Subgroups — C₅×D₄×#208 #14415684

Order 1920.

1088 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×C₃×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₅×#208	C₂	1	2	yes	maximal, complemented
3	C₅×#5207	C₂	1	2	yes	maximal, complemented
4	C₅×#5012	C₂	1	2	yes	maximal, complemented
5	C₅×#5011	C₂	1	4	yes	maximal, complemented
6	C₅×D₄×C₃⋊C₈	C₂	1	2	yes	maximal, complemented
7	C₅×#4924	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×C₅×#208	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×D₄×M₁₆	—	3	1	no	maximal, Hall
10	C₂²×C₃×C₅×D₄	C₄	1	1	yes	characteristic
11	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
12	C₃×C₄×C₅×D₄	C₄	1	2	yes	—
13	C₃×C₄×C₅×D₄	C₄	1	1	yes	characteristic
14	C₃×C₄×C₅×D₄	C₄	1	1	yes	characteristic
15	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
16	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
17	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₅×C₄⋊C₄	C₄	1	1	yes	characteristic
19	C₂×C₃×C₅×C₂²⋊C₄	C₄	1	2	yes	—
20	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
21	C₂×C₅×#208	—	2	8	no	—
22	C₂×C₅×#208	C₂²	1	1	yes	characteristic
23	C₂×C₅×#208	C₂²	1	2	yes	—
24	C₂×C₅×#208	C₂²	1	1	yes	characteristic
25	C₂×C₅×#208	C₂²	1	4	yes	complemented
26	C₂²×C₅×C₃⋊C₈	C₂²	1	4	yes	complemented
27	C₅×#830	C₂²	1	4	yes	complemented
28	C₅×#830	C₂²	1	4	yes	complemented
29	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	2	yes	complemented
30	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	2	yes	complemented
31	C₅×#803	C₂²	1	2	yes	complemented
32	C₄×C₅×C₃⋊C₈	C₂²	1	2	yes	complemented
33	D₄×#208	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
34	C₂²×C₅×M₁₆	—	3	2	no	—
35	C₂×C₄×C₅×D₄	D₃	1	1	yes	characteristic
36	C₅×#436	—	3	2	no	—
37	C₅×#435	—	3	4	no	—
38	C₅×C₈×D₄	—	3	2	no	—
39	C₅×#423	—	3	1	no	—
40	C₅×#407	—	3	2	no	—
41	C₄×C₅×M₁₆	—	3	1	no	—
42	C₂⁴×C₃×C₅	C₂×C₄	1	2	yes	—
43	C₂×C₃×C₅×D₄	—	2	4	no	—
44	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
45	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
46	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
47	C₂²×C₃×C₄×C₅	—	2	4	no	—
48	C₂²×C₃×C₄×C₅	—	2	4	no	—
49	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
50	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
51	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
52	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
53	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
54	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
55	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
56	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
57	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
58	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
59	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
60	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
61	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
