Subgroups — C₂×C₅×#5041 #14427591

Order 1920.

1128 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×C₅×#121	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₅×#214	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#924	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂³×C₅×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#832	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5041	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₅×#810	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅×#808	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×#465	—	3	1	no	maximal, Hall
10	C₂²×C₃×C₅×D₄	—	2	1	no	—
11	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
12	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
13	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
14	C₃×C₅×#121	—	2	2	no	—
15	C₃×C₅×#121	C₂²	1	4	yes	—
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₅×C₂²⋊C₄	—	2	1	no	—
18	C₂×C₅×#217	—	2	1	no	—
19	C₂×C₅×#214	—	2	4	no	—
20	C₂×C₅×#214	C₂²	1	4	yes	complemented
21	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
22	C₅×#924	—	2	2	no	—
23	C₅×#924	C₂²	1	4	yes	complemented
24	C₂×C₅×Dic₃⋊C₄	—	2	1	no	—
25	C₂²×C₅×C₃⋊C₈	—	2	4	no	—
26	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
27	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
28	C₂²×C₅×C₃⋊C₈	C₂²	1	4	yes	complemented
29	C₅×#832	C₂²	1	4	yes	complemented
30	C₅×#810	C₂²	1	4	yes	complemented
31	C₅×#808	C₂²	1	4	yes	complemented
32	C₂×#5041	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
33	C₂²×C₅×SD₁₆	—	3	1	no	—
34	C₂³×C₅×C₈	—	3	1	no	—
35	C₂×C₅×C₂²⋊Q₈	—	3	1	no	—
36	C₂×C₅×#121	D₃	1	1	yes	characteristic
37	C₅×#465	—	3	8	no	—
38	C₂×C₅×#106	—	3	1	no	—
39	C₂×C₅×#103	—	3	1	no	—
40	C₂×C₅×#102	—	3	1	no	—
41	C₂⁴×C₃×C₅	—	2	1	no	—
42	C₂⁴×C₃×C₅	D₄	1	1	yes	characteristic
43	C₂×C₃×C₅×D₄	—	2	4	no	—
44	C₂×C₃×C₅×D₄	—	2	2	no	—
45	C₂×C₃×C₅×D₄	—	2	1	no	—
46	C₂×C₃×C₅×D₄	—	2	2	no	—
47	C₂×C₃×C₅×D₄	—	4	4	no	—
48	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
49	C₂²×C₃×C₄×C₅	—	2	2	no	—
50	C₂²×C₃×C₄×C₅	—	2	2	no	—
51	C₂²×C₃×C₄×C₅	—	2	1	no	—
52	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
53	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
54	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
55	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
56	C₂²×C₅×Dic₃	—	2	1	no	—
57	C₂²×C₅×Dic₃	—	2	1	no	—
58	C₂×C₅×Dic₆	—	2	2	no	—
59	C₂×C₅×Dic₆	—	2	2	no	—
60	C₂×C₅×Dic₆	—	2	1	no	—
61	C₂×C₅×Dic₆	C₂³	1	2	yes	—
62	C₃×C₅×C₄⋊C₄	—	2	1	no	—
63	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
