Subgroups — C₂×C₅×#5824 #14482673

Order 1920.

3264 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×#237	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5824	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₅×#946	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#944	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×#939	C₂	1	2	yes	maximal, complemented
7	C₂×C₅×#935	C₂	1	2	yes	maximal, complemented
8	C₂×C₅×D₄×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×#929	C₂	1	2	yes	maximal, complemented
10	C₂×C₄×C₅×#67	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅×#924	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₅×Dic₃⋊C₄	C₂	1	2	yes	maximal, complemented
13	C₂×C₅×#547	—	3	1	no	maximal, Hall
14	C₂×C₃×C₅×#41	—	2	8	no	—
15	C₂×C₃×C₅×#41	C₂²	1	8	yes	complemented
16	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
17	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
18	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
19	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
20	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
21	C₂²×C₅×#67	C₂²	1	2	yes	—
22	C₂²×C₅×#67	C₂²	1	1	yes	characteristic
23	C₂³×C₅×Dic₃	C₂²	1	2	yes	—
24	C₂³×C₅×Dic₃	C₂²	1	2	yes	—
25	C₂×C₅×#237	—	2	8	no	—
26	C₂×C₅×#237	C₂²	1	8	yes	complemented
27	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
28	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
29	C₂×C₅×#217	C₂²	1	2	yes	—
30	C₂×C₅×#217	C₂²	1	1	yes	characteristic
31	C₂×C₅×#217	C₂²	1	2	yes	—
32	C₅×#946	C₂²	1	8	yes	complemented
33	C₅×#944	C₂²	1	8	yes	complemented
34	C₅×#939	C₂²	1	16	yes	complemented
35	C₅×#935	C₂²	1	16	yes	complemented
36	C₅×D₄×Dic₃	C₂²	1	8	yes	complemented
37	C₅×#929	C₂²	1	16	yes	complemented
38	C₄×C₅×#67	C₂²	1	8	yes	complemented
39	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
40	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
41	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
42	C₅×#924	C₂²	1	8	yes	complemented
43	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
44	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
45	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
46	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
47	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
48	C₂×C₅×Dic₃⋊C₄	C₂²	1	16	yes	complemented
49	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
50	C₂×#5824	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
51	C₂²×C₅×#41	—	3	1	no	—
52	C₂²×C₅×#41	D₃	1	1	yes	characteristic, complemented
53	C₅×#547	—	3	16	no	—
54	C₂×C₅×C₄⋊Q₈	—	3	1	no	—
55	C₂×C₅×#123	—	3	2	no	—
56	C₂×C₅×#123	—	3	2	no	—
57	C₂×C₅×C₂²⋊Q₈	—	3	1	no	—
58	C₂×C₅×C₂²⋊Q₈	—	3	1	no	—
59	C₂×C₅×#121	—	3	2	no	—
60	C₂×C₄×C₅×D₄	—	3	1	no	—
61	C₂×C₄×C₅×D₄	—	3	1	no	—
62	C₂²×C₅×C₄⋊C₄	—	3	2	no	—
63	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
64	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
65	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
66	C₃×C₅×#41	—	2	32	no	—
67	C₂×C₃×C₅×Q₈	—	2	4	no	—
68	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	—
69	C₂×C₃×C₅×D₄	—	2	8	no	—
70	C₂×C₃×C₅×D₄	D₄	1	8	yes	complemented
71	C₂×C₃×C₅×D₄	C₂³	1	8	yes	—
72	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
73	C₂²×C₃×C₄×C₅	—	2	8	no	—
