Subgroups — C₂×C₅×#4700 #14417842

Order 1920.

944 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#904	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#901	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×C₄×C₅×C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#819	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#805	C₂	1	2	yes	maximal, complemented
6	C₅×#4700	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₅×#443	—	3	1	no	maximal, Hall
8	C₂×C₅×#235	C₂²	1	2	yes	—
9	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
10	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
12	C₂×C₅×#208	C₂²	1	2	yes	—
13	C₂×C₅×Dic₁₂	C₄	1	1	yes	characteristic, complemented
14	C₅×#904	C₄	1	4	yes	complemented
15	C₅×#904	C₂²	1	4	yes	—
16	C₂×C₅×D₂₄	C₄	1	1	yes	characteristic, complemented
17	C₂×C₅×#204	C₄	1	2	yes	complemented
18	C₅×#901	—	2	4	no	—
19	C₅×#901	C₂²	1	8	yes	complemented
20	C₂×C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
21	C₂×C₅×D₃×C₈	—	2	2	no	—
22	C₃×C₄×C₅×C₈	C₂²	1	4	yes	complemented
23	C₅×#819	C₂²	1	4	yes	complemented
24	C₅×#805	C₂²	1	8	yes	complemented
25	C₂×#4700	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
26	C₂×C₅×#135	—	3	1	no	—
27	C₂×C₅×#131	—	3	2	no	—
28	C₅×#443	—	3	8	no	—
29	C₂×C₅×#108	—	3	1	no	—
30	C₂×C₅×#104	—	3	2	no	—
31	C₂×C₄×C₅×C₈	D₃	1	1	yes	characteristic, complemented
32	C₂²×C₃×C₄×C₅	—	2	1	no	—
33	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
34	C₂×C₅×#67	—	2	2	no	—
35	C₅×#235	—	2	2	no	—
36	C₅×#235	—	2	2	no	—
37	C₅×#235	C₂×C₄	1	4	yes	—
38	C₅×#235	C₂³	1	4	yes	—
39	C₂×C₅×D₁₂	C₂×C₄	1	2	yes	—
40	C₂×C₄×C₅×D₃	—	2	2	no	—
41	C₂×C₅×Dic₆	C₂×C₄	1	2	yes	—
42	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
43	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
44	C₂×C₃×C₅×C₈	C₂×C₄	1	2	yes	—
45	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
46	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
47	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
48	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
49	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
50	C₃×C₄²×C₅	—	2	1	no	—
51	C₃×C₄²×C₅	C₂³	1	2	yes	—
52	C₅×#208	—	2	2	no	—
53	C₅×#208	C₂³	1	4	yes	—
54	C₂×C₅×C₃⋊C₈	—	2	2	no	—
55	C₅×Dic₁₂	C₂×C₄	1	4	yes	complemented
56	C₅×D₂₄	C₂×C₄	1	4	yes	complemented
57	C₅×#204	C₂×C₄	1	8	yes	complemented
58	C₅×ΓL(1,𝔽₂₅)	—	2	8	no	—
59	C₅×D₃×C₈	—	2	8	no	—
60	C₂×#904	C₂×C₅	1	1	yes	characteristic
61	C₂×#901	C₂×C₅	1	2	yes	complemented
62	C₂×C₃×C₄×C₈	C₂×C₅	1	1	yes	characteristic, complemented
63	C₂×#819	C₂×C₅	1	1	yes	characteristic, complemented
64	C₂×#805	C₂×C₅	1	2	yes	complemented
65	#4700	C₂×C₅	1	8	yes	direct product factor
66	C₂×C₅×#41	—	3	2	no	—
67	C₅×#135	—	3	4	no	—
68	C₅×#135	—	3	4	no	—
69	C₂×C₅×Q₁₆	—	3	1	no	—
70	C₂×C₅×SD₁₆	—	3	2	no	—
71	C₂×C₅×D₈	—	3	1	no	—
72	C₅×#131	—	3	8	no	—
73	C₅×#131	—	6	4	no	—
74	C₂×C₅×M₁₆	—	3	2	no	—
75	C₂×C₅×M₁₆	—	6	2	no	—
76	C₂²×C₅×C₈	—	6	2	no	—
77	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
78	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
