Subgroups — C₂×C₅×#4774 #14431401

Order 1920.

1024 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#938	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×D₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×#102	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#832	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×(C₂×D₃)⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×#818	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#807	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4774	C₂	1	8	yes	maximal, direct product factor
9	C₂×C₅×#480	—	3	1	no	maximal, Hall
10	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
11	C₂²×C₅×#67	—	2	1	no	—
12	C₂²×C₄×C₅×D₃	—	2	1	no	—
13	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₂×C₅×#217	—	2	1	no	—
17	C₅×#938	—	2	2	no	—
18	C₅×#938	C₂²	1	4	yes	—
19	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
20	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
21	C₂×C₅×Dic₃⋊C₄	—	2	1	no	—
22	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
23	C₅×D₃×C₄⋊C₄	—	2	2	no	—
24	C₅×D₃×C₄⋊C₄	C₂²	1	4	yes	complemented
25	C₃×C₅×#102	C₂²	1	4	yes	complemented
26	C₅×#832	C₂²	1	4	yes	complemented
27	C₅×(C₂×D₃)⋊C₈	C₂²	1	4	yes	complemented
28	C₅×#818	C₂²	1	4	yes	complemented
29	C₅×#807	C₂²	1	4	yes	complemented
30	C₂×#4774	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
31	C₂×C₅×#121	—	3	1	no	—
32	C₂²×C₅×C₄⋊C₄	—	3	1	no	—
33	C₅×#480	—	3	8	no	—
34	C₂×C₅×#107	—	3	1	no	—
35	C₂×C₅×#107	—	3	1	no	—
36	C₂×C₅×#102	—	3	1	no	—
37	C₂×C₅×#102	D₃	1	1	yes	characteristic, complemented
38	C₂×C₅×C₂²⋊C₈	—	3	1	no	—
39	C₂⁴×C₃×C₅	—	2	1	no	—
40	C₂³×C₅×D₃	D₄	1	1	yes	characteristic
41	C₂×C₃×C₅×D₄	—	2	1	no	—
42	C₂×C₃×C₅×D₄	—	2	2	no	—
43	C₂×C₃×C₅×D₄	—	2	2	no	—
44	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
45	C₂²×C₃×C₄×C₅	—	2	1	no	—
46	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
47	C₂×C₅×#67	—	2	4	no	—
48	C₂×C₅×#67	—	4	4	no	—
49	C₂²×C₅×Dic₃	—	2	1	no	—
50	C₂²×C₅×Dic₃	—	2	1	no	—
51	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
52	C₂×C₄×C₅×D₃	—	2	2	no	—
53	C₂×C₄×C₅×D₃	—	2	2	no	—
54	C₂×C₄×C₅×D₃	—	2	4	no	—
55	C₂×C₄×C₅×D₃	—	4	4	no	—
56	C₂×C₄×C₅×D₃	D₄	1	2	yes	—
57	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
58	C₂×C₃×C₅×C₈	—	2	2	no	—
59	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
60	C₃×C₅×C₄⋊C₄	—	2	1	no	—
61	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
62	C₅×#217	—	2	4	no	—
63	C₅×C₄⋊Dic₃	—	2	1	no	—
64	C₅×C₄⋊Dic₃	—	2	1	no	—
65	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
66	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
67	C₅×Dic₃⋊C₄	—	2	4	no	—
68	C₂×C₅×C₃⋊C₈	—	2	2	no	—
69	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
70	C₂×#938	C₂×C₅	1	1	yes	characteristic
