Subgroups — C₅×#79276 #14418887

Order 1920.

912 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅×#235	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#431	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₅×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4834	C₂	1	2	yes	maximal, complemented
5	C₅×#4830	C₂	1	2	yes	maximal, complemented
6	C₅×#67⋊C₈	C₂	1	4	yes	maximal, complemented
7	C₅×#4685	C₂	1	2	yes	maximal, complemented
8	C₄×C₅×D₃×C₈	C₂	1	2	yes	maximal, complemented
9	C₅×C₈×#41	—	3	1	no	maximal, Hall
10	C₂×C₅×#235	C₄	1	1	yes	characteristic
11	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
12	C₄×C₅×#67	C₄	1	2	yes	—
13	C₄×C₅×#67	C₂²	1	2	yes	—
14	C₅×#926	C₄	1	1	yes	characteristic
15	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	—
16	C₂×C₅×D₃×C₈	C₂²	1	4	yes	—
17	C₄×C₅×D₁₂	C₄	1	1	yes	characteristic
18	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
19	C₅×#872	C₄	1	2	yes	—
20	C₄²×C₅×D₃	C₂²	1	2	yes	—
21	C₄×C₅×Dic₆	C₄	1	1	yes	characteristic
22	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
23	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	—
24	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
25	C₃×C₄×C₅×C₈	C₂²	1	2	yes	—
26	C₅×(C₂×D₃)⋊C₈	C₂²	1	4	yes	—
27	C₅×Dic₃⋊C₈	C₂²	1	4	yes	—
28	C₅×C₈×Dic₃	C₂²	1	4	yes	—
29	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
30	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
31	C₄×C₅×C₃⋊C₈	C₂²	1	2	yes	—
32	#79276	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
33	C₄×C₅×#41	—	3	1	no	—
34	C₅×C₈×Q₈	—	3	2	no	—
35	C₅×C₈×D₄	—	3	2	no	—
36	C₅×C₈×D₄	—	3	4	no	—
37	C₅×#431	—	3	2	no	—
38	C₅×#431	D₃	1	1	yes	characteristic, complemented
39	C₂×C₄×C₅×C₈	—	3	2	no	—
40	C₂×C₄×C₅×C₈	—	3	1	no	—
41	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₂×C₅×#67	C₂×C₄	1	2	yes	—
45	C₅×#235	C₈	1	8	yes	complemented
46	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
48	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
49	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
50	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
51	C₂×C₃×C₅×C₈	C₂³	1	4	yes	—
52	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
53	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
54	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
55	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
56	C₅×#217	C₂×C₄	1	2	yes	—
57	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
58	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
59	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
60	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
61	C₅×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
62	C₅×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