79	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
80	C₅×#108	—	3	4	no	—
81	C₅×#104	—	3	8	no	—
82	C₄×C₅×C₈	C₂×D₃	1	4	yes	complemented
83	C₂×#443	—	3	1	no	Sylow
84	C₂³×C₃×C₅	#41	1	1	yes	characteristic
85	C₂²×C₅×D₃	—	2	2	no	—
86	C₂×C₃×C₄×C₅	—	2	4	no	—
87	C₂×C₃×C₄×C₅	—	2	2	no	—
88	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
89	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
90	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
91	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
92	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
93	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
94	C₅×#67	—	2	4	no	—
95	C₅×#67	—	2	4	no	—
96	C₂×C₅×Dic₃	—	2	2	no	—
97	C₅×D₁₂	—	2	2	no	—
98	C₅×D₁₂	C₂²×C₄	1	4	yes	—
99	C₄×C₅×D₃	—	2	4	no	—
100	C₄×C₅×D₃	—	2	4	no	—
101	C₅×Dic₆	—	2	2	no	—
102	C₅×Dic₆	C₂²×C₄	1	4	yes	—
103	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
104	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
105	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
106	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
107	C₅×C₃⋊C₈	—	2	4	no	—
108	C₂×#235	C₂²×C₅	1	2	yes	—
109	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
110	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
111	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
112	C₂×#208	C₂²×C₅	1	2	yes	—
113	C₂×Dic₁₂	C₄×C₅	1	1	yes	characteristic, complemented
114	#904	C₄×C₅	1	4	yes	complemented
115	#904	C₂²×C₅	1	4	yes	—
116	C₂×D₂₄	C₄×C₅	1	1	yes	characteristic, complemented
117	C₂×#204	C₄×C₅	1	2	yes	complemented
118	#901	—	2	4	no	—
119	#901	C₂²×C₅	1	8	yes	complemented
120	C₂×ΓL(1,𝔽₂₅)	—	2	2	no	—
121	C₂×D₃×C₈	—	2	2	no	—
122	C₃×C₄×C₈	C₂²×C₅	1	4	yes	complemented
123	#819	C₂²×C₅	1	4	yes	complemented
124	#805	C₂²×C₅	1	8	yes	complemented
125	C₅×#41	—	3	4	no	—
126	C₅×#41	—	3	4	no	—
127	C₅×#41	—	6	2	no	—
128	C₅×#41	—	6	2	no	—
129	C₂×C₅×Q₈	—	3	2	no	—
130	C₂×C₅×D₄	—	3	2	no	—
131	C₂×C₅×D₄	—	6	2	no	—
132	C₂²×C₄×C₅	—	2	1	no	—
133	C₂²×C₄×C₅	—	6	2	no	—
134	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
135	C₅×Q₁₆	—	3	4	no	—
136	C₅×SD₁₆	—	3	8	no	—
137	C₅×D₈	—	3	4	no	—
138	C₅×M₁₆	—	3	4	no	—
139	C₅×M₁₆	—	6	2	no	—
140	C₅×M₁₆	—	6	8	no	—
141	C₂×C₅×C₈	—	6	2	no	—
142	C₂×C₅×C₈	—	6	8	no	—
143	C₂×C₅×C₈	C₄×D₃	1	1	yes	characteristic
144	C₂×C₅×C₈	C₄×D₃	1	1	yes	characteristic
145	C₂×C₅×C₈	C₄×D₃	1	2	yes	—
146	C₂×C₅×C₈	D₁₂	1	1	yes	characteristic
147	C₂×C₅×C₈	D₁₂	1	2	yes	—
148	C₂×C₅×C₈	D₁₂	1	1	yes	characteristic
149	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
150	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
151	C₄²×C₅	—	2	1	no	—
152	C₄²×C₅	C₂²×D₃	1	2	yes	—
153	C₂×#135	—	3	1	no	—
154	C₂×#131	—	3	2	no	—
155	#443	—	3	8	no	—
156	C₂×#108	—	3	1	no	—
157	C₂×#104	—	3	2	no	—
158	C₂×C₄×C₈	C₅×D₃	1	1	yes	characteristic, complemented
159	C₂²×C₃×C₅	—	2	2	no	—
160	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
161	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
162	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
