Subgroups — C₂×C₅×#5769 #14509954

Order 1920.

3024 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#1009	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×C₅×#135	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#949	C₂	1	2	yes	maximal, complemented
4	C₅×#5769	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₅×#919	C₂	1	2	yes	maximal, complemented
6	C₂×C₅×#914	C₂	1	4	yes	maximal, complemented
7	C₂×C₅×D₃×D₈	C₂	1	2	yes	maximal, complemented
8	C₂²×C₅×D₂₄	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×#901	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅×#576	—	3	1	no	maximal, Hall
11	C₂×C₃×C₅×#41	C₂²	1	2	yes	complemented
12	C₅×#1009	—	2	8	no	—
13	C₅×#1009	C₂²	1	16	yes	complemented
14	C₂×C₅×#239	C₂²	1	4	yes	complemented
15	C₂×C₅×D₃×D₄	—	2	4	no	—
16	C₂×C₅×D₃×D₄	C₂²	1	4	yes	complemented
17	C₂×C₅×#235	—	2	2	no	—
18	C₂×C₅×#235	C₂²	1	1	yes	characteristic
19	C₂²×C₅×D₁₂	—	2	2	no	—
20	C₂²×C₅×D₁₂	C₂²	1	2	yes	complemented
21	C₃×C₅×#135	C₂²	1	8	yes	complemented
22	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	complemented
24	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic, complemented
25	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
26	C₅×#949	C₂²	1	16	yes	complemented
27	C₂×C₅×#215	C₂²	1	4	yes	complemented
28	C₂×C₅×#213	C₂²	1	4	yes	complemented
29	C₂×C₅×#208	C₂²	1	1	yes	characteristic, complemented
30	C₅×#919	C₂²	1	16	yes	complemented
31	C₅×#914	C₂²	1	32	yes	complemented
32	C₅×D₃×D₈	C₂²	1	16	yes	complemented
33	C₂×C₅×D₂₄	C₂²	1	2	yes	complemented
34	C₂×C₅×D₂₄	C₂²	1	2	yes	complemented
35	C₂×C₅×D₂₄	C₂²	1	8	yes	complemented
36	C₅×#901	C₂²	1	8	yes	complemented
37	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	complemented
38	C₂×C₅×D₃×C₈	C₂²	1	2	yes	complemented
39	C₂×#5769	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
40	C₂×C₅×H(5,𝔽₂)	—	3	2	no	—
41	C₅×#576	—	3	16	no	—
42	C₂×C₅×AGL(1,ℤ/8)	—	3	2	no	—
43	C₂×C₅×AGL(1,ℤ/8)	—	3	4	no	—
44	C₂×C₅×#135	—	3	2	no	—
45	C₂×C₅×#135	D₃	1	1	yes	characteristic, complemented
46	C₂²×C₅×D₈	—	3	2	no	—
47	C₂²×C₅×D₈	—	3	1	no	—
48	C₂×C₅×#131	—	3	1	no	—
49	C₂³×C₅×D₃	—	2	2	no	—
50	C₂³×C₅×D₃	—	2	4	no	—
51	C₃×C₅×#41	—	2	4	no	—
52	C₃×C₅×#41	C₂³	1	8	yes	complemented
53	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
54	C₂×C₃×C₅×D₄	—	2	2	no	—
55	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
56	C₂²×C₃×C₄×C₅	—	2	2	no	—
57	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
58	C₂×C₅×#67	—	2	4	no	—
59	C₂×C₅×#67	D₄	1	2	yes	—
60	C₅×#239	—	2	8	no	—
61	C₅×#239	C₂³	1	16	yes	complemented
62	C₅×D₃×D₄	—	2	32	no	—
63	C₅×D₃×D₄	—	2	8	no	—
64	C₅×D₃×D₄	C₂³	1	16	yes	complemented
65	C₅×#235	—	2	16	no	—
66	C₅×#235	D₄	1	4	yes	—
67	C₅×#235	C₂³	1	4	yes	—
68	C₂×C₅×D₁₂	—	2	4	no	—
69	C₂×C₅×D₁₂	—	2	2	no	—
70	C₂×C₅×D₁₂	—	2	4	no	—
71	C₂×C₅×D₁₂	—	2	16	no	—
72	C₂×C₅×D₁₂	D₄	1	1	yes	characteristic
