Subgroups — C₂×C₅×#4688 #14414825

Order 1920.

1104 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×ΓL(1,𝔽₂₅)	C₂	1	2	yes	maximal, complemented
2	C₂×C₄×C₅×D₁₂	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₄×C₅×C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×(C₂×D₃)⋊C₈	C₂	1	2	yes	maximal, complemented
5	C₂×C₅×C₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4688	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₅×#436	—	3	1	no	maximal, Hall
8	C₂²×C₅×D₁₂	C₄	1	1	yes	characteristic
9	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
10	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
13	C₂×C₅×(C₂×D₃)⋊C₄	C₄	1	2	yes	—
14	C₂×C₅×C₄⋊Dic₃	C₄	1	1	yes	characteristic
15	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	—
16	C₂×C₅×ΓL(1,𝔽₂₅)	—	2	8	no	—
17	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	8	yes	complemented
18	C₄×C₅×D₁₂	C₄	1	4	yes	—
19	C₄×C₅×D₁₂	C₂²	1	4	yes	—
20	C₃×C₄×C₅×C₈	C₂²	1	4	yes	complemented
21	C₅×(C₂×D₃)⋊C₈	C₂²	1	8	yes	complemented
22	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	4	yes	complemented
23	C₂×#4688	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
24	C₂²×C₅×M₁₆	—	3	2	no	—
25	C₂×C₄×C₅×D₄	—	3	1	no	—
26	C₅×#436	—	3	8	no	—
27	C₂×C₅×C₄⋊C₈	—	3	1	no	—
28	C₂×C₅×C₂²⋊C₈	—	3	2	no	—
29	C₂×C₄×C₅×C₈	D₃	1	1	yes	characteristic, complemented
30	C₂³×C₅×D₃	C₂×C₄	1	2	yes	—
31	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
34	C₂²×C₅×Dic₃	C₂×C₄	1	2	yes	—
35	C₂×C₅×D₁₂	—	2	4	no	—
36	C₂×C₅×D₁₂	C₂×C₄	1	4	yes	—
37	C₂×C₄×C₅×D₃	—	2	4	no	—
38	C₂×C₄×C₅×D₃	—	2	4	no	—
39	C₂×C₄×C₅×D₃	C₂×C₄	1	4	yes	—
40	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
41	C₂×C₃×C₅×C₈	—	2	2	no	—
42	C₂×C₃×C₅×C₈	D₄	1	4	yes	complemented
43	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
44	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
45	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
46	C₃×C₄²×C₅	C₂³	1	2	yes	—
47	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	8	yes	—
48	C₅×C₄⋊Dic₃	C₂×C₄	1	4	yes	—
49	C₂×C₅×C₃⋊C₈	—	2	4	no	—
50	C₂×C₅×C₃⋊C₈	C₂³	1	4	yes	—
51	C₅×ΓL(1,𝔽₂₅)	—	2	16	no	—
52	C₂²×ΓL(1,𝔽₂₅)	C₂×C₅	1	2	yes	complemented
53	C₂×C₄×D₁₂	C₂×C₅	1	1	yes	characteristic
54	C₂×C₃×C₄×C₈	C₂×C₅	1	1	yes	characteristic, complemented
55	C₂×(C₂×D₃)⋊C₈	C₂×C₅	1	2	yes	complemented
56	C₂×C₄⋊(C₃⋊C₈)	C₂×C₅	1	1	yes	characteristic, complemented
57	#4688	C₂×C₅	1	8	yes	direct product factor
58	C₂²×C₅×D₄	—	3	1	no	—
59	C₂³×C₄×C₅	—	3	2	no	—
60	C₂×C₅×M₁₆	—	3	8	no	—
61	C₂×C₅×M₁₆	—	6	8	no	—
62	C₂²×C₅×C₈	—	3	2	no	—
63	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
64	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
65	C₄×C₅×D₄	—	3	4	no	—
66	C₄×C₅×D₄	—	3	4	no	—
67	C₂×C₅×C₄⋊C₄	—	3	1	no	—
68	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
69	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
70	C₅×C₄⋊C₈	—	3	4	no	—
71	C₅×C₂²⋊C₈	—	3	8	no	—
72	C₄×C₅×C₈	C₂×D₃	1	4	yes	complemented
73	C₂×#436	—	3	1	no	Sylow
