Subgroups — C₂×C₅×#5150 #14425809

Order 1920.

1296 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×D₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#940	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×D₄×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₅×#213	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#832	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5150	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₅×#821	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅×Dic₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×#459	—	3	1	no	maximal, Hall
10	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
12	C₂²×C₅×#67	—	2	1	no	—
13	C₂²×C₅×#67	—	2	1	no	—
14	C₂³×C₅×Dic₃	—	2	1	no	—
15	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×D₈	—	2	4	no	—
17	C₂×C₃×C₅×D₈	C₂²	1	4	yes	complemented
18	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
19	C₂×C₅×#217	—	2	1	no	—
20	C₅×#940	—	2	2	no	—
21	C₅×#940	C₂²	1	4	yes	complemented
22	C₅×D₄×Dic₃	—	2	2	no	—
23	C₅×D₄×Dic₃	C₂²	1	4	yes	complemented
24	C₂×C₅×#213	—	2	4	no	—
25	C₂×C₅×#213	C₂²	1	4	yes	complemented
26	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
28	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
29	C₅×#832	C₂²	1	4	yes	complemented
30	C₅×#821	C₂²	1	4	yes	complemented
31	C₅×Dic₃⋊C₈	C₂²	1	4	yes	complemented
32	C₂×#5150	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
33	C₂²×C₅×D₈	—	3	1	no	—
34	C₂²×C₅×D₈	D₃	1	1	yes	characteristic, complemented
35	C₂×C₅×#127	—	3	1	no	—
36	C₂×C₄×C₅×D₄	—	3	1	no	—
37	C₅×#459	—	3	8	no	—
38	C₂×C₅×C₄⋊C₈	—	3	1	no	—
39	C₂×C₅×#102	—	3	1	no	—
40	C₂×C₅×#102	—	3	1	no	—
41	C₂⁴×C₃×C₅	—	2	1	no	—
42	C₂⁴×C₃×C₅	—	2	1	no	—
43	C₂³×C₅×D₃	—	2	1	no	—
44	C₂×C₃×C₅×D₄	—	2	1	no	—
45	C₂×C₃×C₅×D₄	—	2	2	no	—
46	C₂×C₃×C₅×D₄	—	2	1	no	—
47	C₂×C₃×C₅×D₄	—	2	2	no	—
48	C₂×C₃×C₅×D₄	—	2	2	no	—
49	C₂×C₃×C₅×D₄	D₄	1	4	yes	complemented
50	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
51	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
52	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
53	C₂×C₅×#67	—	2	4	no	—
54	C₂×C₅×#67	—	2	4	no	—
55	C₂×C₅×#67	—	4	4	no	—
56	C₂×C₅×#67	—	4	4	no	—
57	C₂²×C₅×Dic₃	—	2	1	no	—
58	C₂²×C₅×Dic₃	—	2	4	no	—
59	C₂²×C₅×Dic₃	—	4	4	no	—
60	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
61	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
62	C₂×C₅×D₁₂	—	2	2	no	—
63	C₂×C₅×D₁₂	—	2	2	no	—
64	C₂×C₅×D₁₂	—	2	1	no	—
65	C₂×C₅×D₁₂	C₂³	1	2	yes	—
66	C₃×C₅×D₈	—	2	8	no	—
67	C₂×C₃×C₅×C₈	—	2	2	no	—
68	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
69	C₅×#217	—	2	4	no	—
70	C₅×#213	—	2	8	no	—
71	C₅×C₄⋊Dic₃	—	2	1	no	—
72	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