163	C₂×C₅×D₃	—	2	4	no	—
164	C₂×C₅×D₃	—	4	4	no	—
165	C₃×C₄×C₅	—	2	4	no	—
166	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
167	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
168	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
169	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
170	C₅×Dic₃	—	2	4	no	—
171	C₂²×C₃×C₄	—	2	1	no	—
172	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
173	C₂×#67	—	2	2	no	—
174	#235	—	2	2	no	—
175	#235	—	2	2	no	—
176	#235	C₂×C₄×C₅	1	4	yes	—
177	#235	C₂³×C₅	1	4	yes	—
178	C₂×D₁₂	C₂×C₄×C₅	1	2	yes	—
179	C₂×C₄×D₃	—	2	2	no	—
180	C₂×Dic₆	C₂×C₄×C₅	1	2	yes	—
181	C₂×C₃×C₈	C₂×C₄×C₅	1	1	yes	characteristic
182	C₂×C₃×C₈	C₂×C₄×C₅	1	1	yes	characteristic
183	C₂×C₃×C₈	C₂×C₄×C₅	1	2	yes	—
184	C₂×C₃×C₈	C₅×D₄	1	1	yes	characteristic
185	C₂×C₃×C₈	C₅×D₄	1	1	yes	characteristic
186	C₂×C₃×C₈	C₅×D₄	1	2	yes	—
187	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
188	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
189	C₃×C₄²	—	2	1	no	—
190	C₃×C₄²	C₂³×C₅	1	2	yes	—
191	#208	—	2	2	no	—
192	#208	C₂³×C₅	1	4	yes	—
193	C₂×C₃⋊C₈	—	2	2	no	—
194	Dic₁₂	C₂×C₄×C₅	1	4	yes	complemented
195	D₂₄	C₂×C₄×C₅	1	4	yes	complemented
196	#204	C₂×C₄×C₅	1	8	yes	complemented
197	ΓL(1,𝔽₂₅)	—	2	8	no	—
198	D₃×C₈	—	2	8	no	—
199	C₂³×C₅	—	6	2	no	—
200	C₂³×C₅	#235	1	1	yes	characteristic
201	C₅×Q₈	—	3	4	no	—
202	C₅×Q₈	—	6	2	no	—
203	C₅×D₄	—	3	4	no	—
204	C₅×D₄	—	6	4	no	—
205	C₅×D₄	—	6	4	no	—
206	C₅×D₄	—	6	2	no	—
207	C₂×C₄×C₅	—	2	4	no	—
208	C₂×C₄×C₅	—	2	2	no	—
209	C₂×C₄×C₅	—	6	2	no	—
210	C₂×C₄×C₅	—	6	4	no	—
211	C₂×C₄×C₅	—	6	4	no	—
212	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
213	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
214	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
215	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
216	C₂×C₄×C₅	#235	1	1	yes	characteristic
217	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
218	C₅×C₈	—	6	4	no	—
219	C₅×C₈	C₂×C₄×D₃	1	2	yes	—
220	C₅×C₈	C₂×C₄×D₃	1	2	yes	—
221	C₅×C₈	C₂×D₁₂	1	2	yes	—
222	C₅×C₈	C₂×D₁₂	1	2	yes	—
223	C₂×#41	—	3	2	no	—
224	#135	—	3	4	no	—
225	#135	—	3	4	no	—
226	C₂×Q₁₆	—	3	1	no	—
227	C₂×SD₁₆	—	3	2	no	—
228	C₂×D₈	—	3	1	no	—
229	#131	—	3	8	no	—
230	#131	—	6	4	no	—
231	C₂×M₁₆	—	3	2	no	—
232	C₂×M₁₆	—	6	2	no	—
233	C₂²×C₈	—	6	2	no	—
234	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
235	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
236	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
237	#108	—	3	4	no	—
238	#104	—	3	8	no	—
239	C₄×C₈	C₂×C₅×D₃	1	4	yes	complemented
240	C₂×C₃×C₅	—	2	1	no	—
241	C₂×C₃×C₅	—	2	1	no	—
242	C₂×C₃×C₅	#443	1	2	yes	complemented
243	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
244	C₅×D₃	—	4	4	no	—
245	C₂³×C₃	C₅×#41	1	1	yes	characteristic
246	C₂²×D₃	—	2	2	no	—
247	C₂×C₃×C₄	—	2	4	no	—
248	C₂×C₃×C₄	—	2	2	no	—
249	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
250	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
251	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
