Subgroups — C₂×C₅×#4775 #14427681

Order 1920.

1232 conjugacy classes of subgroups.

The subgroup lattice has 528 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, complemented
2	C₂²×C₅×#213	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₅×D₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#895	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×C₅×#102	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×#821	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#807	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4775	C₂	1	8	yes	maximal, direct product factor
9	C₂×C₅×#466	—	3	1	no	maximal, Hall
10	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
11	C₂²×C₅×#67	—	2	1	no	—
12	C₂²×C₅×D₁₂	—	2	1	no	—
13	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
14	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂×C₅×#217	—	2	1	no	—
18	C₅×#938	—	2	2	no	—
19	C₅×#938	C₂²	1	4	yes	complemented
20	C₂×C₅×#213	—	2	4	no	—
21	C₂×C₅×#213	C₂²	1	4	yes	complemented
22	C₂×C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
23	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
24	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₅×D₃×C₈	—	2	4	no	—
26	C₂×C₅×D₃×C₈	C₂²	1	4	yes	complemented
27	C₅×#895	—	2	2	no	—
28	C₅×#895	C₂²	1	4	yes	complemented
29	C₃×C₅×#102	C₂²	1	4	yes	complemented
30	C₅×#821	C₂²	1	4	yes	complemented
31	C₅×#807	C₂²	1	4	yes	complemented
32	C₂×#4775	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
33	C₂²×C₅×D₈	—	3	1	no	—
34	C₂³×C₅×C₈	—	3	1	no	—
35	C₂×C₅×#121	—	3	1	no	—
36	C₂×C₅×#121	—	3	1	no	—
37	C₅×#466	—	3	8	no	—
38	C₂×C₅×#107	—	3	1	no	—
39	C₂×C₅×#102	—	3	1	no	—
40	C₂×C₅×#102	D₃	1	1	yes	characteristic, complemented
41	C₂⁴×C₃×C₅	—	2	1	no	—
42	C₂³×C₅×D₃	—	2	1	no	—
43	C₂³×C₅×D₃	D₄	1	1	yes	characteristic
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	C₂³	1	2	yes	—
48	C₂²×C₃×C₄×C₅	—	2	1	no	—
49	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
50	C₂×C₅×#67	—	2	4	no	—
51	C₂×C₅×#67	—	4	4	no	—
52	C₂²×C₅×Dic₃	—	2	1	no	—
53	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
54	C₂×C₅×D₁₂	—	2	2	no	—
55	C₂×C₅×D₁₂	—	2	2	no	—
56	C₂×C₅×D₁₂	—	2	4	no	—
57	C₂×C₅×D₁₂	—	2	1	no	—
58	C₂×C₅×D₁₂	—	4	4	no	—
59	C₂×C₅×D₁₂	C₂³	1	2	yes	—
60	C₂×C₄×C₅×D₃	—	2	2	no	—
61	C₂×C₄×C₅×D₃	—	2	2	no	—
62	C₂×C₄×C₅×D₃	D₄	1	2	yes	—
63	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
64	C₂×C₃×C₅×C₈	—	2	2	no	—
65	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
66	C₃×C₅×C₄⋊C₄	—	2	1	no	—
67	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
68	C₅×#217	—	2	4	no	—
69	C₅×#213	—	2	8	no	—