62	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
63	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
64	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
65	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
66	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
67	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
68	C₅×#208	—	2	4	no	—
69	C₅×#208	—	2	2	no	—
70	C₅×#208	—	2	8	no	—
71	C₅×#208	D₄	1	4	yes	direct product factor
72	C₂×C₅×C₃⋊C₈	—	2	8	no	—
73	C₂×C₅×C₃⋊C₈	C₂³	1	4	yes	—
74	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
75	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
76	C₂×C₃×C₄×D₄	C₂×C₅	1	1	yes	characteristic
77	C₂²×#208	C₂×C₅	1	2	yes	complemented
78	#5207	C₂×C₅	1	2	yes	complemented
79	#5012	C₂×C₅	1	2	yes	complemented
80	#5011	C₂×C₅	1	4	yes	complemented
81	D₄×C₃⋊C₈	C₂×C₅	1	2	yes	complemented
82	#4924	C₂×C₅	1	1	yes	characteristic, complemented
83	C₄×#208	C₂×C₅	1	1	yes	characteristic, complemented
84	C₂²×C₅×D₄	Dic₃	1	1	yes	characteristic
85	C₂³×C₄×C₅	C₂×D₃	1	2	yes	—
86	C₂×C₅×M₁₆	—	3	1	no	—
87	C₂×C₅×M₁₆	—	3	1	no	—
88	C₂×C₅×M₁₆	—	3	2	no	—
89	C₂×C₅×M₁₆	—	3	4	no	—
90	C₂×C₅×M₁₆	—	6	8	no	—
91	C₂²×C₅×C₈	—	3	4	no	—
92	C₄×C₅×D₄	Dic₃	1	2	yes	—
93	C₄×C₅×D₄	Dic₃	1	1	yes	characteristic
94	C₄×C₅×D₄	Dic₃	1	1	yes	characteristic
95	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
96	C₄×C₅×D₄	C₂×D₃	1	2	yes	—
97	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
98	C₂×C₅×C₄⋊C₄	Dic₃	1	1	yes	characteristic
99	C₂×C₅×C₂²⋊C₄	Dic₃	1	2	yes	—
100	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
101	C₅×C₄⋊C₈	—	3	2	no	—
102	C₅×C₄⋊C₈	—	3	2	no	—
103	C₅×C₂²⋊C₈	—	3	4	no	—
104	C₅×C₂²⋊C₈	—	3	4	no	—
105	C₅×#97	—	3	2	no	—
106	C₄×C₅×C₈	—	3	2	no	—
107	D₄×M₁₆	—	3	1	no	Sylow
108	C₂³×C₃×C₅	—	2	4	no	—
109	C₂³×C₃×C₅	—	2	4	no	—
110	C₂³×C₃×C₅	—	4	2	no	—
111	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
112	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
113	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
114	C₃×C₅×D₄	—	2	4	no	—
115	C₃×C₅×D₄	—	2	2	no	—
116	C₃×C₅×D₄	M₁₆	1	4	yes	complemented
117	C₂×C₃×C₄×C₅	—	2	4	no	—
118	C₂×C₃×C₄×C₅	—	2	4	no	—
119	C₂×C₃×C₄×C₅	—	2	4	no	—
120	C₂×C₃×C₄×C₅	—	2	2	no	—
121	C₂×C₃×C₄×C₅	—	2	2	no	—
122	C₂×C₃×C₄×C₅	—	2	2	no	—
123	C₂×C₃×C₄×C₅	—	2	2	no	—
124	C₂×C₃×C₄×C₅	—	2	2	no	—
125	C₂×C₃×C₄×C₅	—	4	1	no	—
126	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
130	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
131	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
134	C₂×C₃×C₄×C₅	#41	1	2	yes	—
135	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
136	C₅×C₃⋊C₈	—	2	4	no	—
137	C₅×C₃⋊C₈	—	2	2	no	—
138	C₅×C₃⋊C₈	C₂×D₄	1	4	yes	complemented
139	C₂²×C₃×D₄	C₄×C₅	1	1	yes	characteristic
140	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
141	C₃×C₄×D₄	C₄×C₅	1	2	yes	—
142	C₃×C₄×D₄	C₄×C₅	1	1	yes	characteristic
143	C₃×C₄×D₄	C₄×C₅	1	1	yes	characteristic