74	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
75	C₂²×C₅×D₃	—	2	4	no	—
76	C₂²×C₅×D₃	—	2	4	no	—
77	C₂²×C₅×D₃	—	2	4	no	—
78	C₂²×C₅×D₃	C₂²×C₄	1	4	yes	—
79	C₂×C₃×C₄×C₅	—	2	2	no	—
80	C₂×C₃×C₄×C₅	M₁₆	1	4	yes	complemented
81	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
82	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
83	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
84	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
85	C₂×C₃×C₄×C₅	#41	1	2	yes	—
86	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
87	C₂×C₅×Dic₃	—	2	4	no	—
88	C₂×C₅×Dic₃	C₂²×C₄	1	4	yes	—
89	C₅×D₁₂	—	2	8	no	—
90	C₄×C₅×D₃	—	2	8	no	—
91	C₄×C₅×D₃	—	2	4	no	—
92	C₄×C₅×D₃	—	2	4	no	—
93	C₃×C₅×C₈	—	2	2	no	—
94	C₃×C₅×C₈	C₂×D₄	1	4	yes	complemented
95	C₅×C₃⋊C₈	—	2	4	no	—
96	C₂²×D₁₂	C₄×C₅	1	1	yes	characteristic
97	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
98	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
99	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
100	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
101	C₂×(C₂×D₃)⋊C₄	C₄×C₅	1	2	yes	—
102	C₂×C₄⋊Dic₃	C₄×C₅	1	1	yes	characteristic
103	C₂²×C₃⋊C₈	C₂²×C₅	1	2	yes	—
104	C₂×ΓL(1,𝔽₂₅)	—	2	8	no	—
105	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	8	yes	complemented
106	C₄×D₁₂	C₄×C₅	1	4	yes	—
107	C₄×D₁₂	C₂²×C₅	1	4	yes	—
108	C₃×C₄×C₈	C₂²×C₅	1	4	yes	complemented
109	(C₂×D₃)⋊C₈	C₂²×C₅	1	8	yes	complemented
110	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	4	yes	complemented
111	C₂⁴×C₅	—	3	2	no	—
112	C₂×C₅×D₄	—	3	4	no	—
113	C₂×C₅×D₄	—	6	4	no	—
114	C₂²×C₄×C₅	—	3	2	no	—
115	C₂²×C₄×C₅	—	3	4	no	—
116	C₂²×C₄×C₅	—	3	4	no	—
117	C₂²×C₄×C₅	—	6	4	no	—
118	C₂²×C₄×C₅	—	6	4	no	—
119	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
120	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
121	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
122	C₅×M₁₆	—	6	16	no	—
123	C₂×C₅×C₈	—	2	2	no	—
124	C₂×C₅×C₈	—	3	4	no	—
125	C₂×C₅×C₈	—	6	4	no	—
126	C₂×C₅×C₈	D₁₂	1	4	yes	complemented
127	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
128	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
129	C₅×C₄⋊C₄	—	3	4	no	—
130	C₅×C₂²⋊C₄	—	3	8	no	—
131	C₄²×C₅	C₄×D₃	1	2	yes	—
132	C₄²×C₅	C₂²×D₃	1	2	yes	—
133	C₂²×M₁₆	—	3	2	no	—
134	C₂×C₄×D₄	—	3	1	no	—
135	#436	—	3	8	no	—
136	C₂×C₄⋊C₈	—	3	1	no	—
137	C₂×C₂²⋊C₈	—	3	2	no	—
138	C₂×C₄×C₈	C₅×D₃	1	1	yes	characteristic, complemented
139	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
140	C₂²×C₃×C₅	C₂×M₁₆	1	2	yes	—
141	C₂²×C₃×C₅	#131	1	2	yes	—
142	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
143	C₂×C₅×D₃	—	2	4	no	—
144	C₂×C₅×D₃	—	2	4	no	—
145	C₂×C₅×D₃	—	2	4	no	—
146	C₂×C₅×D₃	—	4	8	no	—
147	C₃×C₄×C₅	—	2	2	no	—
148	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
149	C₃×C₄×C₅	C₂×M₁₆	1	4	yes	complemented
150	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
151	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