70	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
71	C₅×C₄⋊Dic₃	—	2	1	no	—
72	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
73	C₂×C₅×C₃⋊C₈	D₄	1	4	yes	complemented
74	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
75	C₅×D₃×C₈	—	2	8	no	—
76	C₂×#938	C₂×C₅	1	1	yes	characteristic, complemented
77	C₂²×#213	C₂×C₅	1	1	yes	characteristic, complemented
78	C₂²×D₃×C₈	C₂×C₅	1	1	yes	characteristic, complemented
79	C₂×#895	C₂×C₅	1	1	yes	characteristic, complemented
80	C₂×C₃×#102	C₂×C₅	1	1	yes	characteristic, complemented
81	C₂×#821	C₂×C₅	1	1	yes	characteristic, complemented
82	C₂×#807	C₂×C₅	1	1	yes	characteristic, complemented
83	#4775	C₂×C₅	1	8	yes	direct product factor
84	C₂²×C₅×D₄	—	3	1	no	—
85	C₂²×C₅×D₄	—	6	1	no	—
86	C₂²×C₅×D₄	—	6	1	no	—
87	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
88	C₂³×C₄×C₅	—	3	1	no	—
89	C₂×C₅×D₈	—	3	4	no	—
90	C₂×C₅×D₈	—	6	4	no	—
91	C₂²×C₅×C₈	—	3	1	no	—
92	C₂²×C₅×C₈	—	3	4	no	—
93	C₂²×C₅×C₈	—	6	4	no	—
94	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
95	C₅×#121	—	3	4	no	—
96	C₅×#121	—	3	4	no	—
97	C₅×#121	—	6	2	no	—
98	C₅×#121	—	6	2	no	—
99	C₂×C₅×C₄⋊C₄	—	3	1	no	—
100	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
101	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
102	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
103	C₅×#107	—	3	4	no	—
104	C₅×#102	—	3	4	no	—
105	C₅×#102	C₂×D₃	1	4	yes	complemented
106	C₂×#466	—	3	1	no	Sylow
107	C₂³×C₃×C₅	—	2	2	no	—
108	C₂³×C₃×C₅	—	4	2	no	—
109	C₂³×C₃×C₅	—	4	2	no	—
110	C₂³×C₃×C₅	—	4	2	no	—
111	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₅×D₃	—	2	2	no	—
113	C₂²×C₅×D₃	—	2	2	no	—
114	C₂²×C₅×D₃	—	2	2	no	—
115	C₂²×C₅×D₃	—	4	2	no	—
116	C₂²×C₅×D₃	—	4	2	no	—
117	C₂²×C₅×D₃	—	4	2	no	—
118	C₂²×C₅×D₃	D₈	1	4	yes	complemented
119	C₂²×C₅×D₃	C₂×D₄	1	2	yes	—
120	C₃×C₅×D₄	—	2	2	no	—
121	C₃×C₅×D₄	—	2	2	no	—
122	C₃×C₅×D₄	—	4	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	1	yes	characteristic
126	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
127	C₂×C₃×C₄×C₅	#41	1	2	yes	—
128	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
129	C₅×#67	—	4	8	no	—
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	C₂×D₄	1	2	yes	—
134	C₅×D₁₂	—	2	2	no	—
135	C₅×D₁₂	—	2	2	no	—
136	C₅×D₁₂	—	4	8	no	—
137	C₅×D₁₂	—	4	2	no	—
138	C₄×C₅×D₃	—	2	4	no	—
139	C₄×C₅×D₃	—	2	2	no	—
140	C₄×C₅×D₃	—	2	2	no	—
141	C₃×C₅×C₈	—	2	2	no	—
142	C₅×C₃⋊C₈	C₂×D₄	1	4	yes	complemented
143	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
144	C₂²×#67	—	2	1	no	—
145	C₂²×D₁₂	—	2	1	no	—
146	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
147	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
