Subgroups — C₂×C₅×#4720 #14413820

Order 1920.

824 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#926	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#830	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×#815	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×Dic₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×Dic₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×C₈×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4720	C₂	1	8	yes	maximal, direct product factor
9	C₂×C₅×#433	—	3	1	no	maximal, Hall
10	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₂×C₅×#217	C₄	1	1	yes	characteristic
14	C₂×C₅×#217	C₄	1	1	yes	characteristic
15	C₅×#926	C₄	1	4	yes	—
16	C₅×#926	C₂²	1	4	yes	—
17	C₂×C₅×C₄⋊Dic₃	C₄	1	1	yes	characteristic
18	C₂×C₅×C₄⋊Dic₃	C₄	1	1	yes	characteristic
19	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
21	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
22	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
23	C₃×C₅×C₂²⋊C₈	C₂²	1	4	yes	—
24	C₅×#830	C₂²	1	4	yes	—
25	C₅×#815	C₂²	1	4	yes	complemented
26	C₅×Dic₃⋊C₈	C₂²	1	4	yes	complemented
27	C₅×Dic₃⋊C₈	C₂²	1	4	yes	complemented
28	C₅×C₈×Dic₃	C₂²	1	4	yes	complemented
29	C₂×#4720	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
30	C₂×C₅×#117	—	3	1	no	—
31	C₅×#433	—	3	8	no	—
32	C₂×C₅×C₄⋊C₈	—	3	1	no	—
33	C₂×C₅×C₄⋊C₈	—	3	1	no	—
34	C₂×C₅×C₂²⋊C₈	—	3	1	no	—
35	C₂×C₅×C₂²⋊C₈	D₃	1	1	yes	characteristic
36	C₂×C₅×#97	—	3	1	no	—
37	C₂×C₄×C₅×C₈	—	3	1	no	—
38	C₂⁴×C₃×C₅	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₃×C₄×C₅	—	2	2	no	—
40	C₂²×C₃×C₄×C₅	—	2	2	no	—
41	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
43	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
44	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
45	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
46	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
47	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
49	C₂×C₃×C₅×C₈	—	2	2	no	—
50	C₂×C₃×C₅×C₈	—	2	2	no	—
51	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
52	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
53	C₅×#217	C₂×C₄	1	4	yes	—
54	C₅×#217	C₂×C₄	1	4	yes	—
55	C₅×C₄⋊Dic₃	C₂×C₄	1	4	yes	—
56	C₅×C₄⋊Dic₃	C₂×C₄	1	4	yes	—
57	C₄×C₅×Dic₃	C₂×C₄	1	2	yes	—
58	C₄×C₅×Dic₃	C₂×C₄	1	2	yes	—
59	C₄×C₅×Dic₃	C₂³	1	2	yes	—
60	C₄×C₅×Dic₃	C₂³	1	2	yes	—
61	C₂×C₅×C₃⋊C₈	—	2	2	no	—
62	C₂×C₅×C₃⋊C₈	—	2	2	no	—
63	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
64	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
65	C₂×#926	C₂×C₅	1	1	yes	characteristic
66	C₂×C₃×C₂²⋊C₈	C₂×C₅	1	1	yes	characteristic
67	C₂×#830	C₂×C₅	1	1	yes	characteristic
68	C₂×#815	C₂×C₅	1	1	yes	characteristic, complemented
69	C₂×Dic₃⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
70	C₂×Dic₃⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
71	C₂×C₈×Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
72	#4720	C₂×C₅	1	8	yes	direct product factor
73	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
74	C₂²×C₅×C₈	—	3	1	no	—
75	C₂²×C₅×C₈	—	3	1	no	—
76	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