71	C₂×D₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
72	C₂×C₃×#102	C₂×C₅	1	1	yes	characteristic, complemented
73	C₂×#832	C₂×C₅	1	1	yes	characteristic, complemented
74	C₂×(C₂×D₃)⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
75	C₂×#818	C₂×C₅	1	1	yes	characteristic, complemented
76	C₂×#807	C₂×C₅	1	1	yes	characteristic, complemented
77	#4774	C₂×C₅	1	8	yes	direct product factor
78	C₂²×C₅×D₄	—	6	1	no	—
79	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
80	C₂³×C₄×C₅	—	3	1	no	—
81	C₂³×C₄×C₅	—	6	1	no	—
82	C₂²×C₅×C₈	—	3	1	no	—
83	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
84	C₅×#121	—	3	4	no	—
85	C₅×#121	—	6	2	no	—
86	C₂×C₅×C₄⋊C₄	—	3	1	no	—
87	C₂×C₅×C₄⋊C₄	—	3	1	no	—
88	C₂×C₅×C₄⋊C₄	—	3	4	no	—
89	C₂×C₅×C₄⋊C₄	—	6	2	no	—
90	C₂×C₅×C₄⋊C₄	—	6	1	no	—
91	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
92	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
93	C₅×#107	—	3	4	no	—
94	C₅×#107	—	3	4	no	—
95	C₅×#102	—	3	4	no	—
96	C₅×#102	C₂×D₃	1	4	yes	complemented
97	C₅×C₂²⋊C₈	—	3	4	no	—
98	C₂×#480	—	3	1	no	Sylow
99	C₂³×C₃×C₅	—	2	2	no	—
100	C₂³×C₃×C₅	—	4	2	no	—
101	C₂³×C₃×C₅	—	4	2	no	—
102	C₂³×C₃×C₅	—	4	2	no	—
103	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₅×D₃	—	2	2	no	—
105	C₂²×C₅×D₃	—	2	2	no	—
106	C₂²×C₅×D₃	D₈	1	4	yes	—
107	C₂²×C₅×D₃	C₂×D₄	1	2	yes	—
108	C₃×C₅×D₄	—	2	2	no	—
109	C₃×C₅×D₄	—	2	2	no	—
110	C₃×C₅×D₄	—	4	2	no	—
111	C₂×C₃×C₄×C₅	—	2	2	no	—
112	C₂×C₃×C₄×C₅	—	4	2	no	—
113	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
114	C₂×C₃×C₄×C₅	#41	1	2	yes	—
115	C₂×C₃×C₄×C₅	#41	1	2	yes	—
116	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
117	C₅×#67	—	4	8	no	—
118	C₂×C₅×Dic₃	—	2	2	no	—
119	C₂×C₅×Dic₃	—	2	2	no	—
120	C₂×C₅×Dic₃	—	2	2	no	—
121	C₂×C₅×Dic₃	—	4	2	no	—
122	C₂×C₅×Dic₃	—	4	2	no	—
123	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
124	C₄×C₅×D₃	—	2	4	no	—
125	C₄×C₅×D₃	—	2	2	no	—
126	C₄×C₅×D₃	—	2	2	no	—
127	C₄×C₅×D₃	—	4	8	no	—
128	C₃×C₅×C₈	—	2	2	no	—
129	C₅×C₃⋊C₈	—	2	2	no	—
130	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
131	C₂²×#67	—	2	1	no	—
132	C₂²×C₄×D₃	—	2	1	no	—
133	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
134	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
135	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
136	C₂×#217	—	2	1	no	—
137	#938	—	2	2	no	—
138	#938	C₂²×C₅	1	4	yes	—
139	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
140	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
141	C₂×Dic₃⋊C₄	—	2	1	no	—
142	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
143	D₃×C₄⋊C₄	—	2	2	no	—
144	D₃×C₄⋊C₄	C₂²×C₅	1	4	yes	complemented
145	C₃×#102	C₂²×C₅	1	4	yes	complemented
146	#832	C₂²×C₅	1	4	yes	complemented
147	(C₂×D₃)⋊C₈	C₂²×C₅	1	4	yes	complemented
148	#818	C₂²×C₅	1	4	yes	complemented
