Subgroups — C₅×#70476 #14297464

Order 1920.

624 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#872	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×(C₂×D₃)⋊C₈	C₂	1	2	yes	maximal
4	C₂×C₅×C₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4550	C₂	1	2	yes	maximal, complemented
6	C₅×#1798	—	3	1	no	maximal, Hall
7	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
8	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
9	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
10	C₂×C₅×(C₂×D₃)⋊C₄	C₄	1	1	yes	characteristic
11	C₂×C₅×(C₂×D₃)⋊C₄	C₄	1	1	yes	characteristic
12	C₂×C₅×Dic₃⋊C₄	C₄	1	1	yes	characteristic
13	C₂×C₅×Dic₃⋊C₄	C₄	1	1	yes	characteristic
14	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
15	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	—
16	C₅×#872	—	2	2	no	—
17	C₅×#872	—	2	2	no	—
18	C₃×C₅×C₄⋊C₈	—	2	2	no	—
19	C₅×(C₂×D₃)⋊C₈	—	2	4	no	—
20	C₅×C₄⋊(C₃⋊C₈)	—	2	2	no	—
21	#70476	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
22	C₂×C₅×#117	—	3	1	no	—
23	C₂×C₅×C₄⋊C₈	—	3	1	no	—
24	C₂×C₅×C₄⋊C₈	D₃	1	1	yes	characteristic, complemented
25	C₂×C₅×C₂²⋊C₈	—	3	2	no	—
26	C₅×#336	—	3	2	no	—
27	C₂³×C₅×D₃	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
29	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
31	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄×C₅×D₃	—	2	1	no	—
35	C₂×C₄×C₅×D₃	—	2	1	no	—
36	C₂×C₄×C₅×D₃	—	2	1	no	—
37	C₂×C₄×C₅×D₃	—	2	1	no	—
38	C₂×C₄×C₅×D₃	D₄	1	2	yes	—
39	C₂×C₄×C₅×D₃	Q₈	1	2	yes	—
40	C₂×C₃×C₅×C₈	—	2	2	no	—
41	C₂×C₃×C₅×C₈	—	2	2	no	—
42	C₂×C₃×C₅×C₈	—	2	2	no	—
43	C₃×C₄²×C₅	D₄	1	2	yes	—
44	C₃×C₄²×C₅	D₄	1	2	yes	—
45	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
46	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
47	C₅×Dic₃⋊C₄	—	2	2	no	—
48	C₅×Dic₃⋊C₄	—	2	2	no	—
49	C₄×C₅×Dic₃	—	2	1	no	—
50	C₄×C₅×Dic₃	—	2	1	no	—
51	C₂×C₅×C₃⋊C₈	—	2	2	no	—
52	C₂×C₅×C₃⋊C₈	—	2	2	no	—
53	C₂×C₅×C₃⋊C₈	—	2	2	no	—
54	C₂×#872	C₂×C₅	1	1	yes	characteristic
55	C₂×C₃×C₄⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
56	C₂×(C₂×D₃)⋊C₈	C₂×C₅	1	2	yes	—
57	C₂×C₄⋊(C₃⋊C₈)	C₂×C₅	1	1	yes	characteristic, complemented
58	#4550	C₂×C₅	1	2	yes	complemented
59	C₂³×C₄×C₅	—	3	1	no	—
60	C₂²×C₅×C₈	—	3	2	no	—
61	C₂²×C₅×C₈	C₂×D₃	1	2	yes	—
62	C₅×#117	—	6	2	no	—
63	C₅×#117	—	6	2	no	—
64	C₂×C₅×C₄⋊C₄	—	3	1	no	—
65	C₂×C₅×C₄⋊C₄	—	3	1	no	—
66	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
67	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
68	C₂×C₄²×C₅	—	3	1	no	—
69	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
70	C₅×C₄⋊C₈	—	2	2	no	—
71	C₅×C₄⋊C₈	—	6	2	no	—
72	C₅×C₂²⋊C₈	—	6	4	no	—
73	#1798	—	3	1	no	Sylow
74	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
75	C₂²×C₅×D₃	—	2	1	no	—
76	C₂²×C₅×D₃	—	2	1	no	—
77	C₂²×C₅×D₃	—	2	2	no	—
78	C₂²×C₅×D₃	—	2	2	no	—
79	C₂²×C₅×D₃	C₄⋊C₄	1	2	yes	—
80	C₂×C₃×C₄×C₅	—	2	2	no	—