73	C₂×C₅×D₁₂	C₂³	1	4	yes	—
74	C₂×C₅×D₁₂	C₂³	1	8	yes	complemented
75	C₂×C₄×C₅×D₃	—	2	4	no	—
76	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
77	C₂×C₅×Dic₆	D₄	1	1	yes	characteristic
78	C₃×C₅×Q₁₆	C₂³	1	4	yes	complemented
79	C₃×C₅×SD₁₆	C₂³	1	8	yes	complemented
80	C₃×C₅×D₈	C₂³	1	4	yes	complemented
81	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
82	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
83	C₂×C₃×C₅×C₈	C₂³	1	4	yes	complemented
84	C₅×#215	C₂³	1	16	yes	complemented
85	C₅×#213	C₂³	1	16	yes	complemented
86	C₅×#208	C₂³	1	4	yes	complemented
87	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
88	C₅×D₂₄	C₂³	1	8	yes	complemented
89	C₅×D₂₄	C₂³	1	8	yes	complemented
90	C₅×ΓL(1,𝔽₂₅)	C₂³	1	8	yes	complemented
91	C₅×D₃×C₈	C₂³	1	8	yes	complemented
92	C₂×#1009	C₂×C₅	1	2	yes	complemented
93	C₂×C₃×#135	C₂×C₅	1	1	yes	characteristic, complemented
94	C₂×#949	C₂×C₅	1	2	yes	complemented
95	#5769	C₂×C₅	1	16	yes	direct product factor
96	C₂×#919	C₂×C₅	1	2	yes	complemented
97	C₂×#914	C₂×C₅	1	4	yes	complemented
98	C₂×D₃×D₈	C₂×C₅	1	2	yes	complemented
99	C₂²×D₂₄	C₂×C₅	1	1	yes	characteristic, complemented
100	C₂×#901	C₂×C₅	1	1	yes	characteristic, complemented
101	C₅×H(5,𝔽₂)	—	3	16	no	—
102	C₅×H(5,𝔽₂)	—	6	8	no	—
103	C₂×C₅×#41	—	3	1	no	—
104	C₂×C₅×#41	—	3	4	no	—
105	C₂×C₅×#41	—	6	2	no	—
106	C₂×C₅×#41	C₂×D₃	1	2	yes	complemented
107	C₂²×C₅×D₄	—	3	4	no	—
108	C₂²×C₅×D₄	—	3	2	no	—
109	C₂²×C₅×D₄	—	6	2	no	—
110	C₂²×C₅×D₄	—	6	4	no	—
111	C₅×AGL(1,ℤ/8)	—	3	16	no	—
112	C₅×AGL(1,ℤ/8)	—	3	32	no	—
113	C₅×#135	—	3	16	no	—
114	C₅×#135	C₂×D₃	1	8	yes	complemented
115	C₂×C₅×Q₁₆	C₂×D₃	1	1	yes	characteristic, complemented
116	C₂×C₅×SD₁₆	—	3	4	no	—
117	C₂×C₅×SD₁₆	C₂×D₃	1	2	yes	complemented
118	C₂×C₅×D₈	—	3	4	no	—
119	C₂×C₅×D₈	—	3	16	no	—
120	C₂×C₅×D₈	—	3	2	no	—
121	C₂×C₅×D₈	—	3	2	no	—
122	C₂×C₅×D₈	—	3	8	no	—
123	C₂×C₅×D₈	C₂×D₃	1	1	yes	characteristic, complemented
124	C₅×#131	—	3	8	no	—
125	C₂×C₅×M₁₆	—	3	1	no	—
126	C₂×C₅×M₁₆	—	3	2	no	—
127	C₂²×C₅×C₈	—	3	2	no	—
128	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic, complemented
129	C₂×#576	—	3	1	no	Sylow
130	C₂³×C₃×C₅	—	2	2	no	—
131	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₅×D₃	—	2	4	no	—
133	C₂²×C₅×D₃	—	2	8	no	—
134	C₂²×C₅×D₃	—	2	16	no	—
135	C₂²×C₅×D₃	—	8	8	no	—
136	C₂²×C₅×D₃	—	8	4	no	—
137	C₂²×C₅×D₃	C₂×D₄	1	2	yes	—
138	C₃×C₅×Q₈	—	2	2	no	—
139	C₃×C₅×Q₈	C₂⁴	1	4	yes	—
140	C₃×C₅×D₄	—	2	8	no	—
141	C₃×C₅×D₄	—	2	2	no	—
142	C₃×C₅×D₄	C₂⁴	1	4	yes	—
143	C₂×C₃×C₄×C₅	—	2	2	no	—
144	C₂×C₃×C₄×C₅	—	2	8	no	—
145	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
146	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
147	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
148	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
149	C₅×#67	—	2	16	no	—
150	C₅×#67	C₂×D₄	1	8	yes	—