148	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
149	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
150	C₂×#217	—	2	1	no	—
151	#938	—	2	2	no	—
152	#938	C₂²×C₅	1	4	yes	complemented
153	C₂×#213	—	2	4	no	—
154	C₂×#213	C₂²×C₅	1	4	yes	complemented
155	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
156	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
157	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
158	C₂×D₃×C₈	—	2	4	no	—
159	C₂×D₃×C₈	C₂²×C₅	1	4	yes	complemented
160	#895	—	2	2	no	—
161	#895	C₂²×C₅	1	4	yes	complemented
162	C₃×#102	C₂²×C₅	1	4	yes	complemented
163	#821	C₂²×C₅	1	4	yes	complemented
164	#807	C₂²×C₅	1	4	yes	complemented
165	C₂⁴×C₅	—	2	1	no	—
166	C₂⁴×C₅	—	3	1	no	—
167	C₂⁴×C₅	—	6	1	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	—	3	2	no	—
172	C₂×C₅×D₄	—	6	4	no	—
173	C₂×C₅×D₄	—	6	4	no	—
174	C₂×C₅×D₄	—	6	2	no	—
175	C₂×C₅×D₄	—	6	2	no	—
176	C₂×C₅×D₄	—	6	1	no	—
177	C₂×C₅×D₄	—	12	4	no	—
178	C₂×C₅×D₄	—	12	4	no	—
179	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
180	C₂²×C₄×C₅	—	2	1	no	—
181	C₂²×C₄×C₅	—	3	1	no	—
182	C₂²×C₄×C₅	—	3	2	no	—
183	C₂²×C₄×C₅	—	3	2	no	—
184	C₂²×C₄×C₅	—	6	2	no	—
185	C₂²×C₄×C₅	—	6	2	no	—
186	C₂²×C₄×C₅	—	6	1	no	—
187	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
188	C₅×D₈	—	6	8	no	—
189	C₂×C₅×C₈	—	2	2	no	—
190	C₂×C₅×C₈	—	3	4	no	—
191	C₂×C₅×C₈	—	3	2	no	—
192	C₂×C₅×C₈	—	6	8	no	—
193	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
194	C₅×C₄⋊C₄	—	2	1	no	—
195	C₅×C₄⋊C₄	—	3	2	no	—
196	C₅×C₄⋊C₄	—	6	1	no	—
197	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
198	C₅×C₂²⋊C₄	—	6	4	no	—
199	C₅×C₂²⋊C₄	—	6	4	no	—
200	C₂²×D₈	—	3	1	no	—
201	C₂³×C₈	—	3	1	no	—
202	C₂×#121	—	3	1	no	—
203	C₂×#121	—	3	1	no	—
204	#466	—	3	8	no	—
205	C₂×#107	—	3	1	no	—
206	C₂×#102	—	3	1	no	—
207	C₂×#102	C₅×D₃	1	1	yes	characteristic, complemented
208	C₂²×C₃×C₅	—	4	2	no	—
209	C₂²×C₃×C₅	—	4	2	no	—
210	C₂²×C₃×C₅	—	4	2	no	—
211	C₂²×C₃×C₅	—	8	4	no	—
212	C₂²×C₃×C₅	#121	1	2	yes	—
213	C₂²×C₃×C₅	C₂×D₈	1	2	yes	—
214	C₂²×C₃×C₅	#135	1	2	yes	—
215	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
216	C₂×C₅×D₃	—	2	2	no	—
217	C₂×C₅×D₃	—	2	2	no	—
218	C₂×C₅×D₃	—	2	8	no	—
219	C₂×C₅×D₃	—	4	2	no	—
220	C₂×C₅×D₃	—	4	2	no	—
221	C₂×C₅×D₃	—	4	2	no	—
222	C₂×C₅×D₃	—	8	4	no	—
223	C₂×C₅×D₃	C₂×D₈	1	4	yes	complemented
224	C₃×C₄×C₅	—	4	2	no	—
225	C₃×C₄×C₅	#121	1	2	yes	—
226	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
227	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
228	C₅×Dic₃	—	2	2	no	—
229	C₅×Dic₃	—	4	2	no	—
230	C₂⁴×C₃	—	2	1	no	—
231	C₂³×D₃	—	2	1	no	—