77	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
78	C₅×#117	—	3	4	no	—
79	C₅×#117	—	3	4	no	—
80	C₂×C₅×C₄⋊C₄	—	3	1	no	—
81	C₂×C₅×C₄⋊C₄	—	3	1	no	—
82	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
83	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
84	C₂×C₄²×C₅	—	3	1	no	—
85	C₂×C₄²×C₅	—	3	1	no	—
86	C₅×C₄⋊C₈	—	3	4	no	—
87	C₅×C₄⋊C₈	—	3	4	no	—
88	C₅×C₂²⋊C₈	—	3	4	no	—
89	C₅×C₂²⋊C₈	C₂×D₃	1	4	yes	—
90	C₅×#97	—	3	4	no	—
91	C₄×C₅×C₈	—	3	4	no	—
92	C₂×#433	—	3	1	no	Sylow
93	C₂³×C₃×C₅	—	2	2	no	—
94	C₂³×C₃×C₅	—	2	2	no	—
95	C₂³×C₃×C₅	—	2	2	no	—
96	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
97	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₃×C₄×C₅	—	2	2	no	—
99	C₂×C₃×C₄×C₅	—	2	4	no	—
100	C₂×C₃×C₄×C₅	—	2	2	no	—
101	C₂×C₃×C₄×C₅	—	2	2	no	—
102	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
103	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₃×C₄×C₅	#41	1	2	yes	—
105	C₂×C₃×C₄×C₅	#41	1	2	yes	—
106	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
107	C₂×C₅×Dic₃	—	2	2	no	—
108	C₂×C₅×Dic₃	—	2	2	no	—
109	C₂×C₅×Dic₃	—	2	2	no	—
110	C₂×C₅×Dic₃	—	2	2	no	—
111	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
112	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
113	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
114	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
115	C₃×C₅×C₈	—	2	2	no	—
116	C₃×C₅×C₈	—	2	2	no	—
117	C₅×C₃⋊C₈	—	2	2	no	—
118	C₅×C₃⋊C₈	—	2	2	no	—
119	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
120	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
121	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
122	C₂×#217	C₄×C₅	1	1	yes	characteristic
123	C₂×#217	C₄×C₅	1	1	yes	characteristic
124	#926	C₄×C₅	1	4	yes	—
125	#926	C₂²×C₅	1	4	yes	—
126	C₂×C₄⋊Dic₃	C₄×C₅	1	1	yes	characteristic
127	C₂×C₄⋊Dic₃	C₄×C₅	1	1	yes	characteristic
128	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
129	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
130	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
131	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
132	C₃×C₂²⋊C₈	C₂²×C₅	1	4	yes	—
133	#830	C₂²×C₅	1	4	yes	—
134	#815	C₂²×C₅	1	4	yes	complemented
135	Dic₃⋊C₈	C₂²×C₅	1	4	yes	complemented
136	Dic₃⋊C₈	C₂²×C₅	1	4	yes	complemented
137	C₈×Dic₃	C₂²×C₅	1	4	yes	complemented
138	C₂⁴×C₅	C₄×D₃	1	1	yes	characteristic
139	C₂²×C₄×C₅	—	2	2	no	—
140	C₂²×C₄×C₅	—	2	2	no	—
141	C₂²×C₄×C₅	—	3	1	no	—
142	C₂²×C₄×C₅	—	3	1	no	—
143	C₂²×C₄×C₅	—	3	1	no	—
144	C₂²×C₄×C₅	—	3	1	no	—
145	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
146	C₂²×C₄×C₅	C₄×D₃	1	2	yes	—
147	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
148	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
149	C₂×C₅×C₈	—	2	2	no	—
150	C₂×C₅×C₈	—	2	2	no	—
151	C₂×C₅×C₈	—	3	2	no	—
152	C₂×C₅×C₈	—	3	2	no	—
153	C₂×C₅×C₈	—	6	2	no	—
154	C₂×C₅×C₈	—	6	2	no	—
155	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
156	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
157	C₅×C₄⋊C₄	—	3	4	no	—
158	C₅×C₄⋊C₄	—	3	4	no	—
159	C₅×C₂²⋊C₄	—	3	4	no	—
160	C₅×C₂²⋊C₄	—	3	4	no	—
161	C₄²×C₅	—	3	2	no	—
162	C₄²×C₅	—	3	2	no	—