63	C₄×C₅×Dic₃	C₂×C₄	1	2	yes	—
64	C₄×C₅×Dic₃	C₂×C₄	1	2	yes	—
65	C₄×C₅×Dic₃	C₂³	1	2	yes	—
66	C₂×C₅×C₃⋊C₈	—	2	4	no	—
67	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
68	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
69	C₅×D₃×C₈	—	2	8	no	—
70	C₄×#235	C₂×C₅	1	1	yes	characteristic
71	C₃×#431	C₂×C₅	1	1	yes	characteristic, complemented
72	C₂×C₄×C₃⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
73	#4834	C₂×C₅	1	2	yes	complemented
74	#4830	C₂×C₅	1	2	yes	complemented
75	#67⋊C₈	C₂×C₅	1	4	yes	complemented
76	#4685	C₂×C₅	1	2	yes	complemented
77	C₄×D₃×C₈	C₂×C₅	1	2	yes	complemented
78	C₂×C₅×#41	—	3	1	no	—
79	C₂²×C₅×C₈	—	3	2	no	—
80	C₂²×C₅×C₈	—	3	4	no	—
81	C₄×C₅×Q₈	—	3	1	no	—
82	C₄×C₅×Q₈	—	3	1	no	—
83	C₄×C₅×D₄	—	3	2	no	—
84	C₄×C₅×D₄	—	3	2	no	—
85	C₄×C₅×D₄	—	3	1	no	—
86	C₄×C₅×D₄	—	3	1	no	—
87	C₅×#117	—	3	1	no	—
88	C₅×#117	—	3	2	no	—
89	C₂×C₄²×C₅	—	3	2	no	—
90	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
91	C₅×C₄⋊C₈	—	3	4	no	—
92	C₅×C₄⋊C₈	C₂×D₃	1	2	yes	—
93	C₅×C₂²⋊C₈	—	3	4	no	—
94	C₅×C₂²⋊C₈	C₂×D₃	1	2	yes	—
95	C₄×C₅×C₈	—	3	4	no	—
96	C₄×C₅×C₈	—	3	2	no	—
97	C₄×C₅×C₈	—	3	1	no	—
98	C₄×C₅×C₈	—	3	1	no	—
99	C₄×C₅×C₈	C₂×D₃	1	2	yes	—
100	C₈×#41	—	3	1	no	Sylow
101	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
103	C₂×C₃×C₄×C₅	—	2	2	no	—
104	C₂×C₃×C₄×C₅	—	2	2	no	—
105	C₂×C₃×C₄×C₅	C₂×C₈	1	4	yes	complemented
106	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
112	C₅×#67	C₂×C₈	1	8	yes	complemented
113	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
114	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
115	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
116	C₅×D₁₂	C₂×C₈	1	4	yes	complemented
117	C₄×C₅×D₃	—	2	4	no	—
118	C₄×C₅×D₃	—	2	4	no	—
119	C₄×C₅×D₃	C₂×C₈	1	8	yes	complemented
120	C₅×Dic₆	C₂×C₈	1	4	yes	complemented
121	C₃×C₅×C₈	—	2	4	no	—
122	C₅×C₃⋊C₈	—	2	2	no	—
123	C₅×C₃⋊C₈	#41	1	4	yes	complemented
124	C₂×#235	C₄×C₅	1	1	yes	characteristic
125	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
126	C₄×#67	C₄×C₅	1	2	yes	—
127	C₄×#67	C₂²×C₅	1	2	yes	—
128	#926	C₄×C₅	1	1	yes	characteristic
129	C₂²×C₃⋊C₈	C₂²×C₅	1	2	yes	—
130	C₂×D₃×C₈	C₂²×C₅	1	4	yes	—
131	C₄×D₁₂	C₄×C₅	1	1	yes	characteristic
132	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
133	#872	C₄×C₅	1	2	yes	—
134	C₄²×D₃	C₂²×C₅	1	2	yes	—
135	C₄×Dic₆	C₄×C₅	1	1	yes	characteristic
136	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic
137	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	—
138	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
139	C₃×C₄×C₈	C₂²×C₅	1	2	yes	—
140	(C₂×D₃)⋊C₈	C₂²×C₅	1	4	yes	—
141	Dic₃⋊C₈	C₂²×C₅	1	4	yes	—
142	C₈×Dic₃	C₂²×C₅	1	4	yes	—
143	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