149	#807	C₂²×C₅	1	4	yes	complemented
150	C₂⁴×C₅	—	2	1	no	—
151	C₂⁴×C₅	—	3	1	no	—
152	C₂×C₅×D₄	—	2	2	no	—
153	C₂×C₅×D₄	—	2	1	no	—
154	C₂×C₅×D₄	—	2	2	no	—
155	C₂×C₅×D₄	—	6	4	no	—
156	C₂×C₅×D₄	—	12	4	no	—
157	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
158	C₂²×C₄×C₅	—	2	1	no	—
159	C₂²×C₄×C₅	—	3	1	no	—
160	C₂²×C₄×C₅	—	3	2	no	—
161	C₂²×C₄×C₅	—	3	2	no	—
162	C₂²×C₄×C₅	—	6	4	no	—
163	C₂²×C₄×C₅	—	6	2	no	—
164	C₂²×C₄×C₅	—	6	2	no	—
165	C₂²×C₄×C₅	—	6	1	no	—
166	C₂²×C₄×C₅	—	6	1	no	—
167	C₂²×C₄×C₅	—	12	4	no	—
168	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
169	C₂×C₅×C₈	—	2	2	no	—
170	C₂×C₅×C₈	—	3	2	no	—
171	C₂×C₅×C₈	—	6	2	no	—
172	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
173	C₅×C₄⋊C₄	—	2	1	no	—
174	C₅×C₄⋊C₄	—	3	2	no	—
175	C₅×C₄⋊C₄	—	3	2	no	—
176	C₅×C₄⋊C₄	—	6	4	no	—
177	C₅×C₄⋊C₄	—	6	1	no	—
178	C₅×C₄⋊C₄	—	6	1	no	—
179	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
180	C₅×C₂²⋊C₄	—	6	4	no	—
181	C₂×#121	—	3	1	no	—
182	C₂²×C₄⋊C₄	—	3	1	no	—
183	#480	—	3	8	no	—
184	C₂×#107	—	3	1	no	—
185	C₂×#107	—	3	1	no	—
186	C₂×#102	—	3	1	no	—
187	C₂×#102	C₅×D₃	1	1	yes	characteristic, complemented
188	C₂×C₂²⋊C₈	—	3	1	no	—
189	C₂²×C₃×C₅	—	4	2	no	—
190	C₂²×C₃×C₅	—	4	2	no	—
191	C₂²×C₃×C₅	—	4	2	no	—
192	C₂²×C₃×C₅	—	8	4	no	—
193	C₂²×C₃×C₅	#123	1	2	yes	—
194	C₂²×C₃×C₅	C₂×D₈	1	2	yes	—
195	C₂²×C₃×C₅	#137	1	2	yes	—
196	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
197	C₂×C₅×D₃	—	2	2	no	—
198	C₂×C₅×D₃	—	2	2	no	—
199	C₂×C₅×D₃	—	2	8	no	—
200	C₂×C₅×D₃	C₂×D₈	1	4	yes	—
201	C₃×C₄×C₅	—	4	2	no	—
202	C₃×C₄×C₅	#123	1	2	yes	—
203	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
204	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
205	C₅×Dic₃	—	2	2	no	—
206	C₅×Dic₃	—	4	2	no	—
207	C₅×Dic₃	—	4	2	no	—
208	C₂⁴×C₃	—	2	1	no	—
209	C₂³×D₃	C₅×D₄	1	1	yes	characteristic
210	C₂×C₃×D₄	—	2	1	no	—
211	C₂×C₃×D₄	—	2	2	no	—
212	C₂×C₃×D₄	—	2	2	no	—
213	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
214	C₂²×C₃×C₄	—	2	1	no	—
215	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
216	C₂×#67	—	2	4	no	—
217	C₂×#67	—	4	4	no	—
218	C₂²×Dic₃	—	2	1	no	—
219	C₂²×Dic₃	—	2	1	no	—
220	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
221	C₂×C₄×D₃	—	2	2	no	—
222	C₂×C₄×D₃	—	2	2	no	—
223	C₂×C₄×D₃	—	2	4	no	—
224	C₂×C₄×D₃	—	4	4	no	—
225	C₂×C₄×D₃	C₅×D₄	1	2	yes	—
226	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
227	C₂×C₃×C₈	—	2	2	no	—
228	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
229	C₃×C₄⋊C₄	—	2	1	no	—
230	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
231	#217	—	2	4	no	—
232	C₄⋊Dic₃	—	2	1	no	—
233	C₄⋊Dic₃	—	2	1	no	—
234	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
235	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
236	Dic₃⋊C₄	—	2	4	no	—