232	C₂³×D₃	C₅×D₄	1	1	yes	characteristic
233	C₂×C₃×D₄	—	2	2	no	—
234	C₂×C₃×D₄	—	2	1	no	—
235	C₂×C₃×D₄	—	2	2	no	—
236	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
237	C₂²×C₃×C₄	—	2	1	no	—
238	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
239	C₂×#67	—	2	4	no	—
240	C₂×#67	—	4	4	no	—
241	C₂²×Dic₃	—	2	1	no	—
242	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
243	C₂×D₁₂	—	2	2	no	—
244	C₂×D₁₂	—	2	2	no	—
245	C₂×D₁₂	—	2	4	no	—
246	C₂×D₁₂	—	2	1	no	—
247	C₂×D₁₂	—	4	4	no	—
248	C₂×D₁₂	C₂³×C₅	1	2	yes	—
249	C₂×C₄×D₃	—	2	2	no	—
250	C₂×C₄×D₃	—	2	2	no	—
251	C₂×C₄×D₃	C₅×D₄	1	2	yes	—
252	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
253	C₂×C₃×C₈	—	2	2	no	—
254	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
255	C₃×C₄⋊C₄	—	2	1	no	—
256	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
257	#217	—	2	4	no	—
258	#213	—	2	8	no	—
259	(C₂×D₃)⋊C₄	—	2	4	no	—
260	C₄⋊Dic₃	—	2	1	no	—
261	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
262	C₂×C₃⋊C₈	C₅×D₄	1	4	yes	complemented
263	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
264	D₃×C₈	—	2	8	no	—
265	C₂³×C₅	—	2	2	no	—
266	C₂³×C₅	—	3	4	no	—
267	C₂³×C₅	—	3	2	no	—
268	C₂³×C₅	—	4	2	no	—
269	C₂³×C₅	—	4	2	no	—
270	C₂³×C₅	—	4	2	no	—
271	C₂³×C₅	—	6	2	no	—
272	C₂³×C₅	—	6	2	no	—
273	C₂³×C₅	—	6	2	no	—
274	C₂³×C₅	—	12	2	no	—
275	C₂³×C₅	—	12	2	no	—
276	C₂³×C₅	—	12	2	no	—
277	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
278	C₅×D₄	—	2	2	no	—
279	C₅×D₄	—	2	2	no	—
280	C₅×D₄	—	4	2	no	—
281	C₅×D₄	—	6	2	no	—
282	C₅×D₄	—	6	2	no	—
283	C₅×D₄	—	12	8	no	—
284	C₅×D₄	—	12	8	no	—
285	C₅×D₄	—	12	2	no	—
286	C₂×C₄×C₅	—	2	2	no	—
287	C₂×C₄×C₅	—	3	2	no	—
288	C₂×C₄×C₅	—	4	2	no	—
289	C₂×C₄×C₅	—	6	2	no	—
290	C₂×C₄×C₅	—	6	4	no	—
291	C₂×C₄×C₅	—	6	2	no	—
292	C₂×C₄×C₅	—	6	2	no	—
293	C₂×C₄×C₅	—	6	2	no	—
294	C₂×C₄×C₅	—	12	2	no	—
295	C₂×C₄×C₅	#235	1	2	yes	—
296	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
297	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
298	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
299	C₅×C₈	—	2	2	no	—
300	C₅×C₈	—	3	4	no	—
301	C₂²×D₄	—	3	1	no	—
302	C₂²×D₄	—	6	1	no	—
303	C₂²×D₄	—	6	1	no	—
304	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
305	C₂³×C₄	—	3	1	no	—
306	C₂×D₈	—	3	4	no	—
307	C₂×D₈	—	6	4	no	—
308	C₂²×C₈	—	3	1	no	—
309	C₂²×C₈	—	3	4	no	—
310	C₂²×C₈	—	6	4	no	—
311	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
312	#121	—	3	4	no	—
313	#121	—	3	4	no	—
314	#121	—	6	2	no	—
315	#121	—	6	2	no	—
316	C₂×C₄⋊C₄	—	3	1	no	—
317	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
318	C₂×C₂²⋊C₄	—	6	1	no	—
319	C₂×C₂²⋊C₄	—	6	1	no	—