152	C₅×Dic₃	—	2	4	no	—
153	C₂³×D₃	C₂×C₄×C₅	1	2	yes	—
154	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
155	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
156	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
157	C₂²×Dic₃	C₂×C₄×C₅	1	2	yes	—
158	C₂×D₁₂	—	2	4	no	—
159	C₂×D₁₂	C₂×C₄×C₅	1	4	yes	—
160	C₂×C₄×D₃	—	2	4	no	—
161	C₂×C₄×D₃	—	2	4	no	—
162	C₂×C₄×D₃	C₂×C₄×C₅	1	4	yes	—
163	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
164	C₂×C₃×C₈	—	2	2	no	—
165	C₂×C₃×C₈	C₅×D₄	1	4	yes	complemented
166	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
167	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
168	C₃×C₄²	C₂×C₄×C₅	1	2	yes	—
169	C₃×C₄²	C₂³×C₅	1	2	yes	—
170	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	8	yes	—
171	C₄⋊Dic₃	C₂×C₄×C₅	1	4	yes	—
172	C₂×C₃⋊C₈	—	2	4	no	—
173	C₂×C₃⋊C₈	C₂³×C₅	1	4	yes	—
174	ΓL(1,𝔽₂₅)	—	2	16	no	—
175	C₂³×C₅	—	3	4	no	—
176	C₂³×C₅	—	6	4	no	—
177	C₂³×C₅	—	6	4	no	—
178	C₂³×C₅	—	6	4	no	—
179	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
180	C₅×D₄	—	6	8	no	—
181	C₂×C₄×C₅	—	2	2	no	—
182	C₂×C₄×C₅	—	3	4	no	—
183	C₂×C₄×C₅	—	6	4	no	—
184	C₂×C₄×C₅	—	6	8	no	—
185	C₂×C₄×C₅	—	6	4	no	—
186	C₂×C₄×C₅	—	6	4	no	—
187	C₂×C₄×C₅	ΓL(1,𝔽₂₅)	1	4	yes	complemented
188	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
189	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
190	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
191	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
192	C₂×C₄×C₅	#235	1	2	yes	—
193	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
194	C₅×C₈	—	2	2	no	—
195	C₅×C₈	—	6	4	no	—
196	C₅×C₈	C₂×D₁₂	1	4	yes	complemented
197	C₂²×D₄	—	3	1	no	—
198	C₂³×C₄	—	3	2	no	—
199	C₂×M₁₆	—	3	8	no	—
200	C₂×M₁₆	—	6	8	no	—
201	C₂²×C₈	—	3	2	no	—
202	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
203	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
204	C₄×D₄	—	3	4	no	—
205	C₄×D₄	—	3	4	no	—
206	C₂×C₄⋊C₄	—	3	1	no	—
207	C₂×C₂²⋊C₄	—	3	2	no	—
208	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
209	C₄⋊C₈	—	3	4	no	—
210	C₂²⋊C₈	—	3	8	no	—
211	C₄×C₈	C₂×C₅×D₃	1	4	yes	complemented
212	C₂×C₃×C₅	#436	1	4	yes	complemented
213	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
214	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
215	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
216	C₅×D₃	—	4	4	no	—
217	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
218	C₂²×D₃	—	2	4	no	—
219	C₂²×D₃	—	2	4	no	—
220	C₂²×D₃	—	2	4	no	—
221	C₂²×D₃	C₂²×C₄×C₅	1	4	yes	—
222	C₂×C₃×C₄	—	2	2	no	—
223	C₂×C₃×C₄	C₅×M₁₆	1	4	yes	complemented
224	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
225	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
226	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
227	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
228	C₂×C₃×C₄	C₅×#41	1	2	yes	—
229	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
230	C₂×Dic₃	—	2	4	no	—
231	C₂×Dic₃	C₂²×C₄×C₅	1	4	yes	—