144	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
145	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
146	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
147	C₂×C₃×C₄⋊C₄	C₄×C₅	1	1	yes	characteristic
148	C₂×C₃×C₂²⋊C₄	C₄×C₅	1	2	yes	—
149	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
150	C₂×#208	—	2	8	no	—
151	C₂×#208	C₂²×C₅	1	1	yes	characteristic
152	C₂×#208	C₂²×C₅	1	2	yes	—
153	C₂×#208	C₂²×C₅	1	1	yes	characteristic
154	C₂×#208	C₂²×C₅	1	4	yes	complemented
155	C₂²×C₃⋊C₈	C₂²×C₅	1	4	yes	complemented
156	#830	C₂²×C₅	1	4	yes	complemented
157	#830	C₂²×C₅	1	4	yes	complemented
158	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	2	yes	complemented
159	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	2	yes	complemented
160	#803	C₂²×C₅	1	2	yes	complemented
161	C₄×C₃⋊C₈	C₂²×C₅	1	2	yes	complemented
162	C₂⁴×C₅	C₂×Dic₃	1	2	yes	—
163	C₂×C₅×D₄	—	2	4	no	—
164	C₂×C₅×D₄	C₂×Dic₃	1	2	yes	—
165	C₂×C₅×D₄	C₂×Dic₃	1	1	yes	characteristic
166	C₂×C₅×D₄	C₂×Dic₃	1	1	yes	characteristic
167	C₂²×C₄×C₅	—	2	4	no	—
168	C₂²×C₄×C₅	—	2	4	no	—
169	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
170	C₂²×C₄×C₅	C₂×Dic₃	1	2	yes	—
171	C₂²×C₄×C₅	C₂×Dic₃	1	2	yes	—
172	C₂²×C₄×C₅	C₂×Dic₃	1	2	yes	—
173	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
174	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
175	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
176	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
177	C₅×M₁₆	—	3	4	no	—
178	C₅×M₁₆	—	6	8	no	—
179	C₅×M₁₆	—	6	4	no	—
180	C₅×M₁₆	—	6	2	no	—
181	C₂×C₅×C₈	—	3	2	no	—
182	C₂×C₅×C₈	—	3	4	no	—
183	C₂×C₅×C₈	—	3	2	no	—
184	C₂×C₅×C₈	—	6	8	no	—
185	C₅×C₄⋊C₄	C₂×Dic₃	1	2	yes	—
186	C₅×C₄⋊C₄	C₂×Dic₃	1	1	yes	characteristic
187	C₅×C₄⋊C₄	C₂×Dic₃	1	1	yes	characteristic
188	C₅×C₂²⋊C₄	C₂×Dic₃	1	2	yes	—
189	C₅×C₂²⋊C₄	C₂×Dic₃	1	2	yes	—
190	C₅×C₂²⋊C₄	C₂×Dic₃	1	2	yes	—
191	C₅×C₂²⋊C₄	C₂×Dic₃	1	2	yes	—
192	C₄²×C₅	C₂×Dic₃	1	1	yes	characteristic
193	C₄²×C₅	C₂×Dic₃	1	1	yes	characteristic
194	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
195	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
196	C₂²×M₁₆	—	3	2	no	—
197	C₂×C₄×D₄	C₅×D₃	1	1	yes	characteristic
198	#436	—	3	2	no	—
199	#435	—	3	4	no	—
200	C₈×D₄	—	3	2	no	—
201	#423	—	3	1	no	—
202	#407	—	3	2	no	—
203	C₄×M₁₆	—	3	1	no	—
204	C₂²×C₃×C₅	—	2	2	no	—
205	C₂²×C₃×C₅	—	2	1	no	—
206	C₂²×C₃×C₅	—	2	1	no	—
207	C₂²×C₃×C₅	—	2	2	no	—
208	C₂²×C₃×C₅	—	2	2	no	—
209	C₂²×C₃×C₅	—	2	2	no	—
210	C₂²×C₃×C₅	—	2	2	no	—
211	C₂²×C₃×C₅	—	4	8	no	—
212	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
213	C₂²×C₃×C₅	C₂×M₁₆	1	4	yes	complemented
214	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
215	C₃×C₄×C₅	—	2	2	no	—
216	C₃×C₄×C₅	—	2	2	no	—
217	C₃×C₄×C₅	—	2	1	no	—
218	C₃×C₄×C₅	—	2	1	no	—
219	C₃×C₄×C₅	—	2	1	no	—
220	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
221	C₃×C₄×C₅	C₂×M₁₆	1	2	yes	complemented
222	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