73	C₄×C₅×Dic₃	D₄	1	2	yes	—
74	C₄×C₅×Dic₃	C₂³	1	2	yes	—
75	C₂×C₅×C₃⋊C₈	—	2	2	no	—
76	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
77	C₂²×C₃×D₈	C₂×C₅	1	1	yes	characteristic, complemented
78	C₂×#940	C₂×C₅	1	1	yes	characteristic, complemented
79	C₂×D₄×Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
80	C₂²×#213	C₂×C₅	1	1	yes	characteristic, complemented
81	C₂×#832	C₂×C₅	1	1	yes	characteristic, complemented
82	#5150	C₂×C₅	1	8	yes	direct product factor
83	C₂×#821	C₂×C₅	1	1	yes	characteristic, complemented
84	C₂×Dic₃⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
85	C₂²×C₅×D₄	—	3	1	no	—
86	C₂²×C₅×D₄	—	6	1	no	—
87	C₂²×C₅×D₄	—	6	1	no	—
88	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
89	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
90	C₂³×C₄×C₅	—	6	1	no	—
91	C₂×C₅×D₈	—	2	4	no	—
92	C₂×C₅×D₈	—	3	4	no	—
93	C₂×C₅×D₈	—	6	4	no	—
94	C₂×C₅×D₈	C₂×D₃	1	4	yes	complemented
95	C₂²×C₅×C₈	—	3	1	no	—
96	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
97	C₅×#127	—	3	4	no	—
98	C₅×#127	—	6	2	no	—
99	C₄×C₅×D₄	—	3	4	no	—
100	C₄×C₅×D₄	—	6	2	no	—
101	C₂×C₅×C₄⋊C₄	—	3	1	no	—
102	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
103	C₂×C₄²×C₅	—	3	1	no	—
104	C₅×C₄⋊C₈	—	3	4	no	—
105	C₅×#102	—	3	4	no	—
106	C₅×#102	—	3	4	no	—
107	C₂×#459	—	3	1	no	Sylow
108	C₂³×C₃×C₅	—	2	4	no	—
109	C₂³×C₃×C₅	—	2	2	no	—
110	C₂³×C₃×C₅	—	2	2	no	—
111	C₂³×C₃×C₅	—	4	2	no	—
112	C₂³×C₃×C₅	—	4	2	no	—
113	C₂³×C₃×C₅	—	4	2	no	—
114	C₂³×C₃×C₅	—	4	2	no	—
115	C₂³×C₃×C₅	—	4	2	no	—
116	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₅×D₃	—	2	2	no	—
118	C₂²×C₅×D₃	—	4	2	no	—
119	C₂²×C₅×D₃	—	4	2	no	—
120	C₂²×C₅×D₃	—	4	2	no	—
121	C₃×C₅×D₄	—	2	4	no	—
122	C₃×C₅×D₄	—	2	2	no	—
123	C₃×C₅×D₄	—	2	2	no	—
124	C₃×C₅×D₄	—	2	2	no	—
125	C₃×C₅×D₄	—	4	2	no	—
126	C₃×C₅×D₄	C₂×D₄	1	4	yes	complemented
127	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
128	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
129	C₂×C₃×C₄×C₅	#41	1	2	yes	—
130	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
131	C₅×#67	—	4	8	no	—
132	C₅×#67	—	4	8	no	—
133	C₂×C₅×Dic₃	—	2	2	no	—
134	C₂×C₅×Dic₃	—	2	2	no	—
135	C₂×C₅×Dic₃	—	4	2	no	—
136	C₂×C₅×Dic₃	—	4	8	no	—
137	C₂×C₅×Dic₃	D₈	1	4	yes	complemented
138	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
139	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
140	C₅×D₁₂	—	2	2	no	—
141	C₅×D₁₂	—	2	2	no	—
142	C₅×D₁₂	—	4	2	no	—
143	C₃×C₅×C₈	—	2	2	no	—
144	C₅×C₃⋊C₈	—	2	2	no	—
145	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
146	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
147	C₂²×#67	—	2	1	no	—
148	C₂²×#67	—	2	1	no	—
149	C₂³×Dic₃	—	2	1	no	—