74	C₂²×C₃×C₄×C₅	—	2	4	no	—
75	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
76	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
77	C₂²×C₃×C₄×C₅	C₂³	1	8	yes	—
78	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
79	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
80	C₂×C₅×#67	—	2	8	no	—
81	C₂×C₅×#67	—	2	4	no	—
82	C₂×C₅×#67	C₂³	1	4	yes	—
83	C₂×C₅×#67	C₂³	1	8	yes	—
84	C₂²×C₅×Dic₃	—	2	8	no	—
85	C₂²×C₅×Dic₃	—	2	8	no	—
86	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
87	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
88	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
89	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
90	C₂²×C₅×Dic₃	C₂³	1	8	yes	—
91	C₂²×C₅×Dic₃	C₂³	1	8	yes	—
92	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
93	C₅×#237	—	2	32	no	—
94	C₂×C₄×C₅×D₃	—	2	4	no	—
95	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
96	C₂×C₅×Dic₆	—	2	4	no	—
97	C₂×C₅×Dic₆	C₂³	1	4	yes	—
98	C₅×#217	C₂³	1	8	yes	—
99	C₅×#217	C₂³	1	4	yes	—
100	C₅×#217	C₂³	1	8	yes	—
101	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
102	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
103	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
104	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
105	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
106	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
107	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
108	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
109	C₄×C₅×Dic₃	C₂³	1	4	yes	—
110	C₂²×C₃×#41	C₂×C₅	1	1	yes	characteristic, complemented
111	C₂²×#237	C₂×C₅	1	1	yes	characteristic, complemented
112	#5824	C₂×C₅	1	16	yes	direct product factor
113	C₂×#946	C₂×C₅	1	1	yes	characteristic, complemented
114	C₂×#944	C₂×C₅	1	1	yes	characteristic, complemented
115	C₂×#939	C₂×C₅	1	2	yes	complemented
116	C₂×#935	C₂×C₅	1	2	yes	complemented
117	C₂×D₄×Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
118	C₂×#929	C₂×C₅	1	2	yes	complemented
119	C₂×C₄×#67	C₂×C₅	1	1	yes	characteristic, complemented
120	C₂×#924	C₂×C₅	1	1	yes	characteristic, complemented
121	C₂²×Dic₃⋊C₄	C₂×C₅	1	2	yes	complemented
122	C₂×C₅×#41	—	2	8	no	—
123	C₂×C₅×#41	—	3	8	no	—
124	C₂×C₅×#41	—	6	8	no	—
125	C₂×C₅×#41	C₂×D₃	1	8	yes	complemented
126	C₂²×C₅×Q₈	—	3	1	no	—
127	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
128	C₂²×C₅×D₄	—	3	1	no	—
129	C₂²×C₅×D₄	—	3	2	no	—
130	C₂²×C₅×D₄	C₂×D₃	1	2	yes	—
131	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
132	C₂³×C₄×C₅	—	3	2	no	—
133	C₂³×C₄×C₅	—	3	2	no	—
134	C₂³×C₄×C₅	—	3	1	no	—
135	C₂³×C₄×C₅	C₂×D₃	1	2	yes	—
136	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
137	C₅×C₄⋊Q₈	—	3	8	no	—
138	C₅×#123	—	3	16	no	—
139	C₅×#123	—	3	16	no	—
140	C₅×C₂²⋊Q₈	—	3	8	no	—
141	C₅×C₂²⋊Q₈	—	3	8	no	—
142	C₅×#121	—	3	16	no	—
143	C₄×C₅×D₄	—	3	8	no	—
144	C₄×C₅×D₄	—	3	8	no	—
145	C₂×C₅×C₄⋊C₄	—	3	1	no	—
146	C₂×C₅×C₄⋊C₄	—	3	2	no	—
147	C₂×C₅×C₄⋊C₄	—	3	2	no	—
148	C₂×C₅×C₄⋊C₄	—	3	2	no	—
149	C₂×C₅×C₄⋊C₄	—	3	2	no	—
150	C₂×C₅×C₄⋊C₄	—	3	16	no	—
151	C₂×C₅×C₄⋊C₄	—	3	1	no	—
152	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
153	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
154	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
155	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