64	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
65	C₅×#217	—	2	4	no	—
66	C₅×#214	—	2	8	no	—
67	C₅×C₄⋊Dic₃	—	2	1	no	—
68	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
69	C₅×Dic₃⋊C₄	—	2	4	no	—
70	C₂×C₅×C₃⋊C₈	—	2	2	no	—
71	C₂×C₅×C₃⋊C₈	—	2	8	no	—
72	C₂×C₅×C₃⋊C₈	D₄	1	4	yes	complemented
73	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
74	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
75	C₂×C₃×#121	C₂×C₅	1	1	yes	characteristic
76	C₂²×#214	C₂×C₅	1	1	yes	characteristic, complemented
77	C₂×#924	C₂×C₅	1	1	yes	characteristic, complemented
78	C₂³×C₃⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
79	C₂×#832	C₂×C₅	1	1	yes	characteristic, complemented
80	#5041	C₂×C₅	1	8	yes	direct product factor
81	C₂×#810	C₂×C₅	1	1	yes	characteristic, complemented
82	C₂×#808	C₂×C₅	1	1	yes	characteristic, complemented
83	C₂²×C₅×Q₈	—	3	1	no	—
84	C₂²×C₅×D₄	—	2	1	no	—
85	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
86	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
87	C₂×C₅×SD₁₆	—	3	4	no	—
88	C₂×C₅×SD₁₆	—	6	4	no	—
89	C₂²×C₅×C₈	—	3	1	no	—
90	C₂²×C₅×C₈	—	3	1	no	—
91	C₂²×C₅×C₈	—	3	4	no	—
92	C₂²×C₅×C₈	—	6	4	no	—
93	C₅×C₂²⋊Q₈	—	3	4	no	—
94	C₅×C₂²⋊Q₈	—	6	2	no	—
95	C₅×#121	—	2	2	no	—
96	C₅×#121	C₂×D₃	1	4	yes	—
97	C₂×C₅×C₄⋊C₄	—	3	1	no	—
98	C₂×C₅×C₄⋊C₄	—	6	1	no	—
99	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
100	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
101	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
102	C₅×#106	—	3	4	no	—
103	C₅×#103	—	3	4	no	—
104	C₅×#102	—	3	4	no	—
105	C₂×#465	—	3	1	no	Sylow
106	C₂³×C₃×C₅	—	2	2	no	—
107	C₂³×C₃×C₅	—	2	2	no	—
108	C₂³×C₃×C₅	—	2	2	no	—
109	C₂³×C₃×C₅	—	4	2	no	—
110	C₂³×C₃×C₅	—	4	2	no	—
111	C₂³×C₃×C₅	—	4	2	no	—
112	C₂³×C₃×C₅	SD₁₆	1	4	yes	complemented
113	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
114	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
115	C₃×C₅×D₄	—	2	2	no	—
116	C₃×C₅×D₄	—	2	2	no	—
117	C₃×C₅×D₄	—	4	8	no	—
118	C₃×C₅×D₄	—	4	2	no	—
119	C₂×C₃×C₄×C₅	—	2	2	no	—
120	C₂×C₃×C₄×C₅	—	2	4	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	—	4	2	no	—
125	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
126	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
127	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
128	C₂×C₃×C₄×C₅	#41	1	2	yes	—
129	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
130	C₂×C₅×Dic₃	—	2	2	no	—
131	C₂×C₅×Dic₃	—	2	2	no	—
132	C₂×C₅×Dic₃	—	4	2	no	—
133	C₂×C₅×Dic₃	—	4	2	no	—
134	C₅×Dic₆	—	2	2	no	—
135	C₅×Dic₆	—	2	2	no	—
136	C₅×Dic₆	—	4	2	no	—