252	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
253	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
254	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
255	#67	—	2	4	no	—
256	#67	—	2	4	no	—
257	C₂×Dic₃	—	2	2	no	—
258	D₁₂	—	2	2	no	—
259	D₁₂	C₂²×C₄×C₅	1	4	yes	—
260	C₄×D₃	—	2	4	no	—
261	C₄×D₃	—	2	4	no	—
262	Dic₆	—	2	2	no	—
263	Dic₆	C₂²×C₄×C₅	1	4	yes	—
264	C₃×C₈	C₂²×C₄×C₅	1	2	yes	—
265	C₃×C₈	C₂²×C₄×C₅	1	2	yes	—
266	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
267	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
268	C₃⋊C₈	—	2	4	no	—
269	C₂²×C₅	—	2	2	no	—
270	C₂²×C₅	—	6	4	no	—
271	C₂²×C₅	—	12	4	no	—
272	C₂²×C₅	C₄×D₁₂	1	1	yes	characteristic
273	C₂²×C₅	C₄×D₁₂	1	1	yes	characteristic
274	C₂²×C₅	C₂×#235	1	1	yes	characteristic
275	C₄×C₅	—	2	4	no	—
276	C₄×C₅	—	6	4	no	—
277	C₄×C₅	C₄×D₁₂	1	1	yes	characteristic
278	C₄×C₅	C₄×D₁₂	1	1	yes	characteristic
279	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
280	C₄×C₅	C₂²×D₁₂	1	1	yes	characteristic
281	#41	—	3	4	no	—
282	#41	—	3	4	no	—
283	#41	—	6	2	no	—
284	#41	—	6	2	no	—
285	C₂×Q₈	—	3	2	no	—
286	C₂×D₄	—	3	2	no	—
287	C₂×D₄	—	6	2	no	—
288	C₂²×C₄	—	2	1	no	—
289	C₂²×C₄	—	6	2	no	—
290	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
291	Q₁₆	—	3	4	no	—
292	SD₁₆	—	3	8	no	—
293	D₈	—	3	4	no	—
294	M₁₆	—	3	4	no	—
295	M₁₆	—	6	2	no	—
296	M₁₆	—	6	8	no	—
297	C₂×C₈	—	6	2	no	—
298	C₂×C₈	—	6	8	no	—
299	C₂×C₈	C₄×C₅×D₃	1	1	yes	characteristic
300	C₂×C₈	C₄×C₅×D₃	1	1	yes	characteristic
301	C₂×C₈	C₄×C₅×D₃	1	2	yes	—
302	C₂×C₈	C₅×D₁₂	1	1	yes	characteristic
303	C₂×C₈	C₅×D₁₂	1	1	yes	characteristic
304	C₂×C₈	C₅×D₁₂	1	2	yes	—
305	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
306	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
307	C₄²	—	2	1	no	—
308	C₄²	C₂²×C₅×D₃	1	2	yes	—
309	C₃×C₅	C₂×#443	1	1	yes	characteristic, complemented, Hall
310	C₂²×C₃	—	2	2	no	—
311	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
312	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
313	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
314	C₂×D₃	—	2	4	no	—
315	C₂×D₃	—	4	4	no	—
316	C₃×C₄	—	2	4	no	—
317	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
318	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
319	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
320	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
321	Dic₃	—	2	4	no	—
322	C₂×C₅	—	2	1	no	—
323	C₂×C₅	—	2	1	no	—
324	C₂×C₅	—	12	4	no	—
325	C₂×C₅	#4700	1	2	yes	direct product factor
326	C₂×C₅	C₂×C₄×D₁₂	1	1	yes	characteristic
327	C₂³	—	6	2	no	—
328	C₂³	C₅×#235	1	1	yes	characteristic
329	Q₈	—	3	4	no	—
330	Q₈	—	6	2	no	—
331	D₄	—	3	4	no	—
332	D₄	—	6	4	no	—
333	D₄	—	6	4	no	—
334	D₄	—	6	2	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	6	2	no	—
338	C₂×C₄	—	6	4	no	—
339	C₂×C₄	—	6	4	no	—
340	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
341	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
342	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
343	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