144	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
145	C₄×C₃⋊C₈	C₂²×C₅	1	2	yes	—
146	C₅×#41	—	3	8	no	—
147	C₂×C₅×Q₈	—	3	1	no	—
148	C₂×C₅×D₄	—	3	2	no	—
149	C₂×C₅×D₄	—	3	1	no	—
150	C₂²×C₄×C₅	—	3	2	no	—
151	C₂²×C₄×C₅	—	3	2	no	—
152	C₂²×C₄×C₅	—	3	2	no	—
153	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
154	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
155	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
156	C₂×C₅×C₈	—	3	2	no	—
157	C₂×C₅×C₈	—	3	2	no	—
158	C₂×C₅×C₈	—	6	8	no	—
159	C₂×C₅×C₈	—	6	4	no	—
160	C₂×C₅×C₈	C₂²×D₃	1	4	yes	—
161	C₅×C₄⋊C₄	—	3	2	no	—
162	C₅×C₄⋊C₄	—	3	2	no	—
163	C₅×C₄⋊C₄	—	3	1	no	—
164	C₅×C₄⋊C₄	—	3	1	no	—
165	C₅×C₂²⋊C₄	—	3	2	no	—
166	C₅×C₂²⋊C₄	—	3	2	no	—
167	C₅×C₂²⋊C₄	—	3	2	no	—
168	C₄²×C₅	—	3	2	no	—
169	C₄²×C₅	—	3	2	no	—
170	C₄²×C₅	—	3	2	no	—
171	C₄²×C₅	C₄×D₃	1	1	yes	characteristic
172	C₄²×C₅	C₄×D₃	1	1	yes	characteristic
173	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
174	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
175	C₄×#41	—	3	1	no	—
176	C₈×Q₈	—	3	2	no	—
177	C₈×D₄	—	3	2	no	—
178	C₈×D₄	—	3	4	no	—
179	#431	—	3	2	no	—
180	#431	C₅×D₃	1	1	yes	characteristic, complemented
181	C₂×C₄×C₈	—	3	1	no	—
182	C₂×C₄×C₈	—	3	2	no	—
183	C₂²×C₃×C₅	—	2	1	no	—
184	C₂²×C₃×C₅	—	2	1	no	—
185	C₂²×C₃×C₅	C₂²×C₈	1	2	yes	—
186	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
187	C₂×C₅×D₃	—	2	2	no	—
188	C₂×C₅×D₃	—	2	2	no	—
189	C₂×C₅×D₃	C₂²×C₈	1	4	yes	—
190	C₃×C₄×C₅	—	2	1	no	—
191	C₃×C₄×C₅	—	2	1	no	—
192	C₃×C₄×C₅	C₂²×C₈	1	2	yes	—
193	C₃×C₄×C₅	C₂²×C₈	1	2	yes	—
194	C₃×C₄×C₅	#131	1	2	yes	—
195	C₃×C₄×C₅	C₂×#41	1	2	yes	—
196	C₅×Dic₃	—	2	2	no	—
197	C₅×Dic₃	—	2	2	no	—
198	C₅×Dic₃	C₂²×C₈	1	4	yes	—
199	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
200	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
201	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
202	C₂×#67	C₂×C₄×C₅	1	2	yes	—
203	#235	C₅×C₈	1	8	yes	complemented
204	C₂×D₁₂	C₂×C₄×C₅	1	1	yes	characteristic
205	C₂×C₄×D₃	C₂×C₄×C₅	1	2	yes	—
206	C₂×C₄×D₃	C₂×C₄×C₅	1	2	yes	—
207	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
208	C₂×Dic₆	C₂×C₄×C₅	1	1	yes	characteristic
209	C₂×C₃×C₈	C₂³×C₅	1	4	yes	—
210	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
211	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
212	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
213	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
214	#217	C₂×C₄×C₅	1	2	yes	—
215	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	2	yes	—
216	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	2	yes	—
217	C₄⋊Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
218	C₄⋊Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
219	Dic₃⋊C₄	C₂×C₄×C₅	1	2	yes	—