223	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
224	C₂⁴×C₃	C₂×C₄×C₅	1	2	yes	—
225	C₂×C₃×D₄	—	2	4	no	—
226	C₂×C₃×D₄	C₂×C₄×C₅	1	2	yes	—
227	C₂×C₃×D₄	C₂×C₄×C₅	1	1	yes	characteristic
228	C₂×C₃×D₄	C₂×C₄×C₅	1	1	yes	characteristic
229	C₂²×C₃×C₄	—	2	4	no	—
230	C₂²×C₃×C₄	—	2	4	no	—
231	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
232	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
233	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
234	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
235	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
236	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
237	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
238	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
239	C₃×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
240	C₃×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
241	C₃×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
242	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
243	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
244	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
245	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
246	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
247	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
248	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
249	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
250	#208	—	2	4	no	—
251	#208	—	2	2	no	—
252	#208	—	2	8	no	—
253	#208	C₅×D₄	1	4	yes	direct product factor
254	C₂×C₃⋊C₈	—	2	8	no	—
255	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
256	C₂×C₃⋊C₈	C₂³×C₅	1	4	yes	—
257	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
258	C₂³×C₅	—	2	4	no	—
259	C₂³×C₅	—	2	4	no	—
260	C₂³×C₅	—	4	2	no	—
261	C₂³×C₅	C₂²×Dic₃	1	2	yes	—
262	C₂³×C₅	C₂²×Dic₃	1	2	yes	—
263	C₂³×C₅	C₂²×Dic₃	1	1	yes	characteristic
264	C₅×D₄	—	2	4	no	—
265	C₅×D₄	—	2	2	no	—
266	C₅×D₄	#208	1	4	yes	direct product factor
267	C₂×C₄×C₅	—	2	4	no	—
268	C₂×C₄×C₅	—	2	2	no	—
269	C₂×C₄×C₅	—	2	4	no	—
270	C₂×C₄×C₅	—	2	4	no	—
271	C₂×C₄×C₅	—	2	2	no	—
272	C₂×C₄×C₅	—	2	2	no	—
273	C₂×C₄×C₅	—	2	2	no	—
274	C₂×C₄×C₅	—	2	2	no	—
275	C₂×C₄×C₅	—	4	1	no	—
276	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
277	C₂×C₄×C₅	#237	1	2	yes	—
278	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
279	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
280	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
281	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
282	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
283	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
284	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
285	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
286	C₅×C₈	—	3	4	no	—
287	C₅×C₈	—	6	4	no	—
288	C₅×C₈	—	6	2	no	—
289	C₂²×D₄	C₅×Dic₃	1	1	yes	characteristic
290	C₂³×C₄	C₂×C₅×D₃	1	2	yes	—