151	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
152	C₅×D₁₂	—	2	16	no	—
153	C₅×D₁₂	—	2	8	no	—
154	C₅×D₁₂	—	2	4	no	—
155	C₅×D₁₂	C₂×D₄	1	4	yes	—
156	C₅×D₁₂	C₂⁴	1	8	yes	—
157	C₄×C₅×D₃	—	2	16	no	—
158	C₄×C₅×D₃	C₂×D₄	1	4	yes	—
159	C₄×C₅×D₃	C₂⁴	1	4	yes	—
160	C₅×Dic₆	C₂×D₄	1	4	yes	—
161	C₃×C₅×C₈	C₂⁴	1	2	yes	—
162	C₃×C₅×C₈	C₂⁴	1	2	yes	—
163	C₅×C₃⋊C₈	C₂⁴	1	4	yes	—
164	C₂×C₃×#41	C₂²×C₅	1	2	yes	complemented
165	#1009	—	2	8	no	—
166	#1009	C₂²×C₅	1	16	yes	complemented
167	C₂×#239	C₂²×C₅	1	4	yes	complemented
168	C₂×D₃×D₄	—	2	4	no	—
169	C₂×D₃×D₄	C₂²×C₅	1	4	yes	complemented
170	C₂×#235	—	2	2	no	—
171	C₂×#235	C₂²×C₅	1	1	yes	characteristic
172	C₂²×D₁₂	—	2	2	no	—
173	C₂²×D₁₂	C₂²×C₅	1	2	yes	complemented
174	C₃×#135	C₂²×C₅	1	8	yes	complemented
175	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
176	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	complemented
177	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic, complemented
178	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
179	#949	C₂²×C₅	1	16	yes	complemented
180	C₂×#215	C₂²×C₅	1	4	yes	complemented
181	C₂×#213	C₂²×C₅	1	4	yes	complemented
182	C₂×#208	C₂²×C₅	1	1	yes	characteristic, complemented
183	#919	C₂²×C₅	1	16	yes	complemented
184	#914	C₂²×C₅	1	32	yes	complemented
185	D₃×D₈	C₂²×C₅	1	16	yes	complemented
186	C₂×D₂₄	C₂²×C₅	1	2	yes	complemented
187	C₂×D₂₄	C₂²×C₅	1	2	yes	complemented
188	C₂×D₂₄	C₂²×C₅	1	8	yes	complemented
189	#901	C₂²×C₅	1	8	yes	complemented
190	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	2	yes	complemented
191	C₂×D₃×C₈	C₂²×C₅	1	2	yes	complemented
192	C₂⁴×C₅	—	6	4	no	—
193	C₂⁴×C₅	—	6	2	no	—
194	C₅×#41	—	2	4	no	—
195	C₅×#41	—	3	4	no	—
196	C₅×#41	—	3	4	no	—
197	C₅×#41	—	3	16	no	—
198	C₅×#41	—	6	16	no	—
199	C₅×#41	—	6	8	no	—
200	C₅×#41	C₂²×D₃	1	8	yes	complemented
201	C₂×C₅×Q₈	—	3	1	no	—
202	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
203	C₂×C₅×D₄	—	2	2	no	—
204	C₂×C₅×D₄	—	3	2	no	—
205	C₂×C₅×D₄	—	3	16	no	—
206	C₂×C₅×D₄	—	3	1	no	—
207	C₂×C₅×D₄	—	3	4	no	—
208	C₂×C₅×D₄	—	3	8	no	—
209	C₂×C₅×D₄	—	6	16	no	—
210	C₂×C₅×D₄	—	6	4	no	—
211	C₂×C₅×D₄	—	6	8	no	—
212	C₂×C₅×D₄	—	6	4	no	—
213	C₂×C₅×D₄	—	6	32	no	—
214	C₂×C₅×D₄	—	6	2	no	—
215	C₂×C₅×D₄	—	6	4	no	—
216	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
217	C₂²×C₄×C₅	—	2	2	no	—
218	C₂²×C₄×C₅	—	3	2	no	—
219	C₂²×C₄×C₅	—	6	4	no	—
220	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
221	C₅×Q₁₆	C₂²×D₃	1	4	yes	complemented
222	C₅×SD₁₆	—	3	16	no	—
223	C₅×SD₁₆	C₂²×D₃	1	8	yes	complemented
224	C₅×D₈	—	3	16	no	—
225	C₅×D₈	—	3	8	no	—
226	C₅×D₈	—	3	8	no	—
227	C₅×D₈	C₂²×D₃	1	4	yes	complemented
228	C₅×M₁₆	—	3	4	no	—
229	C₅×M₁₆	—	3	8	no	—
230	C₂×C₅×C₈	—	3	2	no	—
231	C₂×C₅×C₈	—	3	8	no	—
232	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
233	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
234	C₂×C₅×C₈	C₂²×D₃	1	4	yes	complemented