156	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
157	C₂×C₄²×C₅	—	3	1	no	—
158	C₂×#547	—	3	1	no	Sylow
159	C₂³×C₃×C₅	—	2	4	no	—
160	C₂³×C₃×C₅	—	2	4	no	—
161	C₂³×C₃×C₅	—	2	2	no	—
162	C₂³×C₃×C₅	—	2	2	no	—
163	C₂³×C₃×C₅	—	2	2	no	—
164	C₂³×C₃×C₅	C₂×D₄	1	8	yes	—
165	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
166	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
167	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
168	C₂²×C₅×D₃	—	2	2	no	—
169	C₂²×C₅×D₃	—	2	2	no	—
170	C₂²×C₅×D₃	—	2	2	no	—
171	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
172	C₃×C₅×Q₈	—	2	8	no	—
173	C₃×C₅×D₄	—	2	16	no	—
174	C₃×C₅×D₄	C₂×D₄	1	16	yes	complemented
175	C₂×C₃×C₄×C₅	—	2	2	no	—
176	C₂×C₃×C₄×C₅	—	2	4	no	—
177	C₂×C₃×C₄×C₅	—	2	16	no	—
178	C₂×C₃×C₄×C₅	—	2	8	no	—
179	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
180	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
181	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
182	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
183	C₅×#67	—	2	16	no	—
184	C₅×#67	—	2	8	no	—
185	C₂×C₅×Dic₃	—	2	4	no	—
186	C₂×C₅×Dic₃	—	2	2	no	—
187	C₂×C₅×Dic₃	—	2	16	no	—
188	C₂×C₅×Dic₃	—	2	4	no	—
189	C₂×C₅×Dic₃	—	2	2	no	—
190	C₂×C₅×Dic₃	—	2	16	no	—
191	C₂×C₅×Dic₃	#41	1	4	yes	complemented
192	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
193	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
194	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
195	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
196	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
197	C₄×C₅×D₃	—	2	8	no	—
198	C₅×Dic₆	—	2	8	no	—
199	C₂×C₃×#41	—	2	8	no	—
200	C₂×C₃×#41	C₂²×C₅	1	8	yes	complemented
201	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
202	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
203	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
204	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
205	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
206	C₂²×#67	C₂²×C₅	1	2	yes	—
207	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
208	C₂³×Dic₃	C₂²×C₅	1	2	yes	—
209	C₂³×Dic₃	C₂²×C₅	1	2	yes	—
210	C₂×#237	—	2	8	no	—
211	C₂×#237	C₂²×C₅	1	8	yes	complemented
212	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
213	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
214	C₂×#217	C₂²×C₅	1	2	yes	—
215	C₂×#217	C₂²×C₅	1	1	yes	characteristic
216	C₂×#217	C₂²×C₅	1	2	yes	—
217	#946	C₂²×C₅	1	8	yes	complemented
218	#944	C₂²×C₅	1	8	yes	complemented
219	#939	C₂²×C₅	1	16	yes	complemented
220	#935	C₂²×C₅	1	16	yes	complemented
221	D₄×Dic₃	C₂²×C₅	1	8	yes	complemented
222	#929	C₂²×C₅	1	16	yes	complemented
223	C₄×#67	C₂²×C₅	1	8	yes	complemented
224	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
225	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
226	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
227	#924	C₂²×C₅	1	8	yes	complemented
228	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
229	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
230	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
231	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
232	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
233	C₂×Dic₃⋊C₄	C₂²×C₅	1	16	yes	complemented
234	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