137	C₅×C₃⋊C₈	—	2	2	no	—
138	C₅×C₃⋊C₈	C₂×D₄	1	4	yes	complemented
139	C₂²×C₃×D₄	—	2	1	no	—
140	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
141	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
142	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
143	C₃×#121	—	2	2	no	—
144	C₃×#121	C₂²×C₅	1	4	yes	—
145	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
146	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
147	C₂×#217	—	2	1	no	—
148	C₂×#214	—	2	4	no	—
149	C₂×#214	C₂²×C₅	1	4	yes	complemented
150	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
151	#924	—	2	2	no	—
152	#924	C₂²×C₅	1	4	yes	complemented
153	C₂×Dic₃⋊C₄	—	2	1	no	—
154	C₂²×C₃⋊C₈	—	2	4	no	—
155	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
156	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
157	C₂²×C₃⋊C₈	C₂²×C₅	1	4	yes	complemented
158	#832	C₂²×C₅	1	4	yes	complemented
159	#810	C₂²×C₅	1	4	yes	complemented
160	#808	C₂²×C₅	1	4	yes	complemented
161	C₂⁴×C₅	—	2	1	no	—
162	C₂⁴×C₅	#67	1	1	yes	characteristic
163	C₂×C₅×Q₈	—	3	2	no	—
164	C₂×C₅×Q₈	—	6	1	no	—
165	C₂×C₅×Q₈	—	6	2	no	—
166	C₂×C₅×Q₈	—	6	2	no	—
167	C₂×C₅×D₄	—	2	4	no	—
168	C₂×C₅×D₄	—	2	2	no	—
169	C₂×C₅×D₄	—	2	2	no	—
170	C₂×C₅×D₄	—	2	1	no	—
171	C₂×C₅×D₄	—	4	4	no	—
172	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
173	C₂²×C₄×C₅	—	2	2	no	—
174	C₂²×C₄×C₅	—	2	2	no	—
175	C₂²×C₄×C₅	—	2	1	no	—
176	C₂²×C₄×C₅	—	6	1	no	—
177	C₂²×C₄×C₅	—	6	1	no	—
178	C₂²×C₄×C₅	#67	1	2	yes	—
179	C₂²×C₄×C₅	#67	1	1	yes	characteristic
180	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
181	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
182	C₅×SD₁₆	—	6	8	no	—
183	C₂×C₅×C₈	—	3	4	no	—
184	C₂×C₅×C₈	—	3	2	no	—
185	C₂×C₅×C₈	—	3	2	no	—
186	C₂×C₅×C₈	—	6	8	no	—
187	C₂×C₅×C₈	—	6	2	no	—
188	C₅×C₄⋊C₄	—	2	1	no	—
189	C₅×C₄⋊C₄	—	3	2	no	—
190	C₅×C₄⋊C₄	—	6	1	no	—
191	C₅×C₄⋊C₄	—	6	4	no	—
192	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
193	C₅×C₂²⋊C₄	—	2	4	no	—
194	C₅×C₂²⋊C₄	—	6	4	no	—
195	C₂²×SD₁₆	—	3	1	no	—
196	C₂³×C₈	—	3	1	no	—
197	C₂×C₂²⋊Q₈	—	3	1	no	—
198	C₂×#121	C₅×D₃	1	1	yes	characteristic
199	#465	—	3	8	no	—
200	C₂×#106	—	3	1	no	—
201	C₂×#103	—	3	1	no	—
202	C₂×#102	—	3	1	no	—
203	C₂²×C₃×C₅	—	2	2	no	—
204	C₂²×C₃×C₅	—	2	2	no	—
205	C₂²×C₃×C₅	—	2	8	no	—
206	C₂²×C₃×C₅	—	4	2	no	—
207	C₂²×C₃×C₅	—	4	2	no	—
208	C₂²×C₃×C₅	—	4	2	no	—
209	C₂²×C₃×C₅	—	8	4	no	—
210	C₂²×C₃×C₅	#121	1	2	yes	—
211	C₂²×C₃×C₅	C₂×SD₁₆	1	2	yes	—
212	C₂²×C₃×C₅	C₂×SD₁₆	1	4	yes	complemented
213	C₂²×C₃×C₅	#135	1	2	yes	—
214	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
215	C₃×C₄×C₅	—	2	2	no	—
