C₂×C₄×C₅	—	12	1	no	—
261	C₂×C₄×C₅	—	12	1	no	—
262	C₂×C₄×C₅	—	12	1	no	—
263	C₂×C₄×C₅	C₂×Dic₆	1	1	yes	characteristic
264	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
265	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
266	C₂×C₄×C₅	#237	1	1	yes	characteristic
267	C₂×C₄×C₅	#237	1	1	yes	characteristic
268	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
269	C₅×C₈	—	2	2	no	—
270	C₅×C₈	—	12	1	no	—
271	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
272	C₂³×C₄	—	6	1	no	—
273	C₂²×C₈	—	3	1	no	—
274	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
275	C₄×D₄	—	6	2	no	—
276	C₄×D₄	—	6	2	no	—
277	C₂×C₄⋊C₄	—	3	1	no	—
278	C₂×C₄⋊C₄	—	3	1	no	—
279	C₂×C₄⋊C₄	—	6	1	no	—
280	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
281	C₂×C₂²⋊C₄	—	6	1	no	—
282	C₂×C₄²	—	3	1	no	—
283	#106	—	6	2	no	—
284	#102	—	6	2	no	—
285	#102	C₅×Dic₃	1	4	yes	complemented
286	#95	—	6	1	no	—
287	C₂×C₃×C₅	—	4	4	no	—
288	C₂×C₃×C₅	#385	1	1	yes	characteristic
289	C₂×C₃×C₅	C₄×SD₁₆	1	1	yes	characteristic
290	C₂×C₃×C₅	#442	1	1	yes	characteristic
291	C₂×C₃×C₅	#449	1	1	yes	characteristic
292	C₂×C₃×C₅	#450	1	1	yes	characteristic
293	C₂×C₃×C₅	#476	1	1	yes	characteristic
294	C₂×C₃×C₅	#478	1	1	yes	characteristic
295	C₂³×C₃	—	2	2	no	—
296	C₂³×C₃	—	2	2	no	—
297	C₂³×C₃	—	2	2	no	—
298	C₂³×C₃	—	4	1	no	—
299	C₂³×C₃	—	4	1	no	—
300	C₂³×C₃	—	4	1	no	—
301	C₂³×C₃	—	4	1	no	—
302	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
303	C₃×D₄	—	2	2	no	—
304	C₃×D₄	—	2	2	no	—
305	C₃×D₄	—	2	2	no	—
306	C₃×D₄	C₅×C₄⋊C₄	1	4	yes	complemented
307	C₂×C₃×C₄	—	2	2	no	—
308	C₂×C₃×C₄	—	4	1	no	—
309	C₂×C₃×C₄	—	4	1	no	—
310	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
311	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
312	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
313	C₂×C₃×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
314	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
315	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
316	C₂×Dic₃	—	2	1	no	—
317	C₂×Dic₃	—	2	1	no	—
318	C₂×Dic₃	—	2	1	no	—
319	C₂×Dic₃	—	2	2	no	—
320	C₂×Dic₃	—	2	1	no	—
321	C₂×Dic₃	—	2	1	no	—
322	C₂×Dic₃	—	4	8	no	—
323	C₂×Dic₃	—	4	1	no	—
324	C₂×Dic₃	—	4	1	no	—
325	C₂×Dic₃	—	4	1	no	—
326	C₂×Dic₃	—	4	1	no	—
327	C₂×Dic₃	—	4	1	no	—
328	C₂×Dic₃	C₅×SD₁₆	1	2	yes	—
329	C₃×C₈	—	2	2	no	—
330	C₃⋊C₈	—	4	1	no	—
331	C₂²×C₅	—	2	4	no	—
332	C₂²×C₅	—	4	2	no	—
333	C₂²×C₅	—	4	2	no	—
334	C₂²×C₅	—	4	2	no	—
335	C₂²×C₅	—	4	2	no	—
336	C₂²×C₅	—	4	2	no	—
337	C₂²×C₅	—	4	2	no	—
338	C₂²×C₅	#878	1	1	yes	characteristic
339	C₂²×C₅	#882	1	1	yes	characteristic
340	C₂²×C₅	#911	1	1	yes	characteristic
341	C₂²×C₅	#911	1	1	yes	characteristic
342	C₂²×C₅	D₃×SD₁₆	1	1	yes	characteristic
343	C₂²×C₅	#916	1	1	yes	characteristic
344	C₂²×C₅	D₄×Dic₃	1	1	yes	characteristic
345	C₄×C₅	—	4	2	no	—
346	C₄×C₅	—	6	2	no	—
347	C₄×C₅	—	12	2	no	—
348	C₄×C₅	—	12	1	no	—
349	C₄×C₅	—	24	1	no	—
350	C₄×C₅	#878	1	1	yes	characteristic
351	C₄×C₅	#886	1	1	yes	characteristic
352	C₄×C₅	C₂×C₄⋊Dic₃	1	1	yes	characteristic
353	C₄×C₅	D₄×Dic₃	1	1	yes	characteristic
354	C₂⁴	—	2	1	no	—
355	C₂×D₄	—	2	1	no	—
356	C₂×D₄	—	2	1	no	—
357	C₂×D₄	—	2	1	no	—
358	C₂×D₄	C₅×Dic₆	1	2	yes	—
359	C₂×D₄	C₅×D₁₂	1	2	yes	—
360	C₂×D₄	C₂×C₅×Dic₃	1	2	yes	—
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	—	3	1	no	—
363	C₂²×C₄	—	3	1	no	—
364	C₂²×C₄	—	6	4	no	—
365	C₂²×C₄	—	6	1	no	—
366	C₂²×C₄	—	6	1	no	—
367	C₂²×C₄	—	12	2	no	—
368	C₂²×C₄	—	12	2	no	—
369	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
370	C₂×C₈	—	2	1	no	—
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	6	1	no	—
373	C₂×C₈	—	6	1	no	—
374	C₂×C₈	—	6	1	no	—
375	C₂×C₈	C₂×C₅×Dic₃	1	2	yes	complemented
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	3	2	no	—
378	C₄⋊C₄	—	6	1	no	—
379	C₄⋊C₄	—	6	1	no	—
380	C₄⋊C₄	—	6	1	no	—
381	C₄⋊C₄	—	12	2	no	—
382	C₄⋊C₄	C₂×C₅×Dic₃	1	2	yes	complemented
383	C₂²⋊C₄	—	6	4	no	—
384	C₄²	—	6	1	no	—
385	C₄²	—	6	1	no	—