163	C₄²×C₅	—	3	2	no	—
164	C₄²×C₅	—	3	2	no	—
165	C₂×#117	—	3	1	no	—
166	#433	—	3	8	no	—
167	C₂×C₄⋊C₈	—	3	1	no	—
168	C₂×C₄⋊C₈	—	3	1	no	—
169	C₂×C₂²⋊C₈	—	3	1	no	—
170	C₂×C₂²⋊C₈	C₅×D₃	1	1	yes	characteristic
171	C₂×#97	—	3	1	no	—
172	C₂×C₄×C₈	—	3	1	no	—
173	C₂²×C₃×C₅	—	2	2	no	—
174	C₂²×C₃×C₅	—	2	2	no	—
175	C₂²×C₃×C₅	—	2	2	no	—
176	C₂²×C₃×C₅	—	4	4	no	—
177	C₂²×C₃×C₅	#117	1	2	yes	—
178	C₂²×C₃×C₅	#131	1	2	yes	—
179	C₂²×C₃×C₅	#131	1	2	yes	—
180	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
181	C₃×C₄×C₅	—	2	2	no	—
182	C₃×C₄×C₅	#117	1	2	yes	—
183	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
184	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
185	C₅×Dic₃	—	2	2	no	—
186	C₅×Dic₃	—	2	2	no	—
187	C₅×Dic₃	—	2	2	no	—
188	C₅×Dic₃	—	2	2	no	—
189	C₂⁴×C₃	C₂×C₄×C₅	1	1	yes	characteristic
190	C₂²×C₃×C₄	—	2	2	no	—
191	C₂²×C₃×C₄	—	2	2	no	—
192	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
193	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
194	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
195	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
196	C₂²×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
197	C₂²×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
198	C₂²×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
199	C₂²×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
200	C₂×C₃×C₈	—	2	2	no	—
201	C₂×C₃×C₈	—	2	2	no	—
202	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
203	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
204	#217	C₂×C₄×C₅	1	4	yes	—
205	#217	C₂×C₄×C₅	1	4	yes	—
206	C₄⋊Dic₃	C₂×C₄×C₅	1	4	yes	—
207	C₄⋊Dic₃	C₂×C₄×C₅	1	4	yes	—
208	C₄×Dic₃	C₂×C₄×C₅	1	2	yes	—
209	C₄×Dic₃	C₂×C₄×C₅	1	2	yes	—
210	C₄×Dic₃	C₂³×C₅	1	2	yes	—
211	C₄×Dic₃	C₂³×C₅	1	2	yes	—
212	C₂×C₃⋊C₈	—	2	2	no	—
213	C₂×C₃⋊C₈	—	2	2	no	—
214	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
215	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
216	C₂³×C₅	—	2	2	no	—
217	C₂³×C₅	—	2	2	no	—
218	C₂³×C₅	—	2	2	no	—
219	C₂³×C₅	C₂×C₄×D₃	1	2	yes	—
220	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
221	C₂×C₄×C₅	—	2	2	no	—
222	C₂×C₄×C₅	—	2	4	no	—
223	C₂×C₄×C₅	—	2	2	no	—
224	C₂×C₄×C₅	—	2	2	no	—
225	C₂×C₄×C₅	—	3	2	no	—
226	C₂×C₄×C₅	—	3	2	no	—
227	C₂×C₄×C₅	—	3	2	no	—
228	C₂×C₄×C₅	—	3	2	no	—
229	C₂×C₄×C₅	—	6	2	no	—
230	C₂×C₄×C₅	—	6	2	no	—
231	C₂×C₄×C₅	—	6	2	no	—
232	C₂×C₄×C₅	—	6	2	no	—
233	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
234	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
235	C₂×C₄×C₅	#237	1	2	yes	—
236	C₂×C₄×C₅	#237	1	2	yes	—
237	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
238	C₅×C₈	—	2	2	no	—
239	C₅×C₈	—	2	2	no	—
240	C₅×C₈	—	6	2	no	—
241	C₅×C₈	—	6	2	no	—
242	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
243	C₂²×C₈	—	3	1	no	—
244	C₂²×C₈	—	3	1	no	—
245	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
246	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
247	#117	—	3	4	no	—
248	#117	—	3	4	no	—
249	C₂×C₄⋊C₄	—	3	1	no	—
250	C₂×C₄⋊C₄	—	3	1	no	—
251	C₂×C₂²⋊C₄	—	3	1	no	—
252	C₂×C₂²⋊C₄	—	3	1	no	—
253	C₂×C₄²	—	3	1	no	—
254	C₂×C₄²	—	3	1	no	—
255	C₄⋊C₈	—	3	4	no	—