344	C₂×C₄	C₅×#235	1	1	yes	characteristic
345	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
346	C₈	—	6	4	no	—
347	C₈	C₂×C₄×C₅×D₃	1	2	yes	—
348	C₈	C₂×C₄×C₅×D₃	1	2	yes	—
349	C₈	C₂×C₅×D₁₂	1	2	yes	—
350	C₈	C₂×C₅×D₁₂	1	2	yes	—
351	C₂×C₃	—	2	1	no	—
352	C₂×C₃	—	2	1	no	—
353	C₂×C₃	C₅×#443	1	2	yes	complemented
354	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
355	D₃	—	4	4	no	—
356	C₅	C₂×#4700	1	1	yes	characteristic, direct product factor, Sylow
357	C₂²	—	2	2	no	—
358	C₂²	—	6	4	no	—
359	C₂²	—	12	4	no	—
360	C₂²	C₄×C₅×D₁₂	1	1	yes	characteristic
361	C₂²	C₄×C₅×D₁₂	1	1	yes	characteristic
362	C₂²	C₂×C₅×#235	1	1	yes	characteristic
363	C₄	—	2	4	no	—
364	C₄	—	6	4	no	—
365	C₄	C₄×C₅×D₁₂	1	1	yes	characteristic
366	C₄	C₄×C₅×D₁₂	1	1	yes	characteristic
367	C₄	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
368	C₄	C₂²×C₅×D₁₂	1	1	yes	characteristic
369	C₃	C₂×C₅×#443	1	1	yes	characteristic, complemented, Sylow
370	C₂	—	2	1	no	—
371	C₂	—	2	1	no	—
372	C₂	—	12	4	no	—
373	C₂	C₅×#4700	1	2	yes	direct product factor
374	C₂	C₂×C₄×C₅×D₁₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅×C₈	D₁₂
commutator	C₃×C₄	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂×C₃×C₄×C₅×C₈	C₂
socle	C₂²×C₃×C₅	C₄×D₄
prime radical	C₂×C₅×#904	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₂×C₄×C₅×C₈	D₃
hypocenter	C₃	C₂×C₅×#443
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₅×C₈ ◁ C₂²×C₅×C₈ ◁ C₂×C₄×C₅×C₈

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#901	C₂	semidirect
3. C₂×C₃×C₄×C₅×C₈	C₂	semidirect
4. C₂×C₅×#819	C₂	semidirect
5. C₂×C₅×#805	C₂	semidirect
6. C₅×#4700	C₂	direct (N × H)
13. C₂×C₅×Dic₁₂	C₄	semidirect
14. C₅×#904	C₄	semidirect
16. C₂×C₅×D₂₄	C₄	semidirect
17. C₂×C₅×#204	C₄	semidirect
19. C₅×#901	C₂²	semidirect
22. C₃×C₄×C₅×C₈	C₂²	semidirect
23. C₅×#819	C₂²	semidirect
24. C₅×#805	C₂²	semidirect
25. C₂×#4700	C₅	direct (N × H)
31. C₂×C₄×C₅×C₈	D₃	semidirect
55. C₅×Dic₁₂	C₂×C₄	semidirect
56. C₅×D₂₄	C₂×C₄	semidirect
57. C₅×#204	C₂×C₄	semidirect
61. C₂×#901	C₂×C₅	semidirect
62. C₂×C₃×C₄×C₈	C₂×C₅	semidirect
63. C₂×#819	C₂×C₅	semidirect
64. C₂×#805	C₂×C₅	semidirect
65. #4700	C₂×C₅	direct (N × H)
82. C₄×C₅×C₈	C₂×D₃	semidirect
113. C₂×Dic₁₂	C₄×C₅	semidirect
114. #904	C₄×C₅	semidirect
116. C₂×D₂₄	C₄×C₅	semidirect
117. C₂×#204	C₄×C₅	semidirect
119. #901	C₂²×C₅	semidirect
122. C₃×C₄×C₈	C₂²×C₅	semidirect
123. #819	C₂²×C₅	semidirect
124. #805	C₂²×C₅	semidirect
158. C₂×C₄×C₈	C₅×D₃	semidirect
194. Dic₁₂	C₂×C₄×C₅	semidirect
195. D₂₄	C₂×C₄×C₅	semidirect
196. #204	C₂×C₄×C₅	semidirect
239. C₄×C₈	C₂×C₅×D₃	semidirect
242. C₂×C₃×C₅	#443	semidirect
309. C₃×C₅	C₂×#443	semidirect
325. C₂×C₅	#4700	direct (N × H)
353. C₂×C₃	C₅×#443	semidirect
356. C₅	C₂×#4700	direct (N × H)
369. C₃	C₂×C₅×#443	semidirect
373. C₂	C₅×#4700	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×#904	2
C₂×C₅×#901	2
C₂×C₃×C₄×C₅×C₈	2
C₂×C₅×#819	2
C₂×C₅×#805	2
C₅×#4700	2
C₂×C₅×#443	3
C₂×#4700	5

Subgroups — C2×C5×#4700 #14417842

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#4700 #14417842