235	C₂⁴×C₅	—	3	1	no	—
236	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
237	C₂⁴×C₅	C₂²×D₃	1	2	yes	—
238	C₅×#41	—	2	32	no	—
239	C₅×#41	—	6	32	no	—
240	C₂×C₅×Q₈	—	2	4	no	—
241	C₂×C₅×Q₈	—	3	4	no	—
242	C₂×C₅×Q₈	—	6	4	no	—
243	C₂×C₅×Q₈	C₂²×D₃	1	4	yes	—
244	C₂×C₅×D₄	—	2	8	no	—
245	C₂×C₅×D₄	—	3	4	no	—
246	C₂×C₅×D₄	—	3	8	no	—
247	C₂×C₅×D₄	—	6	4	no	—
248	C₂×C₅×D₄	—	6	8	no	—
249	C₂×C₅×D₄	#67	1	8	yes	complemented
250	C₂×C₅×D₄	C₂²×D₃	1	8	yes	—
251	C₂×C₅×D₄	C₂²×D₃	1	4	yes	—
252	C₂²×C₄×C₅	—	2	8	no	—
253	C₂²×C₄×C₅	—	2	4	no	—
254	C₂²×C₄×C₅	—	3	1	no	—
255	C₂²×C₄×C₅	—	3	8	no	—
256	C₂²×C₄×C₅	—	3	8	no	—
257	C₂²×C₄×C₅	—	3	1	no	—
258	C₂²×C₄×C₅	—	3	2	no	—
259	C₂²×C₄×C₅	—	3	1	no	—
260	C₂²×C₄×C₅	—	3	2	no	—
261	C₂²×C₄×C₅	—	3	4	no	—
262	C₂²×C₄×C₅	—	6	8	no	—
263	C₂²×C₄×C₅	—	6	8	no	—
264	C₂²×C₄×C₅	—	6	4	no	—
265	C₂²×C₄×C₅	C₂²×D₃	1	8	yes	—
266	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
267	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
268	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
269	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
270	C₅×C₄⋊C₄	—	3	4	no	—
271	C₅×C₄⋊C₄	—	3	8	no	—
272	C₅×C₄⋊C₄	—	3	8	no	—
273	C₅×C₄⋊C₄	—	3	8	no	—
274	C₅×C₄⋊C₄	—	3	4	no	—
275	C₅×C₄⋊C₄	—	3	8	no	—
276	C₅×C₂²⋊C₄	—	3	8	no	—
277	C₅×C₂²⋊C₄	—	3	4	no	—
278	C₅×C₂²⋊C₄	—	3	8	no	—
279	C₅×C₂²⋊C₄	—	3	4	no	—
280	C₅×C₂²⋊C₄	—	3	8	no	—
281	C₄²×C₅	—	3	4	no	—
282	C₂²×#41	—	3	1	no	—
283	C₂²×#41	C₅×D₃	1	1	yes	characteristic, complemented
284	#547	—	3	16	no	—
285	C₂×C₄⋊Q₈	—	3	1	no	—
286	C₂×#123	—	3	2	no	—
287	C₂×#123	—	3	2	no	—
288	C₂×C₂²⋊Q₈	—	3	1	no	—
289	C₂×C₂²⋊Q₈	—	3	1	no	—
290	C₂×#121	—	3	2	no	—
291	C₂×C₄×D₄	—	3	1	no	—
292	C₂×C₄×D₄	—	3	1	no	—
293	C₂²×C₄⋊C₄	—	3	2	no	—
294	C₂²×C₃×C₅	—	2	16	no	—
295	C₂²×C₃×C₅	—	2	4	no	—
296	C₂²×C₃×C₅	—	2	4	no	—
297	C₂²×C₃×C₅	—	2	2	no	—
298	C₂²×C₃×C₅	—	2	2	no	—
299	C₂²×C₃×C₅	—	2	2	no	—
300	C₂²×C₃×C₅	—	4	4	no	—
301	C₂²×C₃×C₅	C₂²×D₄	1	8	yes	—
302	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
303	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
304	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
305	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
306	C₂×C₅×D₃	—	2	2	no	—
307	C₂×C₅×D₃	—	2	2	no	—
308	C₂×C₅×D₃	—	2	2	no	—
309	C₂×C₅×D₃	—	4	4	no	—
310	C₃×C₄×C₅	—	2	2	no	—
311	C₃×C₄×C₅	—	2	4	no	—
312	C₃×C₄×C₅	C₂²×D₄	1	4	yes	—
313	C₅×Dic₃	—	2	4	no	—
314	C₅×Dic₃	—	2	2	no	—
315	C₅×Dic₃	—	2	4	no	—
316	C₅×Dic₃	—	2	2	no	—
317	C₅×Dic₃	C₂×#41	1	4	yes	complemented
318	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
319	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
320	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
321	C₃×#41	—	2	32	no	—
322	C₂×C₃×Q₈	—	2	4	no	—
323	C₂×C₃×Q₈	C₂³×C₅	1	4	yes	—
324	C₂×C₃×D₄	—	2	8	no	—
325	C₂×C₃×D₄	C₅×D₄	1	8	yes	complemented
326	C₂×C₃×D₄	C₂³×C₅	1	8	yes	—
327	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
328	C₂²×C₃×C₄	—	2	8	no	—
329	C₂²×C₃×C₄	—	2	4	no	—
330	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
331	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
332	C₂²×C₃×C₄	C₂³×C₅	1	8	yes	—
333	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
334	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
335	C₂×#67	—	2	8	no	—
336	C₂×#67	—	2	4	no	—
337	C₂×#67	C₂³×C₅	1	4	yes	—