150	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
151	C₂×C₃×D₈	—	2	4	no	—
152	C₂×C₃×D₈	C₂²×C₅	1	4	yes	complemented
153	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
154	C₂×#217	—	2	1	no	—
155	#940	—	2	2	no	—
156	#940	C₂²×C₅	1	4	yes	complemented
157	D₄×Dic₃	—	2	2	no	—
158	D₄×Dic₃	C₂²×C₅	1	4	yes	complemented
159	C₂×#213	—	2	4	no	—
160	C₂×#213	C₂²×C₅	1	4	yes	complemented
161	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
162	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
163	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
164	#832	C₂²×C₅	1	4	yes	complemented
165	#821	C₂²×C₅	1	4	yes	complemented
166	Dic₃⋊C₈	C₂²×C₅	1	4	yes	complemented
167	C₂⁴×C₅	—	2	1	no	—
168	C₂⁴×C₅	—	2	1	no	—
169	C₂⁴×C₅	—	6	1	no	—
170	C₂×C₅×D₄	—	2	1	no	—
171	C₂×C₅×D₄	—	2	1	no	—
172	C₂×C₅×D₄	—	2	2	no	—
173	C₂×C₅×D₄	—	2	2	no	—
174	C₂×C₅×D₄	—	2	2	no	—
175	C₂×C₅×D₄	—	3	2	no	—
176	C₂×C₅×D₄	—	6	4	no	—
177	C₂×C₅×D₄	—	6	4	no	—
178	C₂×C₅×D₄	—	6	1	no	—
179	C₂×C₅×D₄	—	6	2	no	—
180	C₂×C₅×D₄	—	6	2	no	—
181	C₂×C₅×D₄	—	12	4	no	—
182	C₂×C₅×D₄	—	12	4	no	—
183	C₂×C₅×D₄	#67	1	4	yes	complemented
184	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
185	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
186	C₂²×C₄×C₅	—	3	1	no	—
187	C₂²×C₄×C₅	—	3	1	no	—
188	C₂²×C₄×C₅	—	6	4	no	—
189	C₂²×C₄×C₅	—	6	1	no	—
190	C₂²×C₄×C₅	—	12	4	no	—
191	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
192	C₅×D₈	—	2	8	no	—
193	C₅×D₈	—	6	8	no	—
194	C₂×C₅×C₈	—	2	2	no	—
195	C₂×C₅×C₈	—	3	2	no	—
196	C₂×C₅×C₈	—	6	2	no	—
197	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
198	C₅×C₄⋊C₄	—	3	2	no	—
199	C₅×C₄⋊C₄	—	6	1	no	—
200	C₅×C₂²⋊C₄	—	6	4	no	—
201	C₄²×C₅	—	3	2	no	—
202	C₄²×C₅	—	3	2	no	—
203	C₂²×D₈	—	3	1	no	—
204	C₂²×D₈	C₅×D₃	1	1	yes	characteristic, complemented
205	C₂×#127	—	3	1	no	—
206	C₂×C₄×D₄	—	3	1	no	—
207	#459	—	3	8	no	—
208	C₂×C₄⋊C₈	—	3	1	no	—
209	C₂×#102	—	3	1	no	—
210	C₂×#102	—	3	1	no	—
211	C₂²×C₃×C₅	—	2	4	no	—
212	C₂²×C₃×C₅	—	4	2	no	—
213	C₂²×C₃×C₅	—	4	2	no	—
214	C₂²×C₃×C₅	—	4	8	no	—
215	C₂²×C₃×C₅	—	4	2	no	—
216	C₂²×C₃×C₅	—	4	2	no	—
217	C₂²×C₃×C₅	—	4	2	no	—
218	C₂²×C₃×C₅	—	8	4	no	—
219	C₂²×C₃×C₅	#121	1	2	yes	—
220	C₂²×C₃×C₅	C₂×D₈	1	2	yes	—
221	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	—
222	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₅×D₃	—	4	2	no	—
224	C₂×C₅×D₃	—	4	2	no	—
225	C₂×C₅×D₃	—	4	2	no	—
226	C₂×C₅×D₃	—	8	4	no	—
227	C₃×C₄×C₅	#121	1	2	yes	—
228	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
229	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
230	C₅×Dic₃	—	2	2	no	—
231	C₅×Dic₃	—	4	2	no	—
232	C₅×Dic₃	C₂×D₈	1	4	yes	complemented
233	C₂⁴×C₃	—	2	1	no	—
234	C₂⁴×C₃	—	2	1	no	—
235	C₂³×D₃	—	2	1	no	—