232	D₁₂	—	2	8	no	—
233	C₄×D₃	—	2	8	no	—
234	C₄×D₃	—	2	4	no	—
235	C₄×D₃	—	2	4	no	—
236	C₃×C₈	—	2	2	no	—
237	C₃×C₈	C₂×C₅×D₄	1	4	yes	complemented
238	C₃⋊C₈	—	2	4	no	—
239	C₂²×C₅	—	6	4	no	—
240	C₂²×C₅	—	6	4	no	—
241	C₂²×C₅	—	6	4	no	—
242	C₂²×C₅	—	12	8	no	—
243	C₂²×C₅	C₄×D₁₂	1	2	yes	—
244	C₂²×C₅	C₂×ΓL(1,𝔽₂₅)	1	2	yes	—
245	C₂²×C₅	#901	1	2	yes	—
246	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
247	C₄×C₅	—	2	2	no	—
248	C₄×C₅	—	6	4	no	—
249	C₄×C₅	C₄×D₁₂	1	2	yes	—
250	C₄×C₅	C₂×ΓL(1,𝔽₂₅)	1	4	yes	complemented
251	C₄×C₅	C₂²×D₁₂	1	1	yes	characteristic
252	C₄×C₅	C₂×#235	1	1	yes	characteristic
253	C₂⁴	—	3	2	no	—
254	C₂×D₄	—	3	4	no	—
255	C₂×D₄	—	6	4	no	—
256	C₂²×C₄	—	3	2	no	—
257	C₂²×C₄	—	3	4	no	—
258	C₂²×C₄	—	3	4	no	—
259	C₂²×C₄	—	6	4	no	—
260	C₂²×C₄	—	6	4	no	—
261	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
262	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
263	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
264	M₁₆	—	6	16	no	—
265	C₂×C₈	—	2	2	no	—
266	C₂×C₈	—	3	4	no	—
267	C₂×C₈	—	6	4	no	—
268	C₂×C₈	C₅×D₁₂	1	4	yes	complemented
269	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
270	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
271	C₄⋊C₄	—	3	4	no	—
272	C₂²⋊C₄	—	3	8	no	—
273	C₄²	C₄×C₅×D₃	1	2	yes	—
274	C₄²	C₂²×C₅×D₃	1	2	yes	—
275	C₃×C₅	C₂×#436	1	1	yes	characteristic, complemented, Hall
276	C₂²×C₃	C₄×C₅×D₄	1	2	yes	—
277	C₂²×C₃	C₂×C₅×M₁₆	1	2	yes	—
278	C₂²×C₃	C₅×#131	1	2	yes	—
279	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
280	C₂×D₃	—	2	4	no	—
281	C₂×D₃	—	2	4	no	—
282	C₂×D₃	—	2	4	no	—
283	C₂×D₃	—	4	8	no	—
284	C₃×C₄	—	2	2	no	—
285	C₃×C₄	C₄×C₅×D₄	1	2	yes	—
286	C₃×C₄	C₂×C₅×M₁₆	1	4	yes	complemented
287	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
288	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
289	Dic₃	—	2	4	no	—
290	C₂×C₅	—	12	4	no	—
291	C₂×C₅	#4688	1	4	yes	direct product factor
292	C₂×C₅	C₂×C₄×D₁₂	1	1	yes	characteristic
293	C₂×C₅	C₂²×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
294	C₂×C₅	C₂×#901	1	1	yes	characteristic
295	C₂³	—	3	4	no	—
296	C₂³	—	6	4	no	—
297	C₂³	—	6	4	no	—
298	C₂³	—	6	4	no	—
299	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
300	D₄	—	6	8	no	—
301	C₂×C₄	—	2	2	no	—
302	C₂×C₄	—	3	4	no	—
303	C₂×C₄	—	6	4	no	—
304	C₂×C₄	—	6	8	no	—
305	C₂×C₄	—	6	4	no	—
306	C₂×C₄	—	6	4	no	—
307	C₂×C₄	C₅×ΓL(1,𝔽₂₅)	1	4	yes	complemented
308	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
309	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
310	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
311	C₂×C₄	C₂×C₅×D₁₂	1	2	yes	—
312	C₂×C₄	C₅×#235	1	2	yes	—
313	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
314	C₈	—	2	2	no	—
315	C₈	—	6	4	no	—
316	C₈	C₂×C₅×D₁₂	1	4	yes	complemented
317	C₂×C₃	C₅×#436	1	4	yes	complemented
318	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
319	C₂×C₃	C₂²×C₅×M₁₆	1	1	yes	characteristic
320	C₂×C₃	C₂×C₅×#131	1	1	yes	characteristic