81	C₂×C₃×C₄×C₅	—	2	2	no	—
82	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
83	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
84	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
85	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
86	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
87	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
88	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
89	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
90	C₂×C₅×Dic₃	—	2	1	no	—
91	C₂×C₅×Dic₃	—	2	1	no	—
92	C₂×C₅×Dic₃	—	2	1	no	—
93	C₂×C₅×Dic₃	—	2	1	no	—
94	C₂×C₅×Dic₃	—	2	2	no	—
95	C₂×C₅×Dic₃	—	2	2	no	—
96	C₂×C₅×Dic₃	C₄⋊C₄	1	2	yes	—
97	C₄×C₅×D₃	—	2	2	no	—
98	C₄×C₅×D₃	—	2	2	no	—
99	C₄×C₅×D₃	—	2	2	no	—
100	C₄×C₅×D₃	—	2	2	no	—
101	C₃×C₅×C₈	—	4	2	no	—
102	C₅×C₃⋊C₈	—	4	2	no	—
103	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
104	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
105	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
106	C₂×(C₂×D₃)⋊C₄	C₄×C₅	1	1	yes	characteristic
107	C₂×(C₂×D₃)⋊C₄	C₄×C₅	1	1	yes	characteristic
108	C₂×Dic₃⋊C₄	C₄×C₅	1	1	yes	characteristic
109	C₂×Dic₃⋊C₄	C₄×C₅	1	1	yes	characteristic
110	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
111	C₂²×C₃⋊C₈	C₂²×C₅	1	2	yes	—
112	#872	—	2	2	no	—
113	#872	—	2	2	no	—
114	C₃×C₄⋊C₈	—	2	2	no	—
115	(C₂×D₃)⋊C₈	—	2	4	no	—
116	C₄⋊(C₃⋊C₈)	—	2	2	no	—
117	C₂⁴×C₅	—	3	1	no	—
118	C₂²×C₄×C₅	—	3	1	no	—
119	C₂²×C₄×C₅	—	3	2	no	—
120	C₂²×C₄×C₅	—	3	2	no	—
121	C₂²×C₄×C₅	—	3	1	no	—
122	C₂²×C₄×C₅	—	3	1	no	—
123	C₂²×C₄×C₅	—	6	1	no	—
124	C₂²×C₄×C₅	—	6	1	no	—
125	C₂²×C₄×C₅	—	6	1	no	—
126	C₂²×C₄×C₅	—	6	1	no	—
127	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
128	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
129	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
130	C₂×C₅×C₈	—	2	2	no	—
131	C₂×C₅×C₈	—	2	2	no	—
132	C₂×C₅×C₈	—	2	2	no	—
133	C₂×C₅×C₈	—	6	2	no	—
134	C₂×C₅×C₈	—	6	2	no	—
135	C₂×C₅×C₈	—	6	2	no	—
136	C₅×C₄⋊C₄	—	6	2	no	—
137	C₅×C₄⋊C₄	—	6	2	no	—
138	C₅×C₂²⋊C₄	—	6	2	no	—
139	C₅×C₂²⋊C₄	—	6	2	no	—
140	C₄²×C₅	—	6	1	no	—
141	C₄²×C₅	—	6	1	no	—
142	C₄²×C₅	D₁₂	1	2	yes	—
143	C₄²×C₅	#67	1	2	yes	—
144	C₂×#117	—	3	1	no	—
145	C₂×C₄⋊C₈	—	3	1	no	—
146	C₂×C₄⋊C₈	C₅×D₃	1	1	yes	characteristic, complemented
147	C₂×C₂²⋊C₈	—	3	2	no	—
148	#336	—	3	2	no	—
149	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
150	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₂²×C₃×C₅	#117	1	1	yes	characteristic
152	C₂²×C₃×C₅	#131	1	2	yes	—
153	C₂²×C₃×C₅	#131	1	2	yes	—
154	C₂×C₅×D₃	—	2	2	no	—
155	C₂×C₅×D₃	—	2	4	no	—
156	C₂×C₅×D₃	—	4	1	no	—
157	C₂×C₅×D₃	—	4	1	no	—
158	C₂×C₅×D₃	—	4	2	no	—
159	C₃×C₄×C₅	—	2	2	no	—
160	C₃×C₄×C₅	—	2	2	no	—
161	C₃×C₄×C₅	#121	1	1	yes	characteristic
162	C₃×C₄×C₅	#121	1	1	yes	characteristic
163	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