236	C₂×C₃×D₄	—	2	1	no	—
237	C₂×C₃×D₄	—	2	2	no	—
238	C₂×C₃×D₄	—	2	1	no	—
239	C₂×C₃×D₄	—	2	2	no	—
240	C₂×C₃×D₄	—	2	2	no	—
241	C₂×C₃×D₄	C₅×D₄	1	4	yes	complemented
242	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
243	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
244	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
245	C₂×#67	—	2	4	no	—
246	C₂×#67	—	2	4	no	—
247	C₂×#67	—	4	4	no	—
248	C₂×#67	—	4	4	no	—
249	C₂²×Dic₃	—	2	1	no	—
250	C₂²×Dic₃	—	2	4	no	—
251	C₂²×Dic₃	—	4	4	no	—
252	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
253	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
254	C₂×D₁₂	—	2	2	no	—
255	C₂×D₁₂	—	2	2	no	—
256	C₂×D₁₂	—	2	1	no	—
257	C₂×D₁₂	C₂³×C₅	1	2	yes	—
258	C₃×D₈	—	2	8	no	—
259	C₂×C₃×C₈	—	2	2	no	—
260	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
261	#217	—	2	4	no	—
262	#213	—	2	8	no	—
263	C₄⋊Dic₃	—	2	1	no	—
264	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
265	C₄×Dic₃	C₅×D₄	1	2	yes	—
266	C₄×Dic₃	C₂³×C₅	1	2	yes	—
267	C₂×C₃⋊C₈	—	2	2	no	—
268	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
269	C₂³×C₅	—	2	4	no	—
270	C₂³×C₅	—	2	2	no	—
271	C₂³×C₅	—	2	2	no	—
272	C₂³×C₅	—	4	2	no	—
273	C₂³×C₅	—	4	2	no	—
274	C₂³×C₅	—	4	2	no	—
275	C₂³×C₅	—	4	2	no	—
276	C₂³×C₅	—	4	2	no	—
277	C₂³×C₅	—	6	2	no	—
278	C₂³×C₅	—	12	2	no	—
279	C₂³×C₅	—	12	2	no	—
280	C₂³×C₅	—	12	2	no	—
281	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
282	C₅×D₄	—	2	4	no	—
283	C₅×D₄	—	2	2	no	—
284	C₅×D₄	—	2	2	no	—
285	C₅×D₄	—	2	2	no	—
286	C₅×D₄	—	4	2	no	—
287	C₅×D₄	—	6	2	no	—
288	C₅×D₄	—	6	2	no	—
289	C₅×D₄	—	12	8	no	—
290	C₅×D₄	—	12	8	no	—
291	C₅×D₄	—	12	2	no	—
292	C₅×D₄	C₂×#67	1	4	yes	complemented
293	C₂×C₄×C₅	—	3	4	no	—
294	C₂×C₄×C₅	—	3	2	no	—
295	C₂×C₄×C₅	—	3	2	no	—
296	C₂×C₄×C₅	—	6	2	no	—
297	C₂×C₄×C₅	—	6	2	no	—
298	C₂×C₄×C₅	—	12	8	no	—
299	C₂×C₄×C₅	—	12	2	no	—
300	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
301	C₂×C₄×C₅	#237	1	2	yes	—
302	C₂×C₄×C₅	C₂×#67	1	2	yes	—
303	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
304	C₅×C₈	—	2	2	no	—
305	C₅×C₈	—	6	2	no	—
306	C₂²×D₄	—	3	1	no	—
307	C₂²×D₄	—	6	1	no	—
308	C₂²×D₄	—	6	1	no	—
309	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
310	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
311	C₂³×C₄	—	6	1	no	—
312	C₂×D₈	—	2	4	no	—
313	C₂×D₈	—	3	4	no	—
314	C₂×D₈	—	6	4	no	—
315	C₂×D₈	C₂×C₅×D₃	1	4	yes	complemented
316	C₂²×C₈	—	3	1	no	—
317	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
318	#127	—	3	4	no	—
319	#127	—	6	2	no	—
320	C₄×D₄	—	3	4	no	—
321	C₄×D₄	—	6	2	no	—
322	C₂×C₄⋊C₄	—	3	1	no	—
323	C₂×C₂²⋊C₄	—	6	1	no	—
324	C₂×C₄²	—	3	1	no	—
325	C₄⋊C₈	—	3	4	no	—
326	#102	—	3	4	no	—
327	#102	—	3	4	no	—