321	D₃	—	4	4	no	—
322	C₅	C₂×#4688	1	1	yes	characteristic, direct product factor, Sylow
323	C₂²	—	6	4	no	—
324	C₂²	—	6	4	no	—
325	C₂²	—	6	4	no	—
326	C₂²	—	12	8	no	—
327	C₂²	C₄×C₅×D₁₂	1	2	yes	—
328	C₂²	C₂×C₅×ΓL(1,𝔽₂₅)	1	2	yes	—
329	C₂²	C₅×#901	1	2	yes	—
330	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
331	C₄	—	2	2	no	—
332	C₄	—	6	4	no	—
333	C₄	C₄×C₅×D₁₂	1	2	yes	—
334	C₄	C₂×C₅×ΓL(1,𝔽₂₅)	1	4	yes	complemented
335	C₄	C₂²×C₅×D₁₂	1	1	yes	characteristic
336	C₄	C₂×C₅×#235	1	1	yes	characteristic
337	C₃	C₂×C₅×#436	1	1	yes	characteristic, complemented, Sylow
338	C₂	—	12	4	no	—
339	C₂	C₅×#4688	1	4	yes	direct product factor
340	C₂	C₂×C₄×C₅×D₁₂	1	1	yes	characteristic
341	C₂	C₂²×C₅×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
342	C₂	C₂×C₅×#901	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×C₄×C₅×C₈	C₂
socle	C₂³×C₃×C₅	C₂²×C₄
prime radical	C₂²×C₅×D₁₂	C₄
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₂×C₄×C₅×C₈	D₃
hypocenter	C₃	C₂×C₅×#436
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ C₂×C₄×C₅×C₈

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×ΓL(1,𝔽₂₅)	C₂	semidirect
3. C₂×C₃×C₄×C₅×C₈	C₂	semidirect
4. C₂×C₅×(C₂×D₃)⋊C₈	C₂	semidirect
5. C₂×C₅×C₄⋊(C₃⋊C₈)	C₂	semidirect
6. C₅×#4688	C₂	direct (N × H)
17. C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	semidirect
20. C₃×C₄×C₅×C₈	C₂²	semidirect
21. C₅×(C₂×D₃)⋊C₈	C₂²	semidirect
22. C₅×C₄⋊(C₃⋊C₈)	C₂²	semidirect
23. C₂×#4688	C₅	direct (N × H)
29. C₂×C₄×C₅×C₈	D₃	semidirect
42. C₂×C₃×C₅×C₈	D₄	semidirect
52. C₂²×ΓL(1,𝔽₂₅)	C₂×C₅	semidirect
54. C₂×C₃×C₄×C₈	C₂×C₅	semidirect
55. C₂×(C₂×D₃)⋊C₈	C₂×C₅	semidirect
56. C₂×C₄⋊(C₃⋊C₈)	C₂×C₅	semidirect
57. #4688	C₂×C₅	direct (N × H)
72. C₄×C₅×C₈	C₂×D₃	semidirect
80. C₂×C₃×C₄×C₅	M₁₆	semidirect
94. C₃×C₅×C₈	C₂×D₄	semidirect
105. C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	semidirect
108. C₃×C₄×C₈	C₂²×C₅	semidirect
109. (C₂×D₃)⋊C₈	C₂²×C₅	semidirect
110. C₄⋊(C₃⋊C₈)	C₂²×C₅	semidirect
126. C₂×C₅×C₈	D₁₂	semidirect
138. C₂×C₄×C₈	C₅×D₃	semidirect
149. C₃×C₄×C₅	C₂×M₁₆	semidirect
165. C₂×C₃×C₈	C₅×D₄	semidirect
187. C₂×C₄×C₅	ΓL(1,𝔽₂₅)	semidirect
196. C₅×C₈	C₂×D₁₂	semidirect
211. C₄×C₈	C₂×C₅×D₃	semidirect
212. C₂×C₃×C₅	#436	semidirect
223. C₂×C₃×C₄	C₅×M₁₆	semidirect
237. C₃×C₈	C₂×C₅×D₄	semidirect
250. C₄×C₅	C₂×ΓL(1,𝔽₂₅)	semidirect
268. C₂×C₈	C₅×D₁₂	semidirect
275. C₃×C₅	C₂×#436	semidirect
286. C₃×C₄	C₂×C₅×M₁₆	semidirect
291. C₂×C₅	#4688	direct (N × H)
307. C₂×C₄	C₅×ΓL(1,𝔽₂₅)	semidirect
316. C₈	C₂×C₅×D₁₂	semidirect
317. C₂×C₃	C₅×#436	semidirect
322. C₅	C₂×#4688	direct (N × H)
334. C₄	C₂×C₅×ΓL(1,𝔽₂₅)	semidirect
337. C₃	C₂×C₅×#436	semidirect
339. C₂	C₅×#4688	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₅×ΓL(1,𝔽₂₅)	2
C₂×C₄×C₅×D₁₂	2
C₂×C₃×C₄×C₅×C₈	2
C₂×C₅×(C₂×D₃)⋊C₈	2
C₂×C₅×C₄⋊(C₃⋊C₈)	2
C₅×#4688	2
C₂×C₅×#436	3
C₂×#4688	5

Subgroups — C2×C5×#4688 #14414825

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#4688 #14414825