256	C₄⋊C₈	—	3	4	no	—
257	C₂²⋊C₈	—	3	4	no	—
258	C₂²⋊C₈	C₂×C₅×D₃	1	4	yes	—
259	#97	—	3	4	no	—
260	C₄×C₈	—	3	4	no	—
261	C₂×C₃×C₅	—	4	2	no	—
262	C₂×C₃×C₅	#433	1	4	yes	complemented
263	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
264	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
265	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
266	C₂³×C₃	—	2	2	no	—
267	C₂³×C₃	—	2	2	no	—
268	C₂³×C₃	—	2	2	no	—
269	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
270	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
271	C₂×C₃×C₄	—	2	2	no	—
272	C₂×C₃×C₄	—	2	4	no	—
273	C₂×C₃×C₄	—	2	2	no	—
274	C₂×C₃×C₄	—	2	2	no	—
275	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
276	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
277	C₂×C₃×C₄	C₅×#41	1	2	yes	—
278	C₂×C₃×C₄	C₅×#41	1	2	yes	—
279	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
280	C₂×Dic₃	—	2	2	no	—
281	C₂×Dic₃	—	2	2	no	—
282	C₂×Dic₃	—	2	2	no	—
283	C₂×Dic₃	—	2	2	no	—
284	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
285	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
286	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
287	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
288	C₃×C₈	—	2	2	no	—
289	C₃×C₈	—	2	2	no	—
290	C₃⋊C₈	—	2	2	no	—
291	C₃⋊C₈	—	2	2	no	—
292	C₂²×C₅	—	2	2	no	—
293	C₂²×C₅	—	2	2	no	—
294	C₂²×C₅	—	2	2	no	—
295	C₂²×C₅	—	4	4	no	—
296	C₂²×C₅	#877	1	2	yes	—
297	C₂²×C₅	#901	1	2	yes	—
298	C₂²×C₅	#907	1	2	yes	—
299	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
300	C₄×C₅	—	2	2	no	—
301	C₄×C₅	—	6	2	no	—
302	C₄×C₅	—	6	2	no	—
303	C₄×C₅	—	6	2	no	—
304	C₄×C₅	—	6	2	no	—
305	C₄×C₅	#877	1	2	yes	—
306	C₄×C₅	C₂×#237	1	1	yes	characteristic
307	C₄×C₅	C₂×#237	1	1	yes	characteristic
308	C₂⁴	C₄×C₅×D₃	1	1	yes	characteristic
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	3	1	no	—
312	C₂²×C₄	—	3	1	no	—
313	C₂²×C₄	—	3	1	no	—
314	C₂²×C₄	—	3	1	no	—
315	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
316	C₂²×C₄	C₄×C₅×D₃	1	2	yes	—
317	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
318	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	3	2	no	—
322	C₂×C₈	—	3	2	no	—
323	C₂×C₈	—	6	2	no	—
324	C₂×C₈	—	6	2	no	—
325	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
326	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
327	C₄⋊C₄	—	3	4	no	—
328	C₄⋊C₄	—	3	4	no	—
329	C₂²⋊C₄	—	3	4	no	—
330	C₂²⋊C₄	—	3	4	no	—
331	C₄²	—	3	2	no	—
332	C₄²	—	3	2	no	—
333	C₄²	—	3	2	no	—
334	C₄²	—	3	2	no	—
335	C₃×C₅	C₂×#433	1	1	yes	characteristic, complemented, Hall
336	C₂²×C₃	—	2	2	no	—
337	C₂²×C₃	—	2	2	no	—
338	C₂²×C₃	—	2	2	no	—
339	C₂²×C₃	—	4	4	no	—
340	C₂²×C₃	C₅×#117	1	2	yes	—
341	C₂²×C₃	C₅×#131	1	2	yes	—
342	C₂²×C₃	C₅×#131	1	2	yes	—
343	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
344	C₃×C₄	—	2	2	no	—
345	C₃×C₄	C₅×#117	1	2	yes	—
346	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
347	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
348	Dic₃	—	2	2	no	—
349	Dic₃	—	2	2	no	—
350	Dic₃	—	2	2	no	—
351	Dic₃	—	2	2	no	—
352	C₂×C₅	—	4	2	no	—
353	C₂×C₅	#4720	1	4	yes	direct product factor
354	C₂×C₅	C₂×#877	1	1	yes	characteristic