328	C₂×C₃×C₅	—	4	4	no	—
329	C₂×C₃×C₅	—	8	2	no	—
330	C₂×C₃×C₅	#459	1	4	yes	complemented
331	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
332	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
333	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
334	C₅×D₃	—	8	2	no	—
335	C₂³×C₃	—	2	4	no	—
336	C₂³×C₃	—	2	2	no	—
337	C₂³×C₃	—	2	2	no	—
338	C₂³×C₃	—	4	2	no	—
339	C₂³×C₃	—	4	2	no	—
340	C₂³×C₃	—	4	2	no	—
341	C₂³×C₃	—	4	2	no	—
342	C₂³×C₃	—	4	2	no	—
343	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
344	C₂²×D₃	—	2	2	no	—
345	C₂²×D₃	—	4	2	no	—
346	C₂²×D₃	—	4	2	no	—
347	C₂²×D₃	—	4	2	no	—
348	C₃×D₄	—	2	4	no	—
349	C₃×D₄	—	2	2	no	—
350	C₃×D₄	—	2	2	no	—
351	C₃×D₄	—	2	2	no	—
352	C₃×D₄	—	4	2	no	—
353	C₃×D₄	C₂×C₅×D₄	1	4	yes	complemented
354	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
355	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
356	C₂×C₃×C₄	C₅×#41	1	2	yes	—
357	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
358	#67	—	4	8	no	—
359	#67	—	4	8	no	—
360	C₂×Dic₃	—	2	2	no	—
361	C₂×Dic₃	—	2	2	no	—
362	C₂×Dic₃	—	4	2	no	—
363	C₂×Dic₃	—	4	8	no	—
364	C₂×Dic₃	C₅×D₈	1	4	yes	complemented
365	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
366	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
367	D₁₂	—	2	2	no	—
368	D₁₂	—	2	2	no	—
369	D₁₂	—	4	2	no	—
370	C₃×C₈	—	2	2	no	—
371	C₃⋊C₈	—	2	2	no	—
372	C₂²×C₅	—	2	4	no	—
373	C₂²×C₅	—	4	8	no	—
374	C₂²×C₅	—	4	2	no	—
375	C₂²×C₅	—	4	2	no	—
376	C₂²×C₅	—	4	2	no	—
377	C₂²×C₅	—	4	2	no	—
378	C₂²×C₅	—	4	2	no	—
379	C₂²×C₅	—	8	4	no	—
380	C₂²×C₅	—	12	2	no	—
381	C₂²×C₅	—	12	2	no	—
382	C₂²×C₅	—	12	2	no	—
383	C₂²×C₅	—	24	4	no	—
384	C₂²×C₅	D₃×D₈	1	2	yes	—
385	C₂²×C₅	#911	1	2	yes	—
386	C₂²×C₅	#939	1	2	yes	—
387	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
388	C₄×C₅	—	3	4	no	—
389	C₄×C₅	—	6	2	no	—
390	C₄×C₅	—	12	2	no	—
391	C₄×C₅	#939	1	2	yes	—
392	C₄×C₅	C₂×#237	1	1	yes	characteristic
393	C₄×C₅	C₂²×#67	1	1	yes	characteristic
394	C₂⁴	—	2	1	no	—
395	C₂⁴	—	2	1	no	—
396	C₂⁴	—	6	1	no	—
397	C₂×D₄	—	2	1	no	—
398	C₂×D₄	—	2	1	no	—
399	C₂×D₄	—	2	2	no	—
400	C₂×D₄	—	2	2	no	—
401	C₂×D₄	—	2	2	no	—
402	C₂×D₄	—	3	2	no	—
403	C₂×D₄	—	6	4	no	—
404	C₂×D₄	—	6	4	no	—
405	C₂×D₄	—	6	1	no	—
406	C₂×D₄	—	6	2	no	—
407	C₂×D₄	—	6	2	no	—
408	C₂×D₄	—	12	4	no	—
409	C₂×D₄	—	12	4	no	—
410	C₂×D₄	C₅×#67	1	4	yes	complemented
411	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
412	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
413	C₂²×C₄	—	3	1	no	—
414	C₂²×C₄	—	3	1	no	—
415	C₂²×C₄	—	6	4	no	—
416	C₂²×C₄	—	6	1	no	—
417	C₂²×C₄	—	12	4	no	—
418	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
419	D₈	—	2	8	no	—
420	D₈	—	6	8	no	—
421	C₂×C₈	—	2	2	no	—
422	C₂×C₈	—	3	2	no	—