235	C₂×H(5,𝔽₂)	—	3	2	no	—
236	#576	—	3	16	no	—
237	C₂×AGL(1,ℤ/8)	—	3	2	no	—
238	C₂×AGL(1,ℤ/8)	—	3	4	no	—
239	C₂×#135	—	3	2	no	—
240	C₂×#135	C₅×D₃	1	1	yes	characteristic, complemented
241	C₂²×D₈	—	3	2	no	—
242	C₂²×D₈	—	3	1	no	—
243	C₂×#131	—	3	1	no	—
244	C₂²×C₃×C₅	—	2	2	no	—
245	C₂²×C₃×C₅	—	2	4	no	—
246	C₂²×C₃×C₅	—	4	4	no	—
247	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
248	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
249	C₂×C₅×D₃	—	2	4	no	—
250	C₂×C₅×D₃	—	2	8	no	—
251	C₂×C₅×D₃	—	4	8	no	—
252	C₂×C₅×D₃	—	8	16	no	—
253	C₂×C₅×D₃	—	8	8	no	—
254	C₂×C₅×D₃	C₂²×D₄	1	4	yes	—
255	C₃×C₄×C₅	—	2	4	no	—
256	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
257	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
258	C₃×C₄×C₅	C₂⁵	1	1	yes	characteristic
259	C₅×Dic₃	C₂²×D₄	1	4	yes	—
260	C₂³×D₃	—	2	2	no	—
261	C₂³×D₃	—	2	4	no	—
262	C₃×#41	—	2	4	no	—
263	C₃×#41	C₂³×C₅	1	8	yes	complemented
264	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
265	C₂×C₃×D₄	—	2	2	no	—
266	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
267	C₂²×C₃×C₄	—	2	2	no	—
268	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
269	C₂×#67	—	2	4	no	—
270	C₂×#67	C₅×D₄	1	2	yes	—
271	#239	—	2	8	no	—
272	#239	C₂³×C₅	1	16	yes	complemented
273	D₃×D₄	—	2	32	no	—
274	D₃×D₄	—	2	8	no	—
275	D₃×D₄	C₂³×C₅	1	16	yes	complemented
276	#235	—	2	16	no	—
277	#235	C₅×D₄	1	4	yes	—
278	#235	C₂³×C₅	1	4	yes	—
279	C₂×D₁₂	—	2	4	no	—
280	C₂×D₁₂	—	2	2	no	—
281	C₂×D₁₂	—	2	4	no	—
282	C₂×D₁₂	—	2	16	no	—
283	C₂×D₁₂	C₅×D₄	1	1	yes	characteristic
284	C₂×D₁₂	C₂³×C₅	1	4	yes	—
285	C₂×D₁₂	C₂³×C₅	1	8	yes	complemented
286	C₂×C₄×D₃	—	2	4	no	—
287	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
288	C₂×Dic₆	C₅×D₄	1	1	yes	characteristic
289	C₃×Q₁₆	C₂³×C₅	1	4	yes	complemented
290	C₃×SD₁₆	C₂³×C₅	1	8	yes	complemented
291	C₃×D₈	C₂³×C₅	1	4	yes	complemented
292	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
293	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
294	C₂×C₃×C₈	C₂³×C₅	1	4	yes	complemented
295	#215	C₂³×C₅	1	16	yes	complemented
296	#213	C₂³×C₅	1	16	yes	complemented
297	#208	C₂³×C₅	1	4	yes	complemented
298	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
299	D₂₄	C₂³×C₅	1	8	yes	complemented
300	D₂₄	C₂³×C₅	1	8	yes	complemented
301	ΓL(1,𝔽₂₅)	C₂³×C₅	1	8	yes	complemented
302	D₃×C₈	C₂³×C₅	1	8	yes	complemented
303	C₂³×C₅	—	2	2	no	—
304	C₂³×C₅	—	3	2	no	—
305	C₂³×C₅	—	6	16	no	—
306	C₂³×C₅	—	6	4	no	—
307	C₂³×C₅	—	6	8	no	—
308	C₂³×C₅	—	24	4	no	—
309	C₂³×C₅	—	24	8	no	—
310	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
311	C₅×Q₈	—	2	2	no	—
312	C₅×Q₈	—	3	4	no	—
313	C₅×Q₈	C₂³×D₃	1	4	yes	—
314	C₅×D₄	—	2	8	no	—
315	C₅×D₄	—	2	2	no	—
316	C₅×D₄	—	3	8	no	—
317	C₅×D₄	—	3	4	no	—
318	C₅×D₄	—	3	8	no	—
319	C₅×D₄	—	6	16	no	—
320	C₅×D₄	—	6	16	no	—
321	C₅×D₄	—	6	8	no	—