220	Dic₃⋊C₄	C₂×C₄×C₅	1	2	yes	—
221	C₄×Dic₃	C₂×C₄×C₅	1	2	yes	—
222	C₄×Dic₃	C₂×C₄×C₅	1	2	yes	—
223	C₄×Dic₃	C₂³×C₅	1	2	yes	—
224	C₂×C₃⋊C₈	—	2	4	no	—
225	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
226	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
227	D₃×C₈	—	2	8	no	—
228	C₂³×C₅	—	3	2	no	—
229	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
230	C₅×Q₈	—	3	4	no	—
231	C₅×D₄	—	3	8	no	—
232	C₅×D₄	—	3	4	no	—
233	C₂×C₄×C₅	—	2	2	no	—
234	C₂×C₄×C₅	—	2	2	no	—
235	C₂×C₄×C₅	—	3	2	no	—
236	C₂×C₄×C₅	—	3	8	no	—
237	C₂×C₄×C₅	—	3	2	no	—
238	C₂×C₄×C₅	—	3	2	no	—
239	C₂×C₄×C₅	—	6	4	no	—
240	C₂×C₄×C₅	—	6	4	no	—
241	C₂×C₄×C₅	D₃×C₈	1	4	yes	complemented
242	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
243	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
244	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
245	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
246	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
247	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
248	C₅×C₈	—	2	4	no	—
249	C₅×C₈	—	3	4	no	—
250	C₅×C₈	—	6	2	no	—
251	C₂×#41	—	3	1	no	—
252	C₂²×C₈	—	3	2	no	—
253	C₂²×C₈	—	3	4	no	—
254	C₄×Q₈	—	3	1	no	—
255	C₄×Q₈	—	3	1	no	—
256	C₄×D₄	—	3	2	no	—
257	C₄×D₄	—	3	2	no	—
258	C₄×D₄	—	3	1	no	—
259	C₄×D₄	—	3	1	no	—
260	#117	—	3	1	no	—
261	#117	—	3	2	no	—
262	C₂×C₄²	—	3	2	no	—
263	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
264	C₄⋊C₈	—	3	4	no	—
265	C₄⋊C₈	C₂×C₅×D₃	1	2	yes	—
266	C₂²⋊C₈	—	3	4	no	—
267	C₂²⋊C₈	C₂×C₅×D₃	1	2	yes	—
268	C₄×C₈	—	3	4	no	—
269	C₄×C₈	—	3	1	no	—
270	C₄×C₈	—	3	1	no	—
271	C₄×C₈	—	3	2	no	—
272	C₄×C₈	C₂×C₅×D₃	1	2	yes	—
273	C₂×C₃×C₅	—	2	2	no	—
274	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
275	C₂×C₃×C₅	C₂³×C₈	1	1	yes	characteristic
276	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
277	C₅×D₃	—	2	4	no	—
278	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
279	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
280	C₂×C₃×C₄	—	2	2	no	—
281	C₂×C₃×C₄	—	2	2	no	—
282	C₂×C₃×C₄	C₂×C₅×C₈	1	4	yes	complemented
283	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
284	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
285	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
286	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
287	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
288	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
289	#67	C₂×C₅×C₈	1	8	yes	complemented
290	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
291	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
292	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
293	D₁₂	C₂×C₅×C₈	1	4	yes	complemented
294	C₄×D₃	—	2	4	no	—
295	C₄×D₃	—	2	4	no	—