423	C₂×C₈	—	6	2	no	—
424	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
425	C₄⋊C₄	—	3	2	no	—
426	C₄⋊C₄	—	6	1	no	—
427	C₂²⋊C₄	—	6	4	no	—
428	C₄²	—	3	2	no	—
429	C₄²	—	3	2	no	—
430	C₃×C₅	C₂×#459	1	1	yes	characteristic, complemented, Hall
431	C₂²×C₃	—	2	4	no	—
432	C₂²×C₃	—	4	8	no	—
433	C₂²×C₃	—	4	2	no	—
434	C₂²×C₃	—	4	2	no	—
435	C₂²×C₃	—	4	2	no	—
436	C₂²×C₃	—	4	2	no	—
437	C₂²×C₃	—	4	2	no	—
438	C₂²×C₃	—	8	4	no	—
439	C₂²×C₃	C₅×#121	1	2	yes	—
440	C₂²×C₃	C₂×C₅×D₈	1	2	yes	—
441	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	2	yes	—
442	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
443	C₂×D₃	—	4	2	no	—
444	C₂×D₃	—	4	2	no	—
445	C₂×D₃	—	4	2	no	—
446	C₂×D₃	—	8	4	no	—
447	C₃×C₄	C₅×#121	1	2	yes	—
448	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
449	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
450	Dic₃	—	2	2	no	—
451	Dic₃	—	4	2	no	—
452	Dic₃	C₂×C₅×D₈	1	4	yes	complemented
453	C₂×C₅	—	4	4	no	—
454	C₂×C₅	—	8	2	no	—
455	C₂×C₅	—	24	2	no	—
456	C₂×C₅	#5150	1	4	yes	direct product factor
457	C₂×C₅	C₂×D₃×D₈	1	1	yes	characteristic
458	C₂×C₅	C₂×#911	1	1	yes	characteristic
459	C₂×C₅	C₂×#939	1	1	yes	characteristic
460	C₂³	—	2	4	no	—
461	C₂³	—	2	2	no	—
462	C₂³	—	2	2	no	—
463	C₂³	—	4	2	no	—
464	C₂³	—	4	2	no	—
465	C₂³	—	4	2	no	—
466	C₂³	—	4	2	no	—
467	C₂³	—	4	2	no	—
468	C₂³	—	6	2	no	—
469	C₂³	—	12	2	no	—
470	C₂³	—	12	2	no	—
471	C₂³	—	12	2	no	—
472	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
473	D₄	—	2	4	no	—
474	D₄	—	2	2	no	—
475	D₄	—	2	2	no	—
476	D₄	—	2	2	no	—
477	D₄	—	4	2	no	—
478	D₄	—	6	2	no	—
479	D₄	—	6	2	no	—
480	D₄	—	12	8	no	—
481	D₄	—	12	8	no	—
482	D₄	—	12	2	no	—
483	D₄	C₂×C₅×#67	1	4	yes	complemented
484	C₂×C₄	—	3	4	no	—
485	C₂×C₄	—	3	2	no	—
486	C₂×C₄	—	3	2	no	—
487	C₂×C₄	—	6	2	no	—
488	C₂×C₄	—	6	2	no	—
489	C₂×C₄	—	12	8	no	—
490	C₂×C₄	—	12	2	no	—
491	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
492	C₂×C₄	C₅×#237	1	2	yes	—
493	C₂×C₄	C₂×C₅×#67	1	2	yes	—
494	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
495	C₈	—	2	2	no	—
496	C₈	—	6	2	no	—
497	C₂×C₃	—	4	4	no	—
498	C₂×C₃	—	8	2	no	—
499	C₂×C₃	C₅×#459	1	4	yes	complemented
500	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
501	C₂×C₃	C₂²×C₅×D₈	1	1	yes	characteristic
502	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
503	D₃	—	8	2	no	—
504	C₅	C₂×#5150	1	1	yes	characteristic, direct product factor, Sylow
505	C₂²	—	2	4	no	—
506	C₂²	—	4	2	no	—
507	C₂²	—	4	2	no	—
508	C₂²	—	4	8	no	—
509	C₂²	—	4	2	no	—
510	C₂²	—	4	2	no	—
511	C₂²	—	4	2	no	—
512	C₂²	—	8	4	no	—
513	C₂²	—	12	2	no	—
514	C₂²	—	12	2	no	—
515	C₂²	—	12	2	no	—
516	C₂²	—	24	4	no	—
517	C₂²	C₅×D₃×D₈	1	2	yes	—
518	C₂²	C₅×#911	1	2	yes	—
519	C₂²	C₅×#939	1	2	yes	—