216	C₃×C₄×C₅	—	4	2	no	—
217	C₃×C₄×C₅	#121	1	2	yes	—
218	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
219	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
220	C₅×Dic₃	—	4	2	no	—
221	C₅×Dic₃	—	4	2	no	—
222	C₂⁴×C₃	—	2	1	no	—
223	C₂⁴×C₃	C₅×D₄	1	1	yes	characteristic
224	C₂×C₃×D₄	—	2	4	no	—
225	C₂×C₃×D₄	—	2	2	no	—
226	C₂×C₃×D₄	—	2	1	no	—
227	C₂×C₃×D₄	—	2	2	no	—
228	C₂×C₃×D₄	—	4	4	no	—
229	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
230	C₂²×C₃×C₄	—	2	2	no	—
231	C₂²×C₃×C₄	—	2	2	no	—
232	C₂²×C₃×C₄	—	2	1	no	—
233	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
234	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
235	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
236	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
237	C₂²×Dic₃	—	2	1	no	—
238	C₂²×Dic₃	—	2	1	no	—
239	C₂×Dic₆	—	2	2	no	—
240	C₂×Dic₆	—	2	2	no	—
241	C₂×Dic₆	—	2	1	no	—
242	C₂×Dic₆	C₂³×C₅	1	2	yes	—
243	C₃×C₄⋊C₄	—	2	1	no	—
244	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
245	C₃×C₂²⋊C₄	—	2	4	no	—
246	#217	—	2	4	no	—
247	#214	—	2	8	no	—
248	C₄⋊Dic₃	—	2	1	no	—
249	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
250	Dic₃⋊C₄	—	2	4	no	—
251	C₂×C₃⋊C₈	—	2	2	no	—
252	C₂×C₃⋊C₈	—	2	8	no	—
253	C₂×C₃⋊C₈	C₅×D₄	1	4	yes	complemented
254	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
255	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
256	C₂³×C₅	—	2	2	no	—
257	C₂³×C₅	—	2	2	no	—
258	C₂³×C₅	—	2	2	no	—
259	C₂³×C₅	—	4	2	no	—
260	C₂³×C₅	—	4	2	no	—
261	C₂³×C₅	—	4	2	no	—
262	C₂³×C₅	#214	1	4	yes	complemented
263	C₂³×C₅	C₂×#67	1	2	yes	—
264	C₂³×C₅	C₂×#67	1	1	yes	characteristic
265	C₅×Q₈	—	6	2	no	—
266	C₅×Q₈	—	6	2	no	—
267	C₅×Q₈	—	12	2	no	—
268	C₅×D₄	—	2	2	no	—
269	C₅×D₄	—	2	2	no	—
270	C₅×D₄	—	4	8	no	—
271	C₅×D₄	—	4	2	no	—
272	C₂×C₄×C₅	—	2	2	no	—
273	C₂×C₄×C₅	—	2	4	no	—
274	C₂×C₄×C₅	—	2	2	no	—
275	C₂×C₄×C₅	—	2	2	no	—
276	C₂×C₄×C₅	—	2	2	no	—
277	C₂×C₄×C₅	—	4	2	no	—
278	C₂×C₄×C₅	—	6	2	no	—
279	C₂×C₄×C₅	—	6	2	no	—
280	C₂×C₄×C₅	—	12	2	no	—
281	C₂×C₄×C₅	—	12	2	no	—
282	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
283	C₂×C₄×C₅	#237	1	2	yes	—
284	C₂×C₄×C₅	C₂×#67	1	2	yes	—
285	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
286	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
287	C₅×C₈	—	3	4	no	—
288	C₅×C₈	—	6	2	no	—
289	C₂²×Q₈	—	3	1	no	—
290	C₂²×D₄	—	2	1	no	—
291	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
292	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
293	C₂×SD₁₆	—	3	4	no	—
294	C₂×SD₁₆	—	6	4	no	—
295	C₂²×C₈	—	3	1	no	—
296	C₂²×C₈	—	3	1	no	—
297	C₂²×C₈	—	3	4	no	—