296	C₄×D₃	C₂×C₅×C₈	1	8	yes	complemented
297	Dic₆	C₂×C₅×C₈	1	4	yes	complemented
298	C₃×C₈	—	2	4	no	—
299	C₃⋊C₈	—	2	2	no	—
300	C₃⋊C₈	C₅×#41	1	4	yes	complemented
301	C₂²×C₅	—	2	1	no	—
302	C₂²×C₅	—	2	1	no	—
303	C₂²×C₅	—	3	4	no	—
304	C₂²×C₅	—	6	2	no	—
305	C₂²×C₅	—	6	2	no	—
306	C₂²×C₅	C₂×D₃×C₈	1	2	yes	—
307	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
308	C₄×C₅	—	2	1	no	—
309	C₄×C₅	—	2	1	no	—
310	C₄×C₅	—	3	4	no	—
311	C₄×C₅	—	6	2	no	—
312	C₄×C₅	—	6	2	no	—
313	C₄×C₅	C₂×D₃×C₈	1	2	yes	—
314	C₄×C₅	C₂×D₃×C₈	1	2	yes	—
315	C₄×C₅	#907	1	2	yes	—
316	C₄×C₅	D₃×#41	1	2	yes	—
317	#41	—	3	8	no	—
318	C₂×Q₈	—	3	1	no	—
319	C₂×D₄	—	3	2	no	—
320	C₂×D₄	—	3	1	no	—
321	C₂²×C₄	—	3	2	no	—
322	C₂²×C₄	—	3	2	no	—
323	C₂²×C₄	—	3	2	no	—
324	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
325	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
326	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
327	C₂×C₈	—	3	2	no	—
328	C₂×C₈	—	3	2	no	—
329	C₂×C₈	—	6	8	no	—
330	C₂×C₈	—	6	4	no	—
331	C₂×C₈	C₂²×C₅×D₃	1	4	yes	—
332	C₄⋊C₄	—	3	2	no	—
333	C₄⋊C₄	—	3	2	no	—
334	C₄⋊C₄	—	3	1	no	—
335	C₄⋊C₄	—	3	1	no	—
336	C₂²⋊C₄	—	3	2	no	—
337	C₂²⋊C₄	—	3	2	no	—
338	C₂²⋊C₄	—	3	2	no	—
339	C₄²	—	3	2	no	—
340	C₄²	—	3	2	no	—
341	C₄²	—	3	2	no	—
342	C₄²	C₄×C₅×D₃	1	1	yes	characteristic
343	C₄²	C₄×C₅×D₃	1	1	yes	characteristic
344	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
345	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
346	C₃×C₅	C₈×#41	1	1	yes	characteristic, complemented, Hall
347	C₂²×C₃	—	2	1	no	—
348	C₂²×C₃	—	2	1	no	—
349	C₂²×C₃	C₂²×C₅×C₈	1	2	yes	—
350	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
351	C₂×D₃	—	2	2	no	—
352	C₂×D₃	—	2	2	no	—
353	C₂×D₃	C₂²×C₅×C₈	1	4	yes	—
354	C₃×C₄	—	2	1	no	—
355	C₃×C₄	—	2	1	no	—
356	C₃×C₄	C₂²×C₅×C₈	1	2	yes	—
357	C₃×C₄	C₂²×C₅×C₈	1	2	yes	—
358	C₃×C₄	C₅×#131	1	2	yes	—
359	C₃×C₄	C₂×C₅×#41	1	2	yes	—
360	Dic₃	—	2	2	no	—
361	Dic₃	—	2	2	no	—
362	Dic₃	C₂²×C₅×C₈	1	4	yes	—
363	C₂×C₅	—	2	2	no	—
364	C₂×C₅	—	6	4	no	—
365	C₂×C₅	#5522	1	1	yes	characteristic
366	C₂×C₅	C₂²×D₃×C₈	1	1	yes	characteristic
367	C₂×C₅	C₂×#907	1	1	yes	characteristic
368	C₂³	—	3	2	no	—
369	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
370	Q₈	—	3	4	no	—
371	D₄	—	3	8	no	—
372	D₄	—	3	4	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	3	2	no	—
376	C₂×C₄	—	3	8	no	—
377	C₂×C₄	—	3	2	no	—
378	C₂×C₄	—	3	2	no	—
379	C₂×C₄	—	6	4	no	—
380	C₂×C₄	—	6	4	no	—
381	C₂×C₄	C₅×D₃×C₈	1	4	yes	complemented
382	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
383	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
384	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
385	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
386	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