320	#107	—	3	4	no	—
321	#102	—	3	4	no	—
322	#102	C₂×C₅×D₃	1	4	yes	complemented
323	C₂×C₃×C₅	—	8	2	no	—
324	C₂×C₃×C₅	#466	1	4	yes	complemented
325	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
326	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
327	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
328	C₅×D₃	—	2	4	no	—
329	C₅×D₃	—	8	2	no	—
330	C₂³×C₃	—	2	2	no	—
331	C₂³×C₃	—	4	2	no	—
332	C₂³×C₃	—	4	2	no	—
333	C₂³×C₃	—	4	2	no	—
334	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
335	C₂²×D₃	—	2	2	no	—
336	C₂²×D₃	—	2	2	no	—
337	C₂²×D₃	—	2	2	no	—
338	C₂²×D₃	—	4	2	no	—
339	C₂²×D₃	—	4	2	no	—
340	C₂²×D₃	—	4	2	no	—
341	C₂²×D₃	C₅×D₈	1	4	yes	complemented
342	C₂²×D₃	C₂×C₅×D₄	1	2	yes	—
343	C₃×D₄	—	2	2	no	—
344	C₃×D₄	—	2	2	no	—
345	C₃×D₄	—	4	2	no	—
346	C₂×C₃×C₄	—	2	2	no	—
347	C₂×C₃×C₄	—	4	2	no	—
348	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
349	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
350	C₂×C₃×C₄	C₅×#41	1	2	yes	—
351	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
352	#67	—	4	8	no	—
353	C₂×Dic₃	—	2	2	no	—
354	C₂×Dic₃	—	2	2	no	—
355	C₂×Dic₃	—	4	2	no	—
356	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
357	D₁₂	—	2	2	no	—
358	D₁₂	—	2	2	no	—
359	D₁₂	—	4	8	no	—
360	D₁₂	—	4	2	no	—
361	C₄×D₃	—	2	4	no	—
362	C₄×D₃	—	2	2	no	—
363	C₄×D₃	—	2	2	no	—
364	C₃×C₈	—	2	2	no	—
365	C₃⋊C₈	C₂×C₅×D₄	1	4	yes	complemented
366	C₂²×C₅	—	3	4	no	—
367	C₂²×C₅	—	4	2	no	—
368	C₂²×C₅	—	4	2	no	—
369	C₂²×C₅	—	4	2	no	—
370	C₂²×C₅	—	6	2	no	—
371	C₂²×C₅	—	6	2	no	—
372	C₂²×C₅	—	6	8	no	—
373	C₂²×C₅	—	8	4	no	—
374	C₂²×C₅	—	12	2	no	—
375	C₂²×C₅	—	12	2	no	—
376	C₂²×C₅	—	12	2	no	—
377	C₂²×C₅	—	24	4	no	—
378	C₂²×C₅	#884	1	2	yes	—
379	C₂²×C₅	D₃×D₈	1	2	yes	—
380	C₂²×C₅	#916	1	2	yes	—
381	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
382	C₄×C₅	—	4	2	no	—
383	C₄×C₅	—	6	2	no	—
384	C₄×C₅	—	12	2	no	—
385	C₄×C₅	#884	1	2	yes	—
386	C₄×C₅	C₂×#235	1	1	yes	characteristic
387	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
388	C₂⁴	—	2	1	no	—
389	C₂⁴	—	3	1	no	—
390	C₂⁴	—	6	1	no	—
391	C₂×D₄	—	2	2	no	—
392	C₂×D₄	—	2	2	no	—
393	C₂×D₄	—	2	1	no	—
394	C₂×D₄	—	3	2	no	—
395	C₂×D₄	—	6	4	no	—
396	C₂×D₄	—	6	4	no	—
397	C₂×D₄	—	6	2	no	—
398	C₂×D₄	—	6	2	no	—
399	C₂×D₄	—	6	1	no	—
400	C₂×D₄	—	12	4	no	—
401	C₂×D₄	—	12	4	no	—
402	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
403	C₂²×C₄	—	2	1	no	—
404	C₂²×C₄	—	3	1	no	—
405	C₂²×C₄	—	3	2	no	—
406	C₂²×C₄	—	3	2	no	—
407	C₂²×C₄	—	6	2	no	—
408	C₂²×C₄	—	6	2	no	—
409	C₂²×C₄	—	6	1	no	—
410	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
411	D₈	—	6	8	no	—
412	C₂×C₈	—	2	2	no	—