237	C₂×C₃⋊C₈	—	2	2	no	—
238	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
239	C₂³×C₅	—	2	2	no	—
240	C₂³×C₅	—	3	4	no	—
241	C₂³×C₅	—	3	2	no	—
242	C₂³×C₅	—	4	2	no	—
243	C₂³×C₅	—	4	2	no	—
244	C₂³×C₅	—	4	2	no	—
245	C₂³×C₅	—	6	2	no	—
246	C₂³×C₅	—	6	2	no	—
247	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
248	C₅×D₄	—	2	2	no	—
249	C₅×D₄	—	2	2	no	—
250	C₅×D₄	—	4	2	no	—
251	C₅×D₄	—	12	8	no	—
252	C₂×C₄×C₅	—	2	2	no	—
253	C₂×C₄×C₅	—	3	2	no	—
254	C₂×C₄×C₅	—	4	2	no	—
255	C₂×C₄×C₅	—	6	2	no	—
256	C₂×C₄×C₅	—	6	4	no	—
257	C₂×C₄×C₅	—	6	2	no	—
258	C₂×C₄×C₅	—	6	2	no	—
259	C₂×C₄×C₅	—	6	2	no	—
260	C₂×C₄×C₅	—	6	2	no	—
261	C₂×C₄×C₅	—	12	8	no	—
262	C₂×C₄×C₅	—	12	2	no	—
263	C₂×C₄×C₅	—	12	2	no	—
264	C₂×C₄×C₅	#235	1	2	yes	—
265	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
266	C₂×C₄×C₅	#237	1	2	yes	—
267	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
268	C₅×C₈	—	2	2	no	—
269	C₅×C₈	—	6	2	no	—
270	C₂²×D₄	—	6	1	no	—
271	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
272	C₂³×C₄	—	3	1	no	—
273	C₂³×C₄	—	6	1	no	—
274	C₂²×C₈	—	3	1	no	—
275	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
276	#121	—	3	4	no	—
277	#121	—	6	2	no	—
278	C₂×C₄⋊C₄	—	3	1	no	—
279	C₂×C₄⋊C₄	—	3	1	no	—
280	C₂×C₄⋊C₄	—	3	4	no	—
281	C₂×C₄⋊C₄	—	6	2	no	—
282	C₂×C₄⋊C₄	—	6	1	no	—
283	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
284	C₂×C₂²⋊C₄	—	6	1	no	—
285	#107	—	3	4	no	—
286	#107	—	3	4	no	—
287	#102	—	3	4	no	—
288	#102	C₂×C₅×D₃	1	4	yes	complemented
289	C₂²⋊C₈	—	3	4	no	—
290	C₂×C₃×C₅	—	8	2	no	—
291	C₂×C₃×C₅	#480	1	4	yes	complemented
292	C₂×C₃×C₅	C₂×#123	1	1	yes	characteristic
293	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
294	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
295	C₅×D₃	—	2	4	no	—
296	C₂³×C₃	—	2	2	no	—
297	C₂³×C₃	—	4	2	no	—
298	C₂³×C₃	—	4	2	no	—
299	C₂³×C₃	—	4	2	no	—
300	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
301	C₂²×D₃	—	2	2	no	—
302	C₂²×D₃	—	2	2	no	—
303	C₂²×D₃	C₅×D₈	1	4	yes	—
304	C₂²×D₃	C₂×C₅×D₄	1	2	yes	—
305	C₃×D₄	—	2	2	no	—
306	C₃×D₄	—	2	2	no	—
307	C₃×D₄	—	4	2	no	—
308	C₂×C₃×C₄	—	2	2	no	—
309	C₂×C₃×C₄	—	4	2	no	—
310	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
311	C₂×C₃×C₄	C₅×#41	1	2	yes	—
312	C₂×C₃×C₄	C₅×#41	1	2	yes	—
313	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
314	#67	—	4	8	no	—
315	C₂×Dic₃	—	2	2	no	—
316	C₂×Dic₃	—	2	2	no	—
317	C₂×Dic₃	—	2	2	no	—
318	C₂×Dic₃	—	4	2	no	—
319	C₂×Dic₃	—	4	2	no	—
320	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
321	C₄×D₃	—	2	4	no	—
322	C₄×D₃	—	2	2	no	—
323	C₄×D₃	—	2	2	no	—
324	C₄×D₃	—	4	8	no	—
325	C₃×C₈	—	2	2	no	—
326	C₃⋊C₈	—	2	2	no	—
327	C₂²×C₅	—	3	4	no	—
328	C₂²×C₅	—	4	2	no	—
329	C₂²×C₅	—	4	2	no	—
330	C₂²×C₅	—	4	2	no	—
331	C₂²×C₅	—	6	2	no	—
332	C₂²×C₅	—	6	2	no	—