387	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
388	C₈	—	2	4	no	—
389	C₈	—	3	4	no	—
390	C₈	—	6	2	no	—
391	C₂×C₃	—	2	2	no	—
392	C₂×C₃	C₄×C₅×#41	1	1	yes	characteristic
393	C₂×C₃	C₂³×C₅×C₈	1	1	yes	characteristic
394	C₂×C₃	C₂×C₅×#131	1	1	yes	characteristic
395	D₃	—	2	4	no	—
396	C₅	#79276	1	1	yes	characteristic, direct product factor, Sylow
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	3	4	no	—
400	C₂²	—	6	2	no	—
401	C₂²	—	6	2	no	—
402	C₂²	C₂×C₅×D₃×C₈	1	2	yes	—
403	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
404	C₄	—	2	1	no	—
405	C₄	—	2	1	no	—
406	C₄	—	3	4	no	—
407	C₄	—	6	2	no	—
408	C₄	—	6	2	no	—
409	C₄	C₂×C₅×D₃×C₈	1	2	yes	—
410	C₄	C₂×C₅×D₃×C₈	1	2	yes	—
411	C₄	C₅×#907	1	2	yes	—
412	C₄	C₅×D₃×#41	1	2	yes	—
413	C₃	C₅×C₈×#41	1	1	yes	characteristic, complemented, Sylow
414	C₂	—	2	2	no	—
415	C₂	—	6	4	no	—
416	C₂	C₅×#5522	1	1	yes	characteristic
417	C₂	C₂²×C₅×D₃×C₈	1	1	yes	characteristic
418	C₂	C₂×C₅×#907	1	1	yes	characteristic

	subgroup	G/H
center	C₄²×C₅	C₂²×D₃
commutator	C₂×C₃	C₂³×C₅×C₈
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#431	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂×C₅×#235	C₄
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₅×#431	D₃
hypocenter	C₃	C₅×C₈×#41
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄²×C₅ ◁ C₅×#431

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#431	C₂	semidirect
3. C₂×C₄×C₅×C₃⋊C₈	C₂	semidirect
4. C₅×#4834	C₂	semidirect
5. C₅×#4830	C₂	semidirect
6. C₅×#67⋊C₈	C₂	semidirect
7. C₅×#4685	C₂	semidirect
8. C₄×C₅×D₃×C₈	C₂	semidirect
32. #79276	C₅	direct (N × H)
38. C₅×#431	D₃	semidirect
45. C₅×#235	C₈	semidirect
71. C₃×#431	C₂×C₅	semidirect
72. C₂×C₄×C₃⋊C₈	C₂×C₅	semidirect
73. #4834	C₂×C₅	semidirect
74. #4830	C₂×C₅	semidirect
75. #67⋊C₈	C₂×C₅	semidirect
76. #4685	C₂×C₅	semidirect
77. C₄×D₃×C₈	C₂×C₅	semidirect
105. C₂×C₃×C₄×C₅	C₂×C₈	semidirect
112. C₅×#67	C₂×C₈	semidirect
116. C₅×D₁₂	C₂×C₈	semidirect
119. C₄×C₅×D₃	C₂×C₈	semidirect
120. C₅×Dic₆	C₂×C₈	semidirect
123. C₅×C₃⋊C₈	#41	semidirect
180. #431	C₅×D₃	semidirect
203. #235	C₅×C₈	semidirect
241. C₂×C₄×C₅	D₃×C₈	semidirect
282. C₂×C₃×C₄	C₂×C₅×C₈	semidirect
289. #67	C₂×C₅×C₈	semidirect
293. D₁₂	C₂×C₅×C₈	semidirect
296. C₄×D₃	C₂×C₅×C₈	semidirect
297. Dic₆	C₂×C₅×C₈	semidirect
300. C₃⋊C₈	C₅×#41	semidirect
346. C₃×C₅	C₈×#41	semidirect
381. C₂×C₄	C₅×D₃×C₈	semidirect
396. C₅	#79276	direct (N × H)
413. C₃	C₅×C₈×#41	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₅×#235	2
C₃×C₅×#431	2
C₂×C₄×C₅×C₃⋊C₈	2
C₅×#4834	2
C₅×#4830	2
C₅×#67⋊C₈	2
C₅×#4685	2
C₄×C₅×D₃×C₈	2
C₅×C₈×#41	3
#79276	5

Subgroups — C5×#79276 #14418887

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#79276 #14418887