322	C₅×D₄	—	6	4	no	—
323	C₅×D₄	C₂³×D₃	1	4	yes	—
324	C₂×C₄×C₅	—	2	2	no	—
325	C₂×C₄×C₅	—	2	8	no	—
326	C₂×C₄×C₅	—	3	2	no	—
327	C₂×C₄×C₅	—	3	4	no	—
328	C₂×C₄×C₅	—	3	4	no	—
329	C₂×C₄×C₅	—	6	16	no	—
330	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
331	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
332	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
333	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
334	C₅×C₈	—	3	4	no	—
335	C₅×C₈	C₂³×D₃	1	2	yes	—
336	C₅×C₈	C₂³×D₃	1	2	yes	—
337	H(5,𝔽₂)	—	3	16	no	—
338	H(5,𝔽₂)	—	6	8	no	—
339	C₂×#41	—	3	1	no	—
340	C₂×#41	—	3	4	no	—
341	C₂×#41	—	6	2	no	—
342	C₂×#41	C₂×C₅×D₃	1	2	yes	complemented
343	C₂²×D₄	—	3	4	no	—
344	C₂²×D₄	—	3	2	no	—
345	C₂²×D₄	—	6	2	no	—
346	C₂²×D₄	—	6	4	no	—
347	AGL(1,ℤ/8)	—	3	16	no	—
348	AGL(1,ℤ/8)	—	3	32	no	—
349	#135	—	3	16	no	—
350	#135	C₂×C₅×D₃	1	8	yes	complemented
351	C₂×Q₁₆	C₂×C₅×D₃	1	1	yes	characteristic, complemented
352	C₂×SD₁₆	—	3	4	no	—
353	C₂×SD₁₆	C₂×C₅×D₃	1	2	yes	complemented
354	C₂×D₈	—	3	4	no	—
355	C₂×D₈	—	3	16	no	—
356	C₂×D₈	—	3	2	no	—
357	C₂×D₈	—	3	2	no	—
358	C₂×D₈	—	3	8	no	—
359	C₂×D₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
360	#131	—	3	8	no	—
361	C₂×M₁₆	—	3	1	no	—
362	C₂×M₁₆	—	3	2	no	—
363	C₂²×C₈	—	3	2	no	—
364	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
365	C₂×C₃×C₅	—	2	2	no	—
366	C₂×C₃×C₅	—	4	4	no	—
367	C₂×C₃×C₅	#576	1	2	yes	complemented
368	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
369	C₅×D₃	—	2	4	no	—
370	C₅×D₃	—	4	8	no	—
371	C₂³×C₃	—	2	2	no	—
372	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
373	C₂²×D₃	—	2	4	no	—
374	C₂²×D₃	—	2	8	no	—
375	C₂²×D₃	—	2	16	no	—
376	C₂²×D₃	—	8	8	no	—
377	C₂²×D₃	—	8	4	no	—
378	C₂²×D₃	C₂×C₅×D₄	1	2	yes	—
379	C₃×Q₈	—	2	2	no	—
380	C₃×Q₈	C₂⁴×C₅	1	4	yes	—
381	C₃×D₄	—	2	8	no	—
382	C₃×D₄	—	2	2	no	—
383	C₃×D₄	C₂⁴×C₅	1	4	yes	—
384	C₂×C₃×C₄	—	2	2	no	—
385	C₂×C₃×C₄	—	2	8	no	—
386	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
387	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
388	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
389	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
390	#67	—	2	16	no	—
391	#67	C₂×C₅×D₄	1	8	yes	—
392	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
393	D₁₂	—	2	16	no	—
394	D₁₂	—	2	8	no	—
395	D₁₂	—	2	4	no	—
396	D₁₂	C₂×C₅×D₄	1	4	yes	—
397	D₁₂	C₂⁴×C₅	1	8	yes	—
398	C₄×D₃	—	2	16	no	—
399	C₄×D₃	C₂×C₅×D₄	1	4	yes	—
400	C₄×D₃	C₂⁴×C₅	1	4	yes	—
401	Dic₆	C₂×C₅×D₄	1	4	yes	—
402	C₃×C₈	C₂⁴×C₅	1	2	yes	—
403	C₃×C₈	C₂⁴×C₅	1	2	yes	—
404	C₃⋊C₈	C₂⁴×C₅	1	4	yes	—
405	C₂²×C₅	—	2	2	no	—
406	C₂²×C₅	—	2	4	no	—
407	C₂²×C₅	—	3	4	no	—
408	C₂²×C₅	—	4	4	no	—
409	C₂²×C₅	—	6	4	no	—
410	C₂²×C₅	—	6	8	no	—
411	C₂²×C₅	—	12	8	no	—
412	C₂²×C₅	—	24	8	no	—
413	C₂²×C₅	—	24	16	no	—
414	C₂²×C₅	C₂×D₃×D₄	1	2	yes	—
415	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