164	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
165	C₅×Dic₃	—	2	2	no	—
166	C₅×Dic₃	—	4	1	no	—
167	C₅×Dic₃	—	4	1	no	—
168	C₂³×D₃	C₂×C₄×C₅	1	1	yes	characteristic
169	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
170	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
171	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
172	C₂²×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
173	C₂²×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
174	C₂²×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
175	C₂×C₄×D₃	—	2	1	no	—
176	C₂×C₄×D₃	—	2	1	no	—
177	C₂×C₄×D₃	—	2	1	no	—
178	C₂×C₄×D₃	—	2	1	no	—
179	C₂×C₄×D₃	C₅×D₄	1	2	yes	—
180	C₂×C₄×D₃	C₅×Q₈	1	2	yes	—
181	C₂×C₃×C₈	—	2	2	no	—
182	C₂×C₃×C₈	—	2	2	no	—
183	C₂×C₃×C₈	—	2	2	no	—
184	C₃×C₄²	C₅×D₄	1	2	yes	—
185	C₃×C₄²	C₅×D₄	1	2	yes	—
186	(C₂×D₃)⋊C₄	—	2	2	no	—
187	(C₂×D₃)⋊C₄	—	2	2	no	—
188	Dic₃⋊C₄	—	2	2	no	—
189	Dic₃⋊C₄	—	2	2	no	—
190	C₄×Dic₃	—	2	1	no	—
191	C₄×Dic₃	—	2	1	no	—
192	C₂×C₃⋊C₈	—	2	2	no	—
193	C₂×C₃⋊C₈	—	2	2	no	—
194	C₂×C₃⋊C₈	—	2	2	no	—
195	C₂³×C₅	—	3	2	no	—
196	C₂³×C₅	—	6	1	no	—
197	C₂³×C₅	—	6	2	no	—
198	C₂³×C₅	—	6	2	no	—
199	C₂³×C₅	—	6	1	no	—
200	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
201	C₂×C₄×C₅	—	2	2	no	—
202	C₂×C₄×C₅	—	2	2	no	—
203	C₂×C₄×C₅	—	3	2	no	—
204	C₂×C₄×C₅	—	6	1	no	—
205	C₂×C₄×C₅	—	6	1	no	—
206	C₂×C₄×C₅	—	6	2	no	—
207	C₂×C₄×C₅	—	6	2	no	—
208	C₂×C₄×C₅	—	6	2	no	—
209	C₂×C₄×C₅	—	6	2	no	—
210	C₂×C₄×C₅	—	6	2	no	—
211	C₂×C₄×C₅	—	6	2	no	—
212	C₂×C₄×C₅	—	6	1	no	—
213	C₂×C₄×C₅	—	6	1	no	—
214	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	2	yes	—
215	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	2	yes	—
216	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
217	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
218	C₂×C₄×C₅	#237	1	1	yes	characteristic
219	C₂×C₄×C₅	D₃×Q₈	1	1	yes	characteristic
220	C₂×C₄×C₅	#239	1	1	yes	characteristic
221	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
222	C₅×C₈	—	4	2	no	—
223	C₅×C₈	—	12	2	no	—
224	C₂³×C₄	—	3	1	no	—
225	C₂²×C₈	—	3	2	no	—
226	C₂²×C₈	C₂×C₅×D₃	1	2	yes	—
227	#117	—	6	2	no	—
228	#117	—	6	2	no	—
229	C₂×C₄⋊C₄	—	3	1	no	—
230	C₂×C₄⋊C₄	—	3	1	no	—
231	C₂×C₂²⋊C₄	—	3	1	no	—
232	C₂×C₂²⋊C₄	—	3	1	no	—
233	C₂×C₄²	—	3	1	no	—
234	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
235	C₄⋊C₈	—	2	2	no	—
236	C₄⋊C₈	—	6	2	no	—
237	C₂²⋊C₈	—	6	4	no	—
238	C₂×C₃×C₅	#380	1	1	yes	characteristic
239	C₂×C₃×C₅	#408	1	1	yes	characteristic
240	C₂×C₃×C₅	#408	1	1	yes	characteristic
241	C₂×C₃×C₅	#424	1	2	yes	—
242	C₂×C₃×C₅	#433	1	2	yes	—
243	C₅×D₃	—	4	2	no	—
244	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
245	C₂²×D₃	—	2	1	no	—
246	C₂²×D₃	—	2	1	no	—
247	C₂²×D₃	—	2	2	no	—
248	C₂²×D₃	—	2	2	no	—
249	C₂²×D₃	C₅×C₄⋊C₄	1	2	yes	—
250	C₂×C₃×C₄	—	2	2	no	—
251	C₂×C₃×C₄	—	2	2	no	—
252	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	2	yes	—