520	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
521	C₄	—	3	4	no	—
522	C₄	—	6	2	no	—
523	C₄	—	12	2	no	—
524	C₄	C₅×#939	1	2	yes	—
525	C₄	C₂×C₅×#237	1	1	yes	characteristic
526	C₄	C₂²×C₅×#67	1	1	yes	characteristic
527	C₃	C₂×C₅×#459	1	1	yes	characteristic, complemented, Sylow
528	C₂	—	4	4	no	—
529	C₂	—	8	2	no	—
530	C₂	—	24	2	no	—
531	C₂	C₅×#5150	1	4	yes	direct product factor
532	C₂	C₂×C₅×D₃×D₈	1	1	yes	characteristic
533	C₂	C₂×C₅×#911	1	1	yes	characteristic
534	C₂	C₂×C₅×#939	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂²×C₃×C₅×D₈	C₂
socle	C₂³×C₃×C₅	C₂×D₄
hypercenter	C₂²×C₅×D₈	D₃
hypocenter	C₃	C₂×C₅×#459
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂²×C₄×C₅ ◁ C₂²×C₅×D₈

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₅×D₈	C₂	semidirect
2. C₂×C₅×#940	C₂	semidirect
3. C₂×C₅×D₄×Dic₃	C₂	semidirect
4. C₂²×C₅×#213	C₂	semidirect
5. C₂×C₅×#832	C₂	semidirect
6. C₅×#5150	C₂	direct (N × H)
7. C₂×C₅×#821	C₂	semidirect
8. C₂×C₅×Dic₃⋊C₈	C₂	semidirect
17. C₂×C₃×C₅×D₈	C₂²	semidirect
21. C₅×#940	C₂²	semidirect
23. C₅×D₄×Dic₃	C₂²	semidirect
25. C₂×C₅×#213	C₂²	semidirect
29. C₅×#832	C₂²	semidirect
30. C₅×#821	C₂²	semidirect
31. C₅×Dic₃⋊C₈	C₂²	semidirect
32. C₂×#5150	C₅	direct (N × H)
34. C₂²×C₅×D₈	D₃	semidirect
49. C₂×C₃×C₅×D₄	D₄	semidirect
77. C₂²×C₃×D₈	C₂×C₅	semidirect
78. C₂×#940	C₂×C₅	semidirect
79. C₂×D₄×Dic₃	C₂×C₅	semidirect
80. C₂²×#213	C₂×C₅	semidirect
81. C₂×#832	C₂×C₅	semidirect
82. #5150	C₂×C₅	direct (N × H)
83. C₂×#821	C₂×C₅	semidirect
84. C₂×Dic₃⋊C₈	C₂×C₅	semidirect
94. C₂×C₅×D₈	C₂×D₃	semidirect
126. C₃×C₅×D₄	C₂×D₄	semidirect
137. C₂×C₅×Dic₃	D₈	semidirect
152. C₂×C₃×D₈	C₂²×C₅	semidirect
156. #940	C₂²×C₅	semidirect
158. D₄×Dic₃	C₂²×C₅	semidirect
160. C₂×#213	C₂²×C₅	semidirect
164. #832	C₂²×C₅	semidirect
165. #821	C₂²×C₅	semidirect
166. Dic₃⋊C₈	C₂²×C₅	semidirect
183. C₂×C₅×D₄	#67	semidirect
204. C₂²×D₈	C₅×D₃	semidirect
232. C₅×Dic₃	C₂×D₈	semidirect
241. C₂×C₃×D₄	C₅×D₄	semidirect
292. C₅×D₄	C₂×#67	semidirect
315. C₂×D₈	C₂×C₅×D₃	semidirect
330. C₂×C₃×C₅	#459	semidirect
353. C₃×D₄	C₂×C₅×D₄	semidirect
364. C₂×Dic₃	C₅×D₈	semidirect
410. C₂×D₄	C₅×#67	semidirect
430. C₃×C₅	C₂×#459	semidirect
452. Dic₃	C₂×C₅×D₈	semidirect
456. C₂×C₅	#5150	direct (N × H)
483. D₄	C₂×C₅×#67	semidirect
499. C₂×C₃	C₅×#459	semidirect
504. C₅	C₂×#5150	direct (N × H)
527. C₃	C₂×C₅×#459	semidirect
531. C₂	C₅×#5150	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×C₃×C₅×D₈	2
C₂×C₅×#940	2
C₂×C₅×D₄×Dic₃	2
C₂²×C₅×#213	2
C₂×C₅×#832	2
C₅×#5150	2
C₂×C₅×#821	2
C₂×C₅×Dic₃⋊C₈	2
C₂×C₅×#459	3
C₂×#5150	5

Subgroups — C2×C5×#5150 #14425809

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5150 #14425809