291	C₂×M₁₆	—	3	1	no	—
292	C₂×M₁₆	—	3	2	no	—
293	C₂×M₁₆	—	3	4	no	—
294	C₂×M₁₆	—	3	1	no	—
295	C₂×M₁₆	—	6	8	no	—
296	C₂²×C₈	—	3	4	no	—
297	C₄×D₄	C₅×Dic₃	1	2	yes	—
298	C₄×D₄	C₅×Dic₃	1	1	yes	characteristic
299	C₄×D₄	C₅×Dic₃	1	1	yes	characteristic
300	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
301	C₄×D₄	C₂×C₅×D₃	1	2	yes	—
302	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
303	C₂×C₄⋊C₄	C₅×Dic₃	1	1	yes	characteristic
304	C₂×C₂²⋊C₄	C₅×Dic₃	1	2	yes	—
305	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
306	C₄⋊C₈	—	3	2	no	—
307	C₄⋊C₈	—	3	2	no	—
308	C₂²⋊C₈	—	3	4	no	—
309	C₂²⋊C₈	—	3	4	no	—
310	#97	—	3	2	no	—
311	C₄×C₈	—	3	2	no	—
312	C₂×C₃×C₅	—	2	2	no	—
313	C₂×C₃×C₅	—	2	4	no	—
314	C₂×C₃×C₅	—	4	2	no	—
315	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
316	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
317	C₂×C₃×C₅	#568	1	1	yes	characteristic
318	C₂³×C₃	—	2	4	no	—
319	C₂³×C₃	—	2	4	no	—
320	C₂³×C₃	—	4	2	no	—
321	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
322	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
323	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
324	C₃×D₄	—	2	4	no	—
325	C₃×D₄	—	2	2	no	—
326	C₃×D₄	C₅×M₁₆	1	4	yes	complemented
327	C₂×C₃×C₄	—	2	4	no	—
328	C₂×C₃×C₄	—	2	4	no	—
329	C₂×C₃×C₄	—	2	4	no	—
330	C₂×C₃×C₄	—	2	2	no	—
331	C₂×C₃×C₄	—	2	2	no	—
332	C₂×C₃×C₄	—	2	2	no	—
333	C₂×C₃×C₄	—	2	2	no	—
334	C₂×C₃×C₄	—	2	2	no	—
335	C₂×C₃×C₄	—	4	1	no	—
336	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
337	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
338	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
339	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
340	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
341	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
342	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
343	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
344	C₂×C₃×C₄	C₅×#41	1	2	yes	—
345	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
346	C₃⋊C₈	—	2	4	no	—
347	C₃⋊C₈	—	2	2	no	—
348	C₃⋊C₈	C₂×C₅×D₄	1	4	yes	complemented
349	C₂²×C₅	—	2	1	no	—
350	C₂²×C₅	—	2	2	no	—
351	C₂²×C₅	—	2	1	no	—
352	C₂²×C₅	—	2	2	no	—
353	C₂²×C₅	—	2	2	no	—
354	C₂²×C₅	—	2	2	no	—
355	C₂²×C₅	—	2	2	no	—
356	C₂²×C₅	—	4	8	no	—
357	C₂²×C₅	C₂×#208	1	4	yes	complemented
358	C₂²×C₅	D₄×Dic₃	1	2	yes	—
359	C₂²×C₅	C₂³×Dic₃	1	1	yes	characteristic
360	C₄×C₅	—	2	1	no	—
361	C₄×C₅	—	2	2	no	—
362	C₄×C₅	—	2	2	no	—
363	C₄×C₅	—	2	1	no	—
364	C₄×C₅	—	2	1	no	—
365	C₄×C₅	C₂×#208	1	2	yes	complemented
366	C₄×C₅	D₄×Dic₃	1	2	yes	—
367	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
368	C₄×C₅	C₂×#237	1	1	yes	characteristic
369	C₂⁴	C₂×C₅×Dic₃	1	2	yes	—
370	C₂×D₄	—	2	4	no	—
371	C₂×D₄	C₂×C₅×Dic₃	1	2	yes	—
372	C₂×D₄	C₂×C₅×Dic₃	1	1	yes	characteristic
373	C₂×D₄	C₂×C₅×Dic₃	1	1	yes	characteristic
374	C₂²×C₄	—	2	4	no	—
375	C₂²×C₄	—	2	4	no	—
376	C₂²×C₄	C₂×C₅×Dic₃	1	1	yes	characteristic