333	C₂²×C₅	—	6	8	no	—
334	C₂²×C₅	—	8	4	no	—
335	C₂²×C₅	#883	1	2	yes	—
336	C₂²×C₅	D₃×D₈	1	2	yes	—
337	C₂²×C₅	#915	1	2	yes	—
338	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
339	C₄×C₅	—	4	2	no	—
340	C₄×C₅	—	6	2	no	—
341	C₄×C₅	—	12	2	no	—
342	C₄×C₅	—	12	2	no	—
343	C₄×C₅	#883	1	2	yes	—
344	C₄×C₅	C₂×#235	1	1	yes	characteristic
345	C₄×C₅	C₂×#237	1	1	yes	characteristic
346	C₂⁴	—	2	1	no	—
347	C₂⁴	—	3	1	no	—
348	C₂×D₄	—	2	2	no	—
349	C₂×D₄	—	2	1	no	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	—	6	4	no	—
352	C₂×D₄	—	12	4	no	—
353	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	3	1	no	—
356	C₂²×C₄	—	3	2	no	—
357	C₂²×C₄	—	3	2	no	—
358	C₂²×C₄	—	6	4	no	—
359	C₂²×C₄	—	6	2	no	—
360	C₂²×C₄	—	6	2	no	—
361	C₂²×C₄	—	6	1	no	—
362	C₂²×C₄	—	6	1	no	—
363	C₂²×C₄	—	12	4	no	—
364	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	3	2	no	—
367	C₂×C₈	—	6	2	no	—
368	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	3	2	no	—
371	C₄⋊C₄	—	3	2	no	—
372	C₄⋊C₄	—	6	4	no	—
373	C₄⋊C₄	—	6	1	no	—
374	C₄⋊C₄	—	6	1	no	—
375	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
376	C₂²⋊C₄	—	6	4	no	—
377	C₃×C₅	C₂×#480	1	1	yes	characteristic, complemented, Hall
378	C₂²×C₃	—	4	2	no	—
379	C₂²×C₃	—	4	2	no	—
380	C₂²×C₃	—	4	2	no	—
381	C₂²×C₃	—	8	4	no	—
382	C₂²×C₃	C₅×#123	1	2	yes	—
383	C₂²×C₃	C₂×C₅×D₈	1	2	yes	—
384	C₂²×C₃	C₅×#137	1	2	yes	—
385	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
386	C₂×D₃	—	2	8	no	—
387	C₂×D₃	—	2	2	no	—
388	C₂×D₃	—	2	2	no	—
389	C₂×D₃	C₂×C₅×D₈	1	4	yes	—
390	C₃×C₄	—	4	2	no	—
391	C₃×C₄	C₅×#123	1	2	yes	—
392	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
393	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
394	Dic₃	—	2	2	no	—
395	Dic₃	—	4	2	no	—
396	Dic₃	—	4	2	no	—
397	C₂×C₅	—	6	4	no	—
398	C₂×C₅	—	8	2	no	—
399	C₂×C₅	#4774	1	4	yes	direct product factor
400	C₂×C₅	C₂×#883	1	1	yes	characteristic
401	C₂×C₅	C₂×D₃×D₈	1	1	yes	characteristic
402	C₂×C₅	C₂×#915	1	1	yes	characteristic
403	C₂³	—	2	2	no	—
404	C₂³	—	3	4	no	—
405	C₂³	—	3	2	no	—
406	C₂³	—	4	2	no	—
407	C₂³	—	4	2	no	—
408	C₂³	—	4	2	no	—
409	C₂³	—	6	2	no	—
410	C₂³	—	6	2	no	—
411	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
412	D₄	—	2	2	no	—
413	D₄	—	2	2	no	—
414	D₄	—	4	2	no	—
415	D₄	—	12	8	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	3	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	6	2	no	—
420	C₂×C₄	—	6	4	no	—
421	C₂×C₄	—	6	2	no	—
422	C₂×C₄	—	6	2	no	—
423	C₂×C₄	—	6	2	no	—
424	C₂×C₄	—	6	2	no	—
425	C₂×C₄	—	12	8	no	—
426	C₂×C₄	—	12	2	no	—
427	C₂×C₄	—	12	2	no	—
428	C₂×C₄	C₅×#235	1	2	yes	—
429	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
430	C₂×C₄	C₅×#237	1	2	yes	—
431	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
432	C₈	—	2	2	no	—
433	C₈	—	6	2	no	—
434	C₂×C₃	—	8	2	no	—