386	C₃×C₅	#1864	1	1	yes	characteristic, complemented, Hall
387	C₂²×C₃	—	2	4	no	—
388	C₂²×C₃	—	4	2	no	—
389	C₂²×C₃	—	4	2	no	—
390	C₂²×C₃	—	4	2	no	—
391	C₂²×C₃	—	4	2	no	—
392	C₂²×C₃	—	4	2	no	—
393	C₂²×C₃	—	4	2	no	—
394	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
395	C₂²×C₃	C₅×#120	1	1	yes	characteristic
396	C₂²×C₃	C₅×C₂²⋊Q₈	1	1	yes	characteristic
397	C₂²×C₃	C₂×C₅×SD₁₆	1	1	yes	characteristic
398	C₂²×C₃	C₅×#135	1	1	yes	characteristic
399	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
400	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
401	C₃×C₄	—	4	2	no	—
402	C₃×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
403	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
404	C₃×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
405	C₃×C₄	C₅×#123	1	1	yes	characteristic
406	Dic₃	—	2	2	no	—
407	Dic₃	—	4	1	no	—
408	Dic₃	—	4	2	no	—
409	Dic₃	—	8	1	no	—
410	C₂×C₅	—	4	4	no	—
411	C₂×C₅	#4761	1	1	yes	characteristic
412	C₂×C₅	#4763	1	1	yes	characteristic
413	C₂×C₅	#4776	1	1	yes	characteristic
414	C₂×C₅	#4781	1	1	yes	characteristic
415	C₂×C₅	#4950	1	1	yes	characteristic
416	C₂×C₅	#5152	1	1	yes	characteristic
417	C₂×C₅	Dic₃×SD₁₆	1	1	yes	characteristic
418	C₂³	—	2	2	no	—
419	C₂³	—	2	2	no	—
420	C₂³	—	2	2	no	—
421	C₂³	—	4	1	no	—
422	C₂³	—	4	1	no	—
423	C₂³	—	4	1	no	—
424	C₂³	—	4	1	no	—
425	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
426	D₄	—	2	2	no	—
427	D₄	—	2	2	no	—
428	D₄	—	2	2	no	—
429	D₄	C₅×C₄⋊Dic₃	1	4	yes	complemented
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	3	2	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	6	1	no	—
435	C₂×C₄	—	6	1	no	—
436	C₂×C₄	—	6	1	no	—
437	C₂×C₄	—	6	2	no	—
438	C₂×C₄	—	6	1	no	—
439	C₂×C₄	—	6	1	no	—
440	C₂×C₄	—	12	8	no	—
441	C₂×C₄	—	12	1	no	—
442	C₂×C₄	—	12	1	no	—
443	C₂×C₄	—	12	1	no	—
444	C₂×C₄	—	12	1	no	—
445	C₂×C₄	—	12	1	no	—
446	C₂×C₄	C₂×C₅×Dic₆	1	1	yes	characteristic
447	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
448	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
449	C₂×C₄	C₅×#237	1	1	yes	characteristic
450	C₂×C₄	C₅×#237	1	1	yes	characteristic
451	C₂×C₄	C₂²×C₅×Dic₃	1	1	yes	characteristic
452	C₈	—	2	2	no	—
453	C₈	—	12	1	no	—
454	C₂×C₃	—	4	4	no	—
455	C₂×C₃	C₅×#385	1	1	yes	characteristic
456	C₂×C₃	C₄×C₅×SD₁₆	1	1	yes	characteristic
457	C₂×C₃	C₅×#442	1	1	yes	characteristic
458	C₂×C₃	C₅×#449	1	1	yes	characteristic
459	C₂×C₃	C₅×#450	1	1	yes	characteristic
460	C₂×C₃	C₅×#476	1	1	yes	characteristic
461	C₂×C₃	C₅×#478	1	1	yes	characteristic
462	C₅	#70170	1	1	yes	characteristic, direct product factor, Sylow
463	C₂²	—	2	4	no	—
464	C₂²	—	4	2	no	—
465	C₂²	—	4	2	no	—
466	C₂²	—	4	2	no	—
467	C₂²	—	4	2	no	—
468	C₂²	—	4	2	no	—
469	C₂²	—	4	2	no	—
470	C₂²	C₅×#878	1	1	yes	characteristic
471	C₂²	C₅×#882	1	1	yes	characteristic
472	C₂²	C₅×#911	1	1	yes	characteristic
473	C₂²	C₅×#911	1	1	yes	characteristic
474	C₂²	C₅×D₃×SD₁₆	1	1	yes	characteristic
475	C₂²	C₅×#916	1	1	yes	characteristic
476	C₂²	C₅×D₄×Dic₃	1	1	yes	characteristic
477	C₄	—	4	2	no	—
478	C₄	—	6	2	no	—
479	C₄	—	12	2	no	—
480	C₄	—	12	1	no	—
481	C₄	—	24	1	no	—
482	C₄	C₅×#878	1	1	yes	characteristic
483	C₄	C₅×#886	1	1	yes	characteristic
484	C₄	C₂×C₅×C₄⋊Dic₃	1	1	yes	characteristic
485	C₄	C₅×D₄×Dic₃	1	1	yes	characteristic
486	C₃	C₅×#1864	1	1	yes	characteristic, complemented, Sylow
487	C₂	—	4	4	no	—
488	C₂	C₅×#4761	1	1	yes	characteristic
489	C₂	C₅×#4763	1	1	yes	characteristic
490	C₂	C₅×#4776	1	1	yes	characteristic
491	C₂	C₅×#4781	1	1	yes	characteristic
492	C₂	C₅×#4950	1	1	yes	characteristic
493	C₂	C₅×#5152	1	1	yes	characteristic
494	C₂	C₅×Dic₃×SD₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	D₃×D₄
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₂×C₃×C₅×#102	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂²×C₃×C₅×D₄	C₂²
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₂×C₅×#102	D₃
hypocenter	C₃	C₅×#1864
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×#102