355	C₂×C₅	C₂×#901	1	1	yes	characteristic
356	C₂×C₅	C₂×#907	1	1	yes	characteristic
357	C₂³	—	2	2	no	—
358	C₂³	—	2	2	no	—
359	C₂³	—	2	2	no	—
360	C₂³	C₂×C₄×C₅×D₃	1	2	yes	—
361	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	3	2	no	—
367	C₂×C₄	—	3	2	no	—
368	C₂×C₄	—	3	2	no	—
369	C₂×C₄	—	3	2	no	—
370	C₂×C₄	—	6	2	no	—
371	C₂×C₄	—	6	2	no	—
372	C₂×C₄	—	6	2	no	—
373	C₂×C₄	—	6	2	no	—
374	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
375	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
376	C₂×C₄	C₅×#237	1	2	yes	—
377	C₂×C₄	C₅×#237	1	2	yes	—
378	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
379	C₈	—	2	2	no	—
380	C₈	—	2	2	no	—
381	C₈	—	6	2	no	—
382	C₈	—	6	2	no	—
383	C₂×C₃	—	4	2	no	—
384	C₂×C₃	C₅×#433	1	4	yes	complemented
385	C₂×C₃	C₂×C₅×#117	1	1	yes	characteristic
386	C₂×C₃	C₂×C₅×#131	1	1	yes	characteristic
387	C₂×C₃	C₂×C₅×#131	1	1	yes	characteristic
388	C₅	C₂×#4720	1	1	yes	characteristic, direct product factor, Sylow
389	C₂²	—	2	2	no	—
390	C₂²	—	2	2	no	—
391	C₂²	—	2	2	no	—
392	C₂²	—	4	4	no	—
393	C₂²	C₅×#877	1	2	yes	—
394	C₂²	C₅×#901	1	2	yes	—
395	C₂²	C₅×#907	1	2	yes	—
396	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
397	C₄	—	2	2	no	—
398	C₄	—	6	2	no	—
399	C₄	—	6	2	no	—
400	C₄	—	6	2	no	—
401	C₄	—	6	2	no	—
402	C₄	C₅×#877	1	2	yes	—
403	C₄	C₂×C₅×#237	1	1	yes	characteristic
404	C₄	C₂×C₅×#237	1	1	yes	characteristic
405	C₃	C₂×C₅×#433	1	1	yes	characteristic, complemented, Sylow
406	C₂	—	4	2	no	—
407	C₂	C₅×#4720	1	4	yes	direct product factor
408	C₂	C₂×C₅×#877	1	1	yes	characteristic
409	C₂	C₂×C₅×#901	1	1	yes	characteristic
410	C₂	C₂×C₅×#907	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅	C₂²×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂×C₃×C₅×C₂²⋊C₈	C₂
socle	C₂³×C₃×C₅	C₂²×C₄
prime radical	C₂⁴×C₃×C₅	C₂×C₄
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₂×C₅×C₂²⋊C₈	D₃
hypocenter	C₃	C₂×C₅×#433
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×C₂²⋊C₈

Complements

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

N	H ≅ G/N	type
4. C₂×C₅×#815	C₂	semidirect
5. C₂×C₅×Dic₃⋊C₈	C₂	semidirect
6. C₂×C₅×Dic₃⋊C₈	C₂	semidirect
7. C₂×C₅×C₈×Dic₃	C₂	semidirect
8. C₅×#4720	C₂	direct (N × H)
25. C₅×#815	C₂²	semidirect
26. C₅×Dic₃⋊C₈	C₂²	semidirect
27. C₅×Dic₃⋊C₈	C₂²	semidirect
28. C₅×C₈×Dic₃	C₂²	semidirect
29. C₂×#4720	C₅	direct (N × H)
68. C₂×#815	C₂×C₅	semidirect
69. C₂×Dic₃⋊C₈	C₂×C₅	semidirect
70. C₂×Dic₃⋊C₈	C₂×C₅	semidirect
71. C₂×C₈×Dic₃	C₂×C₅	semidirect
72. #4720	C₂×C₅	direct (N × H)
134. #815	C₂²×C₅	semidirect
135. Dic₃⋊C₈	C₂²×C₅	semidirect
136. Dic₃⋊C₈	C₂²×C₅	semidirect
137. C₈×Dic₃	C₂²×C₅	semidirect
262. C₂×C₃×C₅	#433	semidirect
335. C₃×C₅	C₂×#433	semidirect
353. C₂×C₅	#4720	direct (N × H)
384. C₂×C₃	C₅×#433	semidirect
388. C₅	C₂×#4720	direct (N × H)
405. C₃	C₂×C₅×#433	semidirect
407. C₂	C₅×#4720	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×#926	2
C₂×C₃×C₅×C₂²⋊C₈	2
C₂×C₅×#830	2
C₂×C₅×#815	2
C₂×C₅×Dic₃⋊C₈	2
C₂×C₅×C₈×Dic₃	2
C₅×#4720	2
C₂×C₅×#433	3
C₂×#4720	5

Subgroups — C2×C5×#4720 #14413820

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#4720 #14413820