416	C₄×C₅	—	2	4	no	—
417	C₄×C₅	—	3	4	no	—
418	C₄×C₅	C₂×D₃×D₄	1	2	yes	—
419	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
420	C₄×C₅	C₂⁴×D₃	1	1	yes	characteristic
421	C₂⁴	—	6	4	no	—
422	C₂⁴	—	6	2	no	—
423	#41	—	2	4	no	—
424	#41	—	3	4	no	—
425	#41	—	3	4	no	—
426	#41	—	3	16	no	—
427	#41	—	6	16	no	—
428	#41	—	6	8	no	—
429	#41	C₂²×C₅×D₃	1	8	yes	complemented
430	C₂×Q₈	—	3	1	no	—
431	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
432	C₂×D₄	—	2	2	no	—
433	C₂×D₄	—	3	2	no	—
434	C₂×D₄	—	3	16	no	—
435	C₂×D₄	—	3	1	no	—
436	C₂×D₄	—	3	4	no	—
437	C₂×D₄	—	3	8	no	—
438	C₂×D₄	—	6	16	no	—
439	C₂×D₄	—	6	4	no	—
440	C₂×D₄	—	6	8	no	—
441	C₂×D₄	—	6	4	no	—
442	C₂×D₄	—	6	32	no	—
443	C₂×D₄	—	6	2	no	—
444	C₂×D₄	—	6	4	no	—
445	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
446	C₂²×C₄	—	2	2	no	—
447	C₂²×C₄	—	3	2	no	—
448	C₂²×C₄	—	6	4	no	—
449	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
450	Q₁₆	C₂²×C₅×D₃	1	4	yes	complemented
451	SD₁₆	—	3	16	no	—
452	SD₁₆	C₂²×C₅×D₃	1	8	yes	complemented
453	D₈	—	3	16	no	—
454	D₈	—	3	8	no	—
455	D₈	—	3	8	no	—
456	D₈	C₂²×C₅×D₃	1	4	yes	complemented
457	M₁₆	—	3	4	no	—
458	M₁₆	—	3	8	no	—
459	C₂×C₈	—	3	2	no	—
460	C₂×C₈	—	3	8	no	—
461	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
462	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
463	C₂×C₈	C₂²×C₅×D₃	1	4	yes	complemented
464	C₃×C₅	C₂×#576	1	1	yes	characteristic, complemented, Hall
465	C₂²×C₃	—	2	2	no	—
466	C₂²×C₃	—	2	4	no	—
467	C₂²×C₃	—	4	4	no	—
468	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
469	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
470	C₂×D₃	—	2	4	no	—
471	C₂×D₃	—	2	8	no	—
472	C₂×D₃	—	4	8	no	—
473	C₂×D₃	—	8	16	no	—
474	C₂×D₃	—	8	8	no	—
475	C₂×D₃	C₂²×C₅×D₄	1	4	yes	—
476	C₃×C₄	—	2	4	no	—
477	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
478	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
479	C₃×C₄	C₂⁵×C₅	1	1	yes	characteristic
480	Dic₃	C₂²×C₅×D₄	1	4	yes	—
481	C₂×C₅	—	2	2	no	—
482	C₂×C₅	—	4	4	no	—
483	C₂×C₅	—	6	4	no	—
484	C₂×C₅	—	12	8	no	—
485	C₂×C₅	#5769	1	2	yes	direct product factor
486	C₂×C₅	C₂²×D₃×D₄	1	1	yes	characteristic
487	C₂³	—	2	2	no	—
488	C₂³	—	3	2	no	—
489	C₂³	—	6	16	no	—
490	C₂³	—	6	4	no	—
491	C₂³	—	6	8	no	—
492	C₂³	—	24	4	no	—
493	C₂³	—	24	8	no	—
494	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
495	Q₈	—	2	2	no	—
496	Q₈	—	3	4	no	—
497	Q₈	C₂³×C₅×D₃	1	4	yes	—
498	D₄	—	2	8	no	—
499	D₄	—	2	2	no	—
500	D₄	—	3	8	no	—
501	D₄	—	3	4	no	—
502	D₄	—	3	8	no	—
503	D₄	—	6	16	no	—
504	D₄	—	6	16	no	—
505	D₄	—	6	8	no	—
506	D₄	—	6	4	no	—
507	D₄	C₂³×C₅×D₃	1	4	yes	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	8	no	—
510	C₂×C₄	—	3	2	no	—
511	C₂×C₄	—	3	4	no	—
512	C₂×C₄	—	3	4	no	—
513	C₂×C₄	—	6	16	no	—
514	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
515	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