253	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	2	yes	—
254	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
255	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
256	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
257	C₂×C₃×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
258	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
259	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
260	C₂×Dic₃	—	2	1	no	—
261	C₂×Dic₃	—	2	1	no	—
262	C₂×Dic₃	—	2	1	no	—
263	C₂×Dic₃	—	2	1	no	—
264	C₂×Dic₃	—	2	2	no	—
265	C₂×Dic₃	—	2	2	no	—
266	C₂×Dic₃	C₅×C₄⋊C₄	1	2	yes	—
267	C₄×D₃	—	2	2	no	—
268	C₄×D₃	—	2	2	no	—
269	C₄×D₃	—	2	2	no	—
270	C₄×D₃	—	2	2	no	—
271	C₃×C₈	—	4	2	no	—
272	C₃⋊C₈	—	4	2	no	—
273	C₂²×C₅	—	6	2	no	—
274	C₂²×C₅	—	6	4	no	—
275	C₂²×C₅	—	12	1	no	—
276	C₂²×C₅	—	12	2	no	—
277	C₂²×C₅	—	12	1	no	—
278	C₂²×C₅	D₃×C₄⋊C₄	1	1	yes	characteristic
279	C₂²×C₅	#892	1	1	yes	characteristic
280	C₂²×C₅	#901	1	2	yes	—
281	C₂²×C₅	#907	1	2	yes	—
282	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
283	C₄×C₅	—	2	2	no	—
284	C₄×C₅	—	2	2	no	—
285	C₄×C₅	—	6	2	no	—
286	C₄×C₅	—	12	1	no	—
287	C₄×C₅	—	12	1	no	—
288	C₄×C₅	#895	1	1	yes	characteristic
289	C₄×C₅	#897	1	1	yes	characteristic
290	C₄×C₅	#938	1	1	yes	characteristic
291	C₄×C₅	#946	1	1	yes	characteristic
292	C₂⁴	—	3	1	no	—
293	C₂²×C₄	—	3	1	no	—
294	C₂²×C₄	—	3	2	no	—
295	C₂²×C₄	—	3	2	no	—
296	C₂²×C₄	—	3	1	no	—
297	C₂²×C₄	—	3	1	no	—
298	C₂²×C₄	—	6	1	no	—
299	C₂²×C₄	—	6	1	no	—
300	C₂²×C₄	—	6	1	no	—
301	C₂²×C₄	—	6	1	no	—
302	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
303	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
304	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	6	2	no	—
309	C₂×C₈	—	6	2	no	—
310	C₂×C₈	—	6	2	no	—
311	C₄⋊C₄	—	6	2	no	—
312	C₄⋊C₄	—	6	2	no	—
313	C₂²⋊C₄	—	6	2	no	—
314	C₂²⋊C₄	—	6	2	no	—
315	C₄²	—	6	1	no	—
316	C₄²	—	6	1	no	—
317	C₄²	C₅×D₁₂	1	2	yes	—
318	C₄²	C₅×#67	1	2	yes	—
319	C₃×C₅	#1798	1	1	yes	characteristic, complemented, Hall
320	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
321	C₂²×C₃	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
322	C₂²×C₃	C₅×#117	1	1	yes	characteristic
323	C₂²×C₃	C₅×#131	1	2	yes	—
324	C₂²×C₃	C₅×#131	1	2	yes	—
325	C₂×D₃	—	2	2	no	—
326	C₂×D₃	—	2	4	no	—
327	C₂×D₃	—	4	1	no	—
328	C₂×D₃	—	4	1	no	—
329	C₂×D₃	—	4	2	no	—
330	C₃×C₄	—	2	2	no	—
331	C₃×C₄	—	2	2	no	—
332	C₃×C₄	C₅×#121	1	1	yes	characteristic
333	C₃×C₄	C₅×#121	1	1	yes	characteristic
334	C₃×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
335	C₃×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
336	Dic₃	—	2	2	no	—
337	Dic₃	—	4	1	no	—
338	Dic₃	—	4	1	no	—
339	C₂×C₅	—	12	2	no	—
340	C₂×C₅	#4839	1	2	yes	—
341	C₂×C₅	#4840	1	2	yes	—
342	C₂×C₅	#4987	1	1	yes	characteristic
343	C₂×C₅	#5110	1	1	yes	characteristic
344	C₂×C₅	#5129	1	1	yes	characteristic
345	C₂³	—	3	2	no	—