298	C₂²×C₈	—	6	4	no	—
299	C₂²⋊Q₈	—	3	4	no	—
300	C₂²⋊Q₈	—	6	2	no	—
301	#121	—	2	2	no	—
302	#121	C₂×C₅×D₃	1	4	yes	—
303	C₂×C₄⋊C₄	—	3	1	no	—
304	C₂×C₄⋊C₄	—	6	1	no	—
305	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
306	C₂×C₂²⋊C₄	—	2	1	no	—
307	C₂×C₂²⋊C₄	—	6	1	no	—
308	#106	—	3	4	no	—
309	#103	—	3	4	no	—
310	#102	—	3	4	no	—
311	C₂×C₃×C₅	—	2	4	no	—
312	C₂×C₃×C₅	—	8	2	no	—
313	C₂×C₃×C₅	#465	1	4	yes	complemented
314	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
315	C₂×C₃×C₅	C₂²×SD₁₆	1	1	yes	characteristic
316	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
317	C₂³×C₃	—	2	2	no	—
318	C₂³×C₃	—	2	2	no	—
319	C₂³×C₃	—	2	2	no	—
320	C₂³×C₃	—	4	2	no	—
321	C₂³×C₃	—	4	2	no	—
322	C₂³×C₃	—	4	2	no	—
323	C₂³×C₃	C₅×SD₁₆	1	4	yes	complemented
324	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
325	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
326	C₃×D₄	—	2	2	no	—
327	C₃×D₄	—	2	2	no	—
328	C₃×D₄	—	4	8	no	—
329	C₃×D₄	—	4	2	no	—
330	C₂×C₃×C₄	—	2	2	no	—
331	C₂×C₃×C₄	—	2	4	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	2	no	—
336	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
337	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
338	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
339	C₂×C₃×C₄	C₅×#41	1	2	yes	—
340	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
341	C₂×Dic₃	—	2	2	no	—
342	C₂×Dic₃	—	2	2	no	—
343	C₂×Dic₃	—	4	2	no	—
344	C₂×Dic₃	—	4	2	no	—
345	Dic₆	—	2	2	no	—
346	Dic₆	—	2	2	no	—
347	Dic₆	—	4	2	no	—
348	C₃⋊C₈	—	2	2	no	—
349	C₃⋊C₈	C₂×C₅×D₄	1	4	yes	complemented
350	C₂²×C₅	—	2	2	no	—
351	C₂²×C₅	—	2	8	no	—
352	C₂²×C₅	—	2	2	no	—
353	C₂²×C₅	—	4	2	no	—
354	C₂²×C₅	—	4	2	no	—
355	C₂²×C₅	—	4	2	no	—
356	C₂²×C₅	—	8	4	no	—
357	C₂²×C₅	C₂×#214	1	2	yes	—
358	C₂²×C₅	C₂×#214	1	4	yes	complemented
359	C₂²×C₅	#939	1	2	yes	—
360	C₂²×C₅	#950	1	2	yes	—
361	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
362	C₄×C₅	—	2	2	no	—
363	C₄×C₅	—	4	2	no	—
364	C₄×C₅	—	12	2	no	—
365	C₄×C₅	—	12	2	no	—
366	C₄×C₅	#939	1	2	yes	—
367	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
368	C₄×C₅	C₂×#237	1	1	yes	characteristic
369	C₂⁴	—	2	1	no	—
370	C₂⁴	C₅×#67	1	1	yes	characteristic
371	C₂×Q₈	—	3	2	no	—
372	C₂×Q₈	—	6	1	no	—
373	C₂×Q₈	—	6	2	no	—
374	C₂×Q₈	—	6	2	no	—
375	C₂×D₄	—	2	4	no	—
376	C₂×D₄	—	2	2	no	—
377	C₂×D₄	—	2	2	no	—
378	C₂×D₄	—	2	1	no	—
379	C₂×D₄	—	4	4	no	—
380	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	6	1	no	—
385	C₂²×C₄	—	6	1	no	—
386	C₂²×C₄	C₅×#67	1	1	yes	characteristic
387	C₂²×C₄	C₅×#67	1	2	yes	—
388	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