516	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
517	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
518	C₈	—	3	4	no	—
519	C₈	C₂³×C₅×D₃	1	2	yes	—
520	C₈	C₂³×C₅×D₃	1	2	yes	—
521	C₂×C₃	—	2	2	no	—
522	C₂×C₃	—	4	4	no	—
523	C₂×C₃	C₅×#576	1	2	yes	complemented
524	C₂×C₃	C₂³×C₅×D₄	1	1	yes	characteristic
525	D₃	—	2	4	no	—
526	D₃	—	4	8	no	—
527	C₅	C₂×#5769	1	1	yes	characteristic, direct product factor, Sylow
528	C₂²	—	2	2	no	—
529	C₂²	—	2	4	no	—
530	C₂²	—	3	4	no	—
531	C₂²	—	4	4	no	—
532	C₂²	—	6	4	no	—
533	C₂²	—	6	8	no	—
534	C₂²	—	12	8	no	—
535	C₂²	—	24	8	no	—
536	C₂²	—	24	16	no	—
537	C₂²	C₂×C₅×D₃×D₄	1	2	yes	—
538	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
539	C₄	—	2	4	no	—
540	C₄	—	3	4	no	—
541	C₄	C₂×C₅×D₃×D₄	1	2	yes	—
542	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
543	C₄	C₂⁴×C₅×D₃	1	1	yes	characteristic
544	C₃	C₂×C₅×#576	1	1	yes	characteristic, complemented, Sylow
545	C₂	—	2	2	no	—
546	C₂	—	4	4	no	—
547	C₂	—	6	4	no	—
548	C₂	—	12	8	no	—
549	C₂	C₅×#5769	1	2	yes	direct product factor
550	C₂	C₂²×C₅×D₃×D₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂×D₃×D₄
commutator, cosocle	C₃×C₄	C₂⁵×C₅
Frattini	C₄	C₂⁴×C₅×D₃
Fitting	C₂×C₃×C₅×#135	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₂×C₅×#135	D₃
hypocenter	C₃	C₂×C₅×#576
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×#135

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#1009	C₂	semidirect
2. C₂×C₃×C₅×#135	C₂	semidirect
3. C₂×C₅×#949	C₂	semidirect
4. C₅×#5769	C₂	direct (N × H)
5. C₂×C₅×#919	C₂	semidirect
6. C₂×C₅×#914	C₂	semidirect
7. C₂×C₅×D₃×D₈	C₂	semidirect
8. C₂²×C₅×D₂₄	C₂	semidirect
9. C₂×C₅×#901	C₂	semidirect
11. C₂×C₃×C₅×#41	C₂²	semidirect
13. C₅×#1009	C₂²	semidirect
14. C₂×C₅×#239	C₂²	semidirect
16. C₂×C₅×D₃×D₄	C₂²	semidirect
20. C₂²×C₅×D₁₂	C₂²	semidirect
21. C₃×C₅×#135	C₂²	semidirect
22. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
23. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
24. C₂×C₃×C₅×D₈	C₂²	semidirect
25. C₂²×C₃×C₅×C₈	C₂²	semidirect
26. C₅×#949	C₂²	semidirect
27. C₂×C₅×#215	C₂²	semidirect
28. C₂×C₅×#213	C₂²	semidirect
29. C₂×C₅×#208	C₂²	semidirect
30. C₅×#919	C₂²	semidirect
31. C₅×#914	C₂²	semidirect
32. C₅×D₃×D₈	C₂²	semidirect
33. C₂×C₅×D₂₄	C₂²	semidirect
34. C₂×C₅×D₂₄	C₂²	semidirect
35. C₂×C₅×D₂₄	C₂²	semidirect
36. C₅×#901	C₂²	semidirect
37. C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	semidirect
38. C₂×C₅×D₃×C₈	C₂²	semidirect
39. C₂×#5769	C₅	direct (N × H)
45. C₂×C₅×#135	D₃	semidirect
52. C₃×C₅×#41	C₂³	semidirect
61. C₅×#239	C₂³	semidirect
64. C₅×D₃×D₄	C₂³	semidirect
74. C₂×C₅×D₁₂	C₂³	semidirect
78. C₃×C₅×Q₁₆	C₂³	semidirect
79. C₃×C₅×SD₁₆	C₂³	semidirect
80. C₃×C₅×D₈	C₂³	semidirect
83. C₂×C₃×C₅×C₈	C₂³	semidirect
84. C₅×#215	C₂³	semidirect
85. C₅×#213	C₂³	semidirect
86. C₅×#208	C₂³	semidirect