346	C₂³	—	6	1	no	—
347	C₂³	—	6	2	no	—
348	C₂³	—	6	2	no	—
349	C₂³	—	6	1	no	—
350	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	3	2	no	—
354	C₂×C₄	—	6	1	no	—
355	C₂×C₄	—	6	1	no	—
356	C₂×C₄	—	6	2	no	—
357	C₂×C₄	—	6	2	no	—
358	C₂×C₄	—	6	2	no	—
359	C₂×C₄	—	6	2	no	—
360	C₂×C₄	—	6	2	no	—
361	C₂×C₄	—	6	2	no	—
362	C₂×C₄	—	6	1	no	—
363	C₂×C₄	—	6	1	no	—
364	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	2	yes	—
365	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	2	yes	—
366	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
367	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
368	C₂×C₄	C₅×#237	1	1	yes	characteristic
369	C₂×C₄	C₅×D₃×Q₈	1	1	yes	characteristic
370	C₂×C₄	C₅×#239	1	1	yes	characteristic
371	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
372	C₈	—	4	2	no	—
373	C₈	—	12	2	no	—
374	C₂×C₃	C₅×#380	1	1	yes	characteristic
375	C₂×C₃	C₅×#408	1	1	yes	characteristic
376	C₂×C₃	C₅×#408	1	1	yes	characteristic
377	C₂×C₃	C₅×#424	1	2	yes	—
378	C₂×C₃	C₅×#433	1	2	yes	—
379	D₃	—	4	2	no	—
380	C₅	#70476	1	1	yes	characteristic, direct product factor, Sylow
381	C₂²	—	6	2	no	—
382	C₂²	—	6	4	no	—
383	C₂²	—	12	2	no	—
384	C₂²	—	12	1	no	—
385	C₂²	—	12	1	no	—
386	C₂²	C₅×D₃×C₄⋊C₄	1	1	yes	characteristic
387	C₂²	C₅×#892	1	1	yes	characteristic
388	C₂²	C₅×#901	1	2	yes	—
389	C₂²	C₅×#907	1	2	yes	—
390	C₂²	C₂×C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
391	C₄	—	2	2	no	—
392	C₄	—	2	2	no	—
393	C₄	—	6	2	no	—
394	C₄	—	12	1	no	—
395	C₄	—	12	1	no	—
396	C₄	C₅×#895	1	1	yes	characteristic
397	C₄	C₅×#897	1	1	yes	characteristic
398	C₄	C₅×#938	1	1	yes	characteristic
399	C₄	C₅×#946	1	1	yes	characteristic
400	C₃	C₅×#1798	1	1	yes	characteristic, complemented, Sylow
401	C₂	—	12	2	no	—
402	C₂	C₅×#4839	1	2	yes	—
403	C₂	C₅×#4840	1	2	yes	—
404	C₂	C₅×#4987	1	1	yes	characteristic
405	C₂	C₅×#5110	1	1	yes	characteristic
406	C₂	C₅×#5129	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅	C₂²×D₃
commutator	C₂³×C₃	C₂²×C₄×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₂×C₃×C₅×C₄⋊C₈	C₂
socle	C₂³×C₃×C₅	C₂²×C₄
prime radical	C₂³×C₅×D₃	C₂×C₄
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₂×C₅×C₄⋊C₈	D₃
hypocenter	C₃	C₅×#1798
LCS	G ▷ C₂³×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₅×C₄⋊C₈	C₂	semidirect
4. C₂×C₅×C₄⋊(C₃⋊C₈)	C₂	semidirect
5. C₅×#4550	C₂	semidirect
21. #70476	C₅	direct (N × H)
24. C₂×C₅×C₄⋊C₈	D₃	semidirect
55. C₂×C₃×C₄⋊C₈	C₂×C₅	semidirect
57. C₂×C₄⋊(C₃⋊C₈)	C₂×C₅	semidirect
58. #4550	C₂×C₅	semidirect
146. C₂×C₄⋊C₈	C₅×D₃	semidirect
319. C₃×C₅	#1798	semidirect
380. C₅	#70476	direct (N × H)
400. C₃	C₅×#1798	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#872	2
C₂×C₃×C₅×C₄⋊C₈	2
C₂×C₅×(C₂×D₃)⋊C₈	2
C₂×C₅×C₄⋊(C₃⋊C₈)	2
C₅×#4550	2
C₅×#1798	3
#70476	5

Subgroups — C5×#70476 #14297464

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#70476 #14297464