Complements

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

N	H ≅ G/N	type
4. C₂×C₅×#817	C₂	semidirect
5. C₅×#4984	C₂	semidirect
6. C₅×#4550	C₂	semidirect
7. C₅×#4529	C₂	semidirect
21. C₃×C₅×#102	C₄	semidirect
25. #70170	C₅	direct (N × H)
51. C₂×C₃×C₅×C₈	C₂×C₄	semidirect
53. C₃×C₅×C₄⋊C₄	C₂×C₄	semidirect
68. C₂×#817	C₂×C₅	semidirect
69. #4984	C₂×C₅	semidirect
70. #4550	C₂×C₅	semidirect
71. #4529	C₂×C₅	semidirect
86. C₅×#102	Dic₃	semidirect
100. C₃×C₅×D₄	C₄⋊C₄	semidirect
137. C₃×#102	C₄×C₅	semidirect
162. C₂×C₅×C₈	C₂×Dic₃	semidirect
169. C₅×C₄⋊C₄	C₂×Dic₃	semidirect
221. C₂×C₃×C₈	C₂×C₄×C₅	semidirect
223. C₃×C₄⋊C₄	C₂×C₄×C₅	semidirect
246. C₅×D₄	C₄⋊Dic₃	semidirect
285. #102	C₅×Dic₃	semidirect
306. C₃×D₄	C₅×C₄⋊C₄	semidirect
375. C₂×C₈	C₂×C₅×Dic₃	semidirect
382. C₄⋊C₄	C₂×C₅×Dic₃	semidirect
386. C₃×C₅	#1864	semidirect
429. D₄	C₅×C₄⋊Dic₃	semidirect
462. C₅	#70170	direct (N × H)
486. C₃	C₅×#1864	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×D₄×Dic₃	2
C₂×C₃×C₅×#102	2
C₂×C₅×#832	2
C₂×C₅×#817	2
C₅×#4984	2
C₅×#4550	2
C₅×#4529	2
C₅×#1864	3
#70170	5

Subgroups — C5×#70170 #14300085

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#70170 #14300085