88. C₅×D₂₄	C₂³	semidirect
89. C₅×D₂₄	C₂³	semidirect
90. C₅×ΓL(1,𝔽₂₅)	C₂³	semidirect
91. C₅×D₃×C₈	C₂³	semidirect
92. C₂×#1009	C₂×C₅	semidirect
93. C₂×C₃×#135	C₂×C₅	semidirect
94. C₂×#949	C₂×C₅	semidirect
95. #5769	C₂×C₅	direct (N × H)
96. C₂×#919	C₂×C₅	semidirect
97. C₂×#914	C₂×C₅	semidirect
98. C₂×D₃×D₈	C₂×C₅	semidirect
99. C₂²×D₂₄	C₂×C₅	semidirect
100. C₂×#901	C₂×C₅	semidirect
106. C₂×C₅×#41	C₂×D₃	semidirect
114. C₅×#135	C₂×D₃	semidirect
115. C₂×C₅×Q₁₆	C₂×D₃	semidirect
117. C₂×C₅×SD₁₆	C₂×D₃	semidirect
123. C₂×C₅×D₈	C₂×D₃	semidirect
128. C₂²×C₅×C₈	C₂×D₃	semidirect
164. C₂×C₃×#41	C₂²×C₅	semidirect
166. #1009	C₂²×C₅	semidirect
167. C₂×#239	C₂²×C₅	semidirect
169. C₂×D₃×D₄	C₂²×C₅	semidirect
173. C₂²×D₁₂	C₂²×C₅	semidirect
174. C₃×#135	C₂²×C₅	semidirect
175. C₂×C₃×Q₁₆	C₂²×C₅	semidirect
176. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
177. C₂×C₃×D₈	C₂²×C₅	semidirect
178. C₂²×C₃×C₈	C₂²×C₅	semidirect
179. #949	C₂²×C₅	semidirect
180. C₂×#215	C₂²×C₅	semidirect
181. C₂×#213	C₂²×C₅	semidirect
182. C₂×#208	C₂²×C₅	semidirect
183. #919	C₂²×C₅	semidirect
184. #914	C₂²×C₅	semidirect
185. D₃×D₈	C₂²×C₅	semidirect
186. C₂×D₂₄	C₂²×C₅	semidirect
187. C₂×D₂₄	C₂²×C₅	semidirect
188. C₂×D₂₄	C₂²×C₅	semidirect
189. #901	C₂²×C₅	semidirect
190. C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	semidirect
191. C₂×D₃×C₈	C₂²×C₅	semidirect
200. C₅×#41	C₂²×D₃	semidirect
221. C₅×Q₁₆	C₂²×D₃	semidirect
223. C₅×SD₁₆	C₂²×D₃	semidirect
227. C₅×D₈	C₂²×D₃	semidirect
234. C₂×C₅×C₈	C₂²×D₃	semidirect
240. C₂×#135	C₅×D₃	semidirect
263. C₃×#41	C₂³×C₅	semidirect
272. #239	C₂³×C₅	semidirect
275. D₃×D₄	C₂³×C₅	semidirect
285. C₂×D₁₂	C₂³×C₅	semidirect
289. C₃×Q₁₆	C₂³×C₅	semidirect
290. C₃×SD₁₆	C₂³×C₅	semidirect
291. C₃×D₈	C₂³×C₅	semidirect
294. C₂×C₃×C₈	C₂³×C₅	semidirect
295. #215	C₂³×C₅	semidirect
296. #213	C₂³×C₅	semidirect
297. #208	C₂³×C₅	semidirect
299. D₂₄	C₂³×C₅	semidirect
300. D₂₄	C₂³×C₅	semidirect
301. ΓL(1,𝔽₂₅)	C₂³×C₅	semidirect
302. D₃×C₈	C₂³×C₅	semidirect
342. C₂×#41	C₂×C₅×D₃	semidirect
350. #135	C₂×C₅×D₃	semidirect
351. C₂×Q₁₆	C₂×C₅×D₃	semidirect
353. C₂×SD₁₆	C₂×C₅×D₃	semidirect
359. C₂×D₈	C₂×C₅×D₃	semidirect
364. C₂²×C₈	C₂×C₅×D₃	semidirect
367. C₂×C₃×C₅	#576	semidirect
429. #41	C₂²×C₅×D₃	semidirect
450. Q₁₆	C₂²×C₅×D₃	semidirect
452. SD₁₆	C₂²×C₅×D₃	semidirect
456. D₈	C₂²×C₅×D₃	semidirect
463. C₂×C₈	C₂²×C₅×D₃	semidirect
464. C₃×C₅	C₂×#576	semidirect
485. C₂×C₅	#5769	direct (N × H)
523. C₂×C₃	C₅×#576	semidirect
527. C₅	C₂×#5769	direct (N × H)
544. C₃	C₂×C₅×#576	semidirect
549. C₂	C₅×#5769	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×#1009	2
C₂×C₃×C₅×#135	2
C₂×C₅×#949	2
C₅×#5769	2
C₂×C₅×#919	2
C₂×C₅×#914	2
C₂×C₅×D₃×D₈	2
C₂²×C₅×D₂₄	2
C₂×C₅×#901	2
C₂×C₅×#576	3
C₂×#5769	5

Subgroups — C2×C5×#5769 #14509954

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5769 #14509954