377	C₂²×C₄	C₂×C₅×Dic₃	1	2	yes	—
378	C₂²×C₄	C₂×C₅×Dic₃	1	2	yes	—
379	C₂²×C₄	C₂×C₅×Dic₃	1	2	yes	—
380	C₂²×C₄	C₂×C₅×Dic₃	1	1	yes	characteristic
381	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
382	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
383	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
384	M₁₆	—	3	4	no	—
385	M₁₆	—	6	8	no	—
386	M₁₆	—	6	4	no	—
387	M₁₆	—	6	2	no	—
388	C₂×C₈	—	3	2	no	—
389	C₂×C₈	—	3	2	no	—
390	C₂×C₈	—	3	4	no	—
391	C₂×C₈	—	6	8	no	—
392	C₄⋊C₄	C₂×C₅×Dic₃	1	2	yes	—
393	C₄⋊C₄	C₂×C₅×Dic₃	1	1	yes	characteristic
394	C₄⋊C₄	C₂×C₅×Dic₃	1	1	yes	characteristic
395	C₂²⋊C₄	C₂×C₅×Dic₃	1	2	yes	—
396	C₂²⋊C₄	C₂×C₅×Dic₃	1	2	yes	—
397	C₂²⋊C₄	C₂×C₅×Dic₃	1	2	yes	—
398	C₂²⋊C₄	C₂×C₅×Dic₃	1	2	yes	—
399	C₄²	C₂×C₅×Dic₃	1	1	yes	characteristic
400	C₄²	C₂×C₅×Dic₃	1	1	yes	characteristic
401	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
402	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
403	C₃×C₅	D₄×M₁₆	1	1	yes	characteristic, complemented, Hall
404	C₂²×C₃	—	2	2	no	—
405	C₂²×C₃	—	2	1	no	—
406	C₂²×C₃	—	2	1	no	—
407	C₂²×C₃	—	2	2	no	—
408	C₂²×C₃	—	2	2	no	—
409	C₂²×C₃	—	2	2	no	—
410	C₂²×C₃	—	2	2	no	—
411	C₂²×C₃	—	4	8	no	—
412	C₂²×C₃	C₄×C₅×D₄	1	2	yes	—
413	C₂²×C₃	C₂×C₅×M₁₆	1	4	yes	complemented
414	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
415	C₃×C₄	—	2	2	no	—
416	C₃×C₄	—	2	2	no	—
417	C₃×C₄	—	2	1	no	—
418	C₃×C₄	—	2	1	no	—
419	C₃×C₄	—	2	1	no	—
420	C₃×C₄	C₄×C₅×D₄	1	2	yes	—
421	C₃×C₄	C₂×C₅×M₁₆	1	2	yes	complemented
422	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
423	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
424	C₂×C₅	—	2	2	no	—
425	C₂×C₅	—	2	4	no	—
426	C₂×C₅	—	4	2	no	—
427	C₂×C₅	C₂²×#208	1	1	yes	characteristic
428	C₂×C₅	C₂×D₄×Dic₃	1	1	yes	characteristic
429	C₂×C₅	#5819	1	1	yes	characteristic
430	C₂³	—	2	4	no	—
431	C₂³	—	2	4	no	—
432	C₂³	—	4	2	no	—
433	C₂³	C₂²×C₅×Dic₃	1	2	yes	—
434	C₂³	C₂²×C₅×Dic₃	1	2	yes	—
435	C₂³	C₂²×C₅×Dic₃	1	1	yes	characteristic
436	D₄	—	2	4	no	—
437	D₄	—	2	2	no	—
438	D₄	C₅×#208	1	4	yes	direct product factor
439	C₂×C₄	—	2	4	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	4	no	—
442	C₂×C₄	—	2	4	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
449	C₂×C₄	C₅×#237	1	2	yes	—
450	C₂×C₄	C₂²×C₅×Dic₃	1	1	yes	characteristic
451	C₂×C₄	C₂²×C₅×Dic₃	1	1	yes	characteristic
452	C₂×C₄	C₂²×C₅×Dic₃	1	1	yes	characteristic
453	C₂×C₄	C₂²×C₅×Dic₃	1	2	yes	—
454	C₂×C₄	C₂²×C₅×Dic₃	1	2	yes	—
455	C₂×C₄	C₂²×C₅×Dic₃	1	1	yes	characteristic
456	C₂×C₄	C₂²×C₅×Dic₃	1	1	yes	characteristic
457	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
458	C₈	—	3	4	no	—
459	C₈	—	6	4	no	—
460	C₈	—	6	2	no	—
461	C₂×C₃	—	2	2	no	—
462	C₂×C₃	—	2	4	no	—
463	C₂×C₃	—	4	2	no	—
464	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
465	C₂×C₃	C₂²×C₅×M₁₆	1	1	yes	characteristic
466	C₂×C₃	C₅×#568	1	1	yes	characteristic
467	C₅	D₄×#208	1	1	yes	characteristic, direct product factor, Sylow