389	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
390	SD₁₆	—	6	8	no	—
391	C₂×C₈	—	3	4	no	—
392	C₂×C₈	—	3	2	no	—
393	C₂×C₈	—	3	2	no	—
394	C₂×C₈	—	6	8	no	—
395	C₂×C₈	—	6	2	no	—
396	C₄⋊C₄	—	2	1	no	—
397	C₄⋊C₄	—	3	2	no	—
398	C₄⋊C₄	—	6	1	no	—
399	C₄⋊C₄	—	6	4	no	—
400	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
401	C₂²⋊C₄	—	2	4	no	—
402	C₂²⋊C₄	—	6	4	no	—
403	C₃×C₅	C₂×#465	1	1	yes	characteristic, complemented, Hall
404	C₂²×C₃	—	2	8	no	—
405	C₂²×C₃	—	2	2	no	—
406	C₂²×C₃	—	2	2	no	—
407	C₂²×C₃	—	4	2	no	—
408	C₂²×C₃	—	4	2	no	—
409	C₂²×C₃	—	4	2	no	—
410	C₂²×C₃	—	8	4	no	—
411	C₂²×C₃	C₅×#121	1	2	yes	—
412	C₂²×C₃	C₂×C₅×SD₁₆	1	2	yes	—
413	C₂²×C₃	C₂×C₅×SD₁₆	1	4	yes	complemented
414	C₂²×C₃	C₅×#135	1	2	yes	—
415	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
416	C₃×C₄	—	2	2	no	—
417	C₃×C₄	—	4	2	no	—
418	C₃×C₄	C₅×#121	1	2	yes	—
419	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
420	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
421	Dic₃	—	4	2	no	—
422	Dic₃	—	4	2	no	—
423	C₂×C₅	—	2	4	no	—
424	C₂×C₅	—	8	2	no	—
425	C₂×C₅	#5041	1	4	yes	direct product factor
426	C₂×C₅	C₂²×#214	1	1	yes	characteristic
427	C₂×C₅	C₂×#939	1	1	yes	characteristic
428	C₂×C₅	C₂×#950	1	1	yes	characteristic
429	C₂³	—	2	2	no	—
430	C₂³	—	2	2	no	—
431	C₂³	—	2	2	no	—
432	C₂³	—	4	2	no	—
433	C₂³	—	4	2	no	—
434	C₂³	—	4	2	no	—
435	C₂³	C₅×#214	1	4	yes	complemented
436	C₂³	C₂×C₅×#67	1	2	yes	—
437	C₂³	C₂×C₅×#67	1	1	yes	characteristic
438	Q₈	—	6	2	no	—
439	Q₈	—	6	2	no	—
440	Q₈	—	12	2	no	—
441	D₄	—	2	2	no	—
442	D₄	—	2	2	no	—
443	D₄	—	4	8	no	—
444	D₄	—	4	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	6	2	no	—
452	C₂×C₄	—	6	2	no	—
453	C₂×C₄	—	12	2	no	—
454	C₂×C₄	—	12	2	no	—
455	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
456	C₂×C₄	C₅×#237	1	2	yes	—
457	C₂×C₄	C₂×C₅×#67	1	2	yes	—
458	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
459	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
460	C₈	—	3	4	no	—
461	C₈	—	6	2	no	—
462	C₂×C₃	—	2	4	no	—
463	C₂×C₃	—	8	2	no	—
464	C₂×C₃	C₅×#465	1	4	yes	complemented
465	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
466	C₂×C₃	C₂²×C₅×SD₁₆	1	1	yes	characteristic
467	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
468	C₅	C₂×#5041	1	1	yes	characteristic, direct product factor, Sylow
469	C₂²	—	2	8	no	—
470	C₂²	—	2	2	no	—
471	C₂²	—	2	2	no	—
472	C₂²	—	4	2	no	—
473	C₂²	—	4	2	no	—
474	C₂²	—	4	2	no	—
475	C₂²	—	8	4	no	—
476	C₂²	C₂×C₅×#214	1	2	yes	—
477	C₂²	C₂×C₅×#214	1	4	yes	complemented
478	C₂²	C₅×#939	1	2	yes	—
479	C₂²	C₅×#950	1	2	yes	—