413	C₂×C₈	—	3	4	no	—
414	C₂×C₈	—	3	2	no	—
415	C₂×C₈	—	6	8	no	—
416	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
417	C₄⋊C₄	—	2	1	no	—
418	C₄⋊C₄	—	3	2	no	—
419	C₄⋊C₄	—	6	1	no	—
420	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
421	C₂²⋊C₄	—	6	4	no	—
422	C₂²⋊C₄	—	6	4	no	—
423	C₃×C₅	C₂×#466	1	1	yes	characteristic, complemented, Hall
424	C₂²×C₃	—	4	2	no	—
425	C₂²×C₃	—	4	2	no	—
426	C₂²×C₃	—	4	2	no	—
427	C₂²×C₃	—	8	4	no	—
428	C₂²×C₃	C₅×#121	1	2	yes	—
429	C₂²×C₃	C₂×C₅×D₈	1	2	yes	—
430	C₂²×C₃	C₅×#135	1	2	yes	—
431	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
432	C₂×D₃	—	2	8	no	—
433	C₂×D₃	—	2	2	no	—
434	C₂×D₃	—	2	2	no	—
435	C₂×D₃	—	4	2	no	—
436	C₂×D₃	—	4	2	no	—
437	C₂×D₃	—	4	2	no	—
438	C₂×D₃	—	8	4	no	—
439	C₂×D₃	C₂×C₅×D₈	1	4	yes	complemented
440	C₃×C₄	—	4	2	no	—
441	C₃×C₄	C₅×#121	1	2	yes	—
442	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
443	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
444	Dic₃	—	2	2	no	—
445	Dic₃	—	4	2	no	—
446	C₂×C₅	—	6	4	no	—
447	C₂×C₅	—	8	2	no	—
448	C₂×C₅	—	24	2	no	—
449	C₂×C₅	#4775	1	4	yes	direct product factor
450	C₂×C₅	C₂×#884	1	1	yes	characteristic
451	C₂×C₅	C₂×D₃×D₈	1	1	yes	characteristic
452	C₂×C₅	C₂×#916	1	1	yes	characteristic
453	C₂³	—	2	2	no	—
454	C₂³	—	3	4	no	—
455	C₂³	—	3	2	no	—
456	C₂³	—	4	2	no	—
457	C₂³	—	4	2	no	—
458	C₂³	—	4	2	no	—
459	C₂³	—	6	2	no	—
460	C₂³	—	6	2	no	—
461	C₂³	—	6	2	no	—
462	C₂³	—	12	2	no	—
463	C₂³	—	12	2	no	—
464	C₂³	—	12	2	no	—
465	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
466	D₄	—	2	2	no	—
467	D₄	—	2	2	no	—
468	D₄	—	4	2	no	—
469	D₄	—	6	2	no	—
470	D₄	—	6	2	no	—
471	D₄	—	12	8	no	—
472	D₄	—	12	8	no	—
473	D₄	—	12	2	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	3	2	no	—
476	C₂×C₄	—	4	2	no	—
477	C₂×C₄	—	6	2	no	—
478	C₂×C₄	—	6	4	no	—
479	C₂×C₄	—	6	2	no	—
480	C₂×C₄	—	6	2	no	—
481	C₂×C₄	—	6	2	no	—
482	C₂×C₄	—	12	2	no	—
483	C₂×C₄	C₅×#235	1	2	yes	—
484	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
485	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
486	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
487	C₈	—	2	2	no	—
488	C₈	—	3	4	no	—
489	C₂×C₃	—	8	2	no	—
490	C₂×C₃	C₅×#466	1	4	yes	complemented
491	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
492	C₂×C₃	C₂²×C₅×D₈	1	1	yes	characteristic
493	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
494	D₃	—	2	4	no	—
495	D₃	—	8	2	no	—
496	C₅	C₂×#4775	1	1	yes	characteristic, direct product factor, Sylow
497	C₂²	—	3	4	no	—
498	C₂²	—	4	2	no	—
499	C₂²	—	4	2	no	—
500	C₂²	—	4	2	no	—
501	C₂²	—	6	2	no	—
502	C₂²	—	6	2	no	—
503	C₂²	—	6	8	no	—
504	C₂²	—	8	4	no	—