468	C₂²	—	2	1	no	—
469	C₂²	—	2	2	no	—
470	C₂²	—	2	1	no	—
471	C₂²	—	2	2	no	—
472	C₂²	—	2	2	no	—
473	C₂²	—	2	2	no	—
474	C₂²	—	2	2	no	—
475	C₂²	—	4	8	no	—
476	C₂²	C₂×C₅×#208	1	4	yes	complemented
477	C₂²	C₅×D₄×Dic₃	1	2	yes	—
478	C₂²	C₂³×C₅×Dic₃	1	1	yes	characteristic
479	C₄	—	2	1	no	—
480	C₄	—	2	2	no	—
481	C₄	—	2	2	no	—
482	C₄	—	2	1	no	—
483	C₄	—	2	1	no	—
484	C₄	C₂×C₅×#208	1	2	yes	complemented
485	C₄	C₅×D₄×Dic₃	1	2	yes	—
486	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
487	C₄	C₂×C₅×#237	1	1	yes	characteristic
488	C₃	C₅×D₄×M₁₆	1	1	yes	characteristic, complemented, Sylow
489	C₂	—	2	2	no	—
490	C₂	—	2	4	no	—
491	C₂	—	4	2	no	—
492	C₂	C₂²×C₅×#208	1	1	yes	characteristic
493	C₂	C₂×C₅×D₄×Dic₃	1	1	yes	characteristic
494	C₂	C₅×#5819	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂×C₃×C₄×C₅×D₄	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂²×C₃×C₅×D₄	C₄
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₂×C₄×C₅×D₄	D₃
hypocenter	C₃	C₅×D₄×M₁₆
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₄×C₅×D₄

Complements

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

N	H ≅ G/N	type
2. C₂²×C₅×#208	C₂	semidirect
3. C₅×#5207	C₂	semidirect
4. C₅×#5012	C₂	semidirect
5. C₅×#5011	C₂	semidirect
6. C₅×D₄×C₃⋊C₈	C₂	semidirect
7. C₅×#4924	C₂	semidirect
8. C₄×C₅×#208	C₂	semidirect
25. C₂×C₅×#208	C₂²	semidirect
26. C₂²×C₅×C₃⋊C₈	C₂²	semidirect
27. C₅×#830	C₂²	semidirect
28. C₅×#830	C₂²	semidirect
29. C₅×C₄⋊(C₃⋊C₈)	C₂²	semidirect
30. C₅×C₄⋊(C₃⋊C₈)	C₂²	semidirect
31. C₅×#803	C₂²	semidirect
32. C₄×C₅×C₃⋊C₈	C₂²	semidirect
33. D₄×#208	C₅	direct (N × H)
71. C₅×#208	D₄	direct (N × H)
77. C₂²×#208	C₂×C₅	semidirect
78. #5207	C₂×C₅	semidirect
79. #5012	C₂×C₅	semidirect
80. #5011	C₂×C₅	semidirect
81. D₄×C₃⋊C₈	C₂×C₅	semidirect
82. #4924	C₂×C₅	semidirect
83. C₄×#208	C₂×C₅	semidirect
116. C₃×C₅×D₄	M₁₆	semidirect
138. C₅×C₃⋊C₈	C₂×D₄	semidirect
154. C₂×#208	C₂²×C₅	semidirect
155. C₂²×C₃⋊C₈	C₂²×C₅	semidirect
156. #830	C₂²×C₅	semidirect
157. #830	C₂²×C₅	semidirect
158. C₄⋊(C₃⋊C₈)	C₂²×C₅	semidirect
159. C₄⋊(C₃⋊C₈)	C₂²×C₅	semidirect
160. #803	C₂²×C₅	semidirect
161. C₄×C₃⋊C₈	C₂²×C₅	semidirect
213. C₂²×C₃×C₅	C₂×M₁₆	semidirect
221. C₃×C₄×C₅	C₂×M₁₆	semidirect
253. #208	C₅×D₄	direct (N × H)
266. C₅×D₄	#208	direct (N × H)
326. C₃×D₄	C₅×M₁₆	semidirect
348. C₃⋊C₈	C₂×C₅×D₄	semidirect
357. C₂²×C₅	C₂×#208	semidirect
365. C₄×C₅	C₂×#208	semidirect
403. C₃×C₅	D₄×M₁₆	semidirect
413. C₂²×C₃	C₂×C₅×M₁₆	semidirect
421. C₃×C₄	C₂×C₅×M₁₆	semidirect
438. D₄	C₅×#208	direct (N × H)
467. C₅	D₄×#208	direct (N × H)
476. C₂²	C₂×C₅×#208	semidirect
484. C₄	C₂×C₅×#208	semidirect
488. C₃	C₅×D₄×M₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₄×C₅×D₄	2
C₂²×C₅×#208	2
C₅×#5207	2
C₅×#5012	2
C₅×#5011	2
C₅×D₄×C₃⋊C₈	2
C₅×#4924	2
C₄×C₅×#208	2
C₅×D₄×M₁₆	3
D₄×#208	5

Subgroups — C5×D4×#208 #14415684

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₄×#208 #14415684