435	C₂×C₃	C₅×#480	1	4	yes	complemented
436	C₂×C₃	C₂×C₅×#123	1	1	yes	characteristic
437	C₂×C₃	C₂²×C₅×D₈	1	1	yes	characteristic
438	C₂×C₃	C₂×C₅×#137	1	1	yes	characteristic
439	D₃	—	2	4	no	—
440	C₅	C₂×#4774	1	1	yes	characteristic, direct product factor, Sylow
441	C₂²	—	3	4	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	4	2	no	—
444	C₂²	—	4	2	no	—
445	C₂²	—	6	2	no	—
446	C₂²	—	6	2	no	—
447	C₂²	—	6	8	no	—
448	C₂²	—	8	4	no	—
449	C₂²	C₅×#883	1	2	yes	—
450	C₂²	C₅×D₃×D₈	1	2	yes	—
451	C₂²	C₅×#915	1	2	yes	—
452	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
453	C₄	—	4	2	no	—
454	C₄	—	6	2	no	—
455	C₄	—	12	2	no	—
456	C₄	—	12	2	no	—
457	C₄	C₅×#883	1	2	yes	—
458	C₄	C₂×C₅×#235	1	1	yes	characteristic
459	C₄	C₂×C₅×#237	1	1	yes	characteristic
460	C₃	C₂×C₅×#480	1	1	yes	characteristic, complemented, Sylow
461	C₂	—	6	4	no	—
462	C₂	—	8	2	no	—
463	C₂	C₅×#4774	1	4	yes	direct product factor
464	C₂	C₂×C₅×#883	1	1	yes	characteristic
465	C₂	C₂×C₅×D₃×D₈	1	1	yes	characteristic
466	C₂	C₂×C₅×#915	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	C₂×C₃×C₅×#102	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂×C₅×#938	C₂
hypercenter	C₂×C₅×#102	D₃
hypocenter	C₃	C₂×C₅×#480
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×#102

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×D₃×C₄⋊C₄	C₂	semidirect
3. C₂×C₃×C₅×#102	C₂	semidirect
4. C₂×C₅×#832	C₂	semidirect
5. C₂×C₅×(C₂×D₃)⋊C₈	C₂	semidirect
6. C₂×C₅×#818	C₂	semidirect
7. C₂×C₅×#807	C₂	semidirect
8. C₅×#4774	C₂	direct (N × H)
24. C₅×D₃×C₄⋊C₄	C₂²	semidirect
25. C₃×C₅×#102	C₂²	semidirect
26. C₅×#832	C₂²	semidirect
27. C₅×(C₂×D₃)⋊C₈	C₂²	semidirect
28. C₅×#818	C₂²	semidirect
29. C₅×#807	C₂²	semidirect
30. C₂×#4774	C₅	direct (N × H)
37. C₂×C₅×#102	D₃	semidirect
71. C₂×D₃×C₄⋊C₄	C₂×C₅	semidirect
72. C₂×C₃×#102	C₂×C₅	semidirect
73. C₂×#832	C₂×C₅	semidirect
74. C₂×(C₂×D₃)⋊C₈	C₂×C₅	semidirect
75. C₂×#818	C₂×C₅	semidirect
76. C₂×#807	C₂×C₅	semidirect
77. #4774	C₂×C₅	direct (N × H)
96. C₅×#102	C₂×D₃	semidirect
144. D₃×C₄⋊C₄	C₂²×C₅	semidirect
145. C₃×#102	C₂²×C₅	semidirect
146. #832	C₂²×C₅	semidirect
147. (C₂×D₃)⋊C₈	C₂²×C₅	semidirect
148. #818	C₂²×C₅	semidirect
149. #807	C₂²×C₅	semidirect
187. C₂×#102	C₅×D₃	semidirect
288. #102	C₂×C₅×D₃	semidirect
291. C₂×C₃×C₅	#480	semidirect
377. C₃×C₅	C₂×#480	semidirect
399. C₂×C₅	#4774	direct (N × H)
435. C₂×C₃	C₅×#480	semidirect
440. C₅	C₂×#4774	direct (N × H)
460. C₃	C₂×C₅×#480	semidirect
463. C₂	C₅×#4774	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×#938	2
C₂×C₅×D₃×C₄⋊C₄	2
C₂×C₃×C₅×#102	2
C₂×C₅×#832	2
C₂×C₅×(C₂×D₃)⋊C₈	2
C₂×C₅×#818	2
C₂×C₅×#807	2
C₅×#4774	2
C₂×C₅×#480	3
C₂×#4774	5

Subgroups — C2×C5×#4774 #14431401

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#4774 #14431401