505	C₂²	—	12	2	no	—
506	C₂²	—	12	2	no	—
507	C₂²	—	12	2	no	—
508	C₂²	—	24	4	no	—
509	C₂²	C₅×#884	1	2	yes	—
510	C₂²	C₅×D₃×D₈	1	2	yes	—
511	C₂²	C₅×#916	1	2	yes	—
512	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
513	C₄	—	4	2	no	—
514	C₄	—	6	2	no	—
515	C₄	—	12	2	no	—
516	C₄	C₅×#884	1	2	yes	—
517	C₄	C₂×C₅×#235	1	1	yes	characteristic
518	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
519	C₃	C₂×C₅×#466	1	1	yes	characteristic, complemented, Sylow
520	C₂	—	6	4	no	—
521	C₂	—	8	2	no	—
522	C₂	—	24	2	no	—
523	C₂	C₅×#4775	1	4	yes	direct product factor
524	C₂	C₂×C₅×#884	1	1	yes	characteristic
525	C₂	C₂×C₅×D₃×D₈	1	1	yes	characteristic
526	C₂	C₂×C₅×#916	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
hypercenter	C₂×C₅×#102	D₃
hypocenter	C₃	C₂×C₅×#466
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
1. C₂×C₅×#938	C₂	semidirect
2. C₂²×C₅×#213	C₂	semidirect
3. C₂²×C₅×D₃×C₈	C₂	semidirect
4. C₂×C₅×#895	C₂	semidirect
5. C₂×C₃×C₅×#102	C₂	semidirect
6. C₂×C₅×#821	C₂	semidirect
7. C₂×C₅×#807	C₂	semidirect
8. C₅×#4775	C₂	direct (N × H)
19. C₅×#938	C₂²	semidirect
21. C₂×C₅×#213	C₂²	semidirect
26. C₂×C₅×D₃×C₈	C₂²	semidirect
28. C₅×#895	C₂²	semidirect
29. C₃×C₅×#102	C₂²	semidirect
30. C₅×#821	C₂²	semidirect
31. C₅×#807	C₂²	semidirect
32. C₂×#4775	C₅	direct (N × H)
40. C₂×C₅×#102	D₃	semidirect
73. C₂×C₅×C₃⋊C₈	D₄	semidirect
76. C₂×#938	C₂×C₅	semidirect
77. C₂²×#213	C₂×C₅	semidirect
78. C₂²×D₃×C₈	C₂×C₅	semidirect
79. C₂×#895	C₂×C₅	semidirect
80. C₂×C₃×#102	C₂×C₅	semidirect
81. C₂×#821	C₂×C₅	semidirect
82. C₂×#807	C₂×C₅	semidirect
83. #4775	C₂×C₅	direct (N × H)
105. C₅×#102	C₂×D₃	semidirect
118. C₂²×C₅×D₃	D₈	semidirect
142. C₅×C₃⋊C₈	C₂×D₄	semidirect
152. #938	C₂²×C₅	semidirect
154. C₂×#213	C₂²×C₅	semidirect
159. C₂×D₃×C₈	C₂²×C₅	semidirect
161. #895	C₂²×C₅	semidirect
162. C₃×#102	C₂²×C₅	semidirect
163. #821	C₂²×C₅	semidirect
164. #807	C₂²×C₅	semidirect
207. C₂×#102	C₅×D₃	semidirect
223. C₂×C₅×D₃	C₂×D₈	semidirect
262. C₂×C₃⋊C₈	C₅×D₄	semidirect
322. #102	C₂×C₅×D₃	semidirect
324. C₂×C₃×C₅	#466	semidirect
341. C₂²×D₃	C₅×D₈	semidirect
365. C₃⋊C₈	C₂×C₅×D₄	semidirect
423. C₃×C₅	C₂×#466	semidirect
439. C₂×D₃	C₂×C₅×D₈	semidirect
449. C₂×C₅	#4775	direct (N × H)
490. C₂×C₃	C₅×#466	semidirect
496. C₅	C₂×#4775	direct (N × H)
519. C₃	C₂×C₅×#466	semidirect
523. C₂	C₅×#4775	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
C₂²×C₅×#213	2
C₂²×C₅×D₃×C₈	2
C₂×C₅×#895	2
C₂×C₃×C₅×#102	2
C₂×C₅×#821	2
C₂×C₅×#807	2
C₅×#4775	2
C₂×C₅×#466	3
C₂×#4775	5

Subgroups — C2×C5×#4775 #14427681

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#4775 #14427681