480	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
481	C₄	—	2	2	no	—
482	C₄	—	4	2	no	—
483	C₄	—	12	2	no	—
484	C₄	—	12	2	no	—
485	C₄	C₅×#939	1	2	yes	—
486	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
487	C₄	C₂×C₅×#237	1	1	yes	characteristic
488	C₃	C₂×C₅×#465	1	1	yes	characteristic, complemented, Sylow
489	C₂	—	2	4	no	—
490	C₂	—	8	2	no	—
491	C₂	C₅×#5041	1	4	yes	direct product factor
492	C₂	C₂²×C₅×#214	1	1	yes	characteristic
493	C₂	C₂×C₅×#939	1	1	yes	characteristic
494	C₂	C₂×C₅×#950	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂×#67
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting, prime radical	C₂×C₃×C₅×#121	C₂
socle	C₂³×C₃×C₅	C₂×D₄
hypercenter	C₂×C₅×#121	D₃
hypocenter	C₃	C₂×C₅×#465
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂³×C₄×C₅ ◁ C₂×C₅×#121

Complements

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

N	H ≅ G/N	type
2. C₂²×C₅×#214	C₂	semidirect
3. C₂×C₅×#924	C₂	semidirect
4. C₂³×C₅×C₃⋊C₈	C₂	semidirect
5. C₂×C₅×#832	C₂	semidirect
6. C₅×#5041	C₂	direct (N × H)
7. C₂×C₅×#810	C₂	semidirect
8. C₂×C₅×#808	C₂	semidirect
20. C₂×C₅×#214	C₂²	semidirect
23. C₅×#924	C₂²	semidirect
28. C₂²×C₅×C₃⋊C₈	C₂²	semidirect
29. C₅×#832	C₂²	semidirect
30. C₅×#810	C₂²	semidirect
31. C₅×#808	C₂²	semidirect
32. C₂×#5041	C₅	direct (N × H)
72. C₂×C₅×C₃⋊C₈	D₄	semidirect
76. C₂²×#214	C₂×C₅	semidirect
77. C₂×#924	C₂×C₅	semidirect
78. C₂³×C₃⋊C₈	C₂×C₅	semidirect
79. C₂×#832	C₂×C₅	semidirect
80. #5041	C₂×C₅	direct (N × H)
81. C₂×#810	C₂×C₅	semidirect
82. C₂×#808	C₂×C₅	semidirect
112. C₂³×C₃×C₅	SD₁₆	semidirect
138. C₅×C₃⋊C₈	C₂×D₄	semidirect
149. C₂×#214	C₂²×C₅	semidirect
152. #924	C₂²×C₅	semidirect
157. C₂²×C₃⋊C₈	C₂²×C₅	semidirect
158. #832	C₂²×C₅	semidirect
159. #810	C₂²×C₅	semidirect
160. #808	C₂²×C₅	semidirect
212. C₂²×C₃×C₅	C₂×SD₁₆	semidirect
253. C₂×C₃⋊C₈	C₅×D₄	semidirect
262. C₂³×C₅	#214	semidirect
313. C₂×C₃×C₅	#465	semidirect
323. C₂³×C₃	C₅×SD₁₆	semidirect
349. C₃⋊C₈	C₂×C₅×D₄	semidirect
358. C₂²×C₅	C₂×#214	semidirect
403. C₃×C₅	C₂×#465	semidirect
413. C₂²×C₃	C₂×C₅×SD₁₆	semidirect
425. C₂×C₅	#5041	direct (N × H)
435. C₂³	C₅×#214	semidirect
464. C₂×C₃	C₅×#465	semidirect
468. C₅	C₂×#5041	direct (N × H)
477. C₂²	C₂×C₅×#214	semidirect
488. C₃	C₂×C₅×#465	semidirect
491. C₂	C₅×#5041	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×C₃×C₅×#121	2
C₂²×C₅×#214	2
C₂×C₅×#924	2
C₂³×C₅×C₃⋊C₈	2
C₂×C₅×#832	2
C₅×#5041	2
C₂×C₅×#810	2
C₂×C₅×#808	2
C₂×C₅×#465	3
C₂×#5041	5

Subgroups — C2×C5×#5041 #14427591

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5041 #14427591