338	C₂×#67	C₂³×C₅	1	8	yes	—
339	C₂²×Dic₃	—	2	8	no	—
340	C₂²×Dic₃	—	2	8	no	—
341	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
342	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
343	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
344	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
345	C₂²×Dic₃	C₂³×C₅	1	8	yes	—
346	C₂²×Dic₃	C₂³×C₅	1	8	yes	—
347	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
348	#237	—	2	32	no	—
349	C₂×C₄×D₃	—	2	4	no	—
350	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
351	C₂×Dic₆	—	2	4	no	—
352	C₂×Dic₆	C₂³×C₅	1	4	yes	—
353	#217	C₂³×C₅	1	8	yes	—
354	#217	C₂³×C₅	1	4	yes	—
355	#217	C₂³×C₅	1	8	yes	—
356	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
357	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
358	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
359	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
360	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
361	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
362	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
363	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
364	C₄×Dic₃	C₂³×C₅	1	4	yes	—
365	C₂³×C₅	—	2	4	no	—
366	C₂³×C₅	—	2	4	no	—
367	C₂³×C₅	—	2	2	no	—
368	C₂³×C₅	—	2	2	no	—
369	C₂³×C₅	—	2	2	no	—
370	C₂³×C₅	—	3	2	no	—
371	C₂³×C₅	—	6	2	no	—
372	C₂³×C₅	—	6	2	no	—
373	C₂³×C₅	—	6	2	no	—
374	C₂³×C₅	C₂×#67	1	8	yes	—
375	C₂³×C₅	C₂³×D₃	1	2	yes	—
376	C₂³×C₅	C₂³×D₃	1	4	yes	—
377	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
378	C₅×Q₈	—	2	8	no	—
379	C₅×Q₈	—	6	8	no	—
380	C₅×D₄	—	2	16	no	—
381	C₅×D₄	—	6	8	no	—
382	C₅×D₄	—	6	16	no	—
383	C₅×D₄	C₂×#67	1	16	yes	complemented
384	C₂×C₄×C₅	—	2	2	no	—
385	C₂×C₄×C₅	—	2	4	no	—
386	C₂×C₄×C₅	—	2	16	no	—
387	C₂×C₄×C₅	—	2	8	no	—
388	C₂×C₄×C₅	—	3	4	no	—
389	C₂×C₄×C₅	—	3	2	no	—
390	C₂×C₄×C₅	—	3	2	no	—
391	C₂×C₄×C₅	—	3	4	no	—
392	C₂×C₄×C₅	—	3	2	no	—
393	C₂×C₄×C₅	—	3	4	no	—
394	C₂×C₄×C₅	—	6	16	no	—
395	C₂×C₄×C₅	—	6	4	no	—
396	C₂×C₄×C₅	—	6	2	no	—
397	C₂×C₄×C₅	—	6	2	no	—
398	C₂×C₄×C₅	—	6	4	no	—
399	C₂×C₄×C₅	—	6	16	no	—
400	C₂×C₄×C₅	—	6	8	no	—
401	C₂×C₄×C₅	C₂×#67	1	4	yes	—
402	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
403	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
404	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
405	C₂×#41	—	2	8	no	—
406	C₂×#41	—	3	8	no	—
407	C₂×#41	—	6	8	no	—
408	C₂×#41	C₂×C₅×D₃	1	8	yes	complemented
409	C₂²×Q₈	—	3	1	no	—
410	C₂²×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
411	C₂²×D₄	—	3	1	no	—
412	C₂²×D₄	—	3	2	no	—
413	C₂²×D₄	C₂×C₅×D₃	1	2	yes	—
414	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
415	C₂³×C₄	—	3	2	no	—
416	C₂³×C₄	—	3	2	no	—
417	C₂³×C₄	—	3	1	no	—
418	C₂³×C₄	C₂×C₅×D₃	1	2	yes	—
419	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
420	C₄⋊Q₈	—	3	8	no	—
421	#123	—	3	16	no	—
422	#123	—	3	16	no	—
423	C₂²⋊Q₈	—	3	8	no	—
424	C₂²⋊Q₈	—	3	8	no	—
425	#121	—	3	16	no	—
426	C₄×D₄	—	3	8	no	—
427	C₄×D₄	—	3	8	no	—
428	C₂×C₄⋊C₄	—	3	1	no	—
429	C₂×C₄⋊C₄	—	3	2	no	—
430	C₂×C₄⋊C₄	—	3	2	no	—
431	C₂×C₄⋊C₄	—	3	2	no	—
432	C₂×C₄⋊C₄	—	3	16	no	—
433	C₂×C₄⋊C₄	—	3	1	no	—
434	C₂×C₄⋊C₄	—	3	2	no	—
435	C₂×C₂²⋊C₄	—	3	2	no	—
436	C₂×C₂²⋊C₄	—	3	1	no	—
437	C₂×C₂²⋊C₄	—	3	2	no	—
438	C₂×C₂²⋊C₄	—	3	1	no	—
439	C₂×C₂²⋊C₄	—	3	2	no	—
440	C₂×C₄²	—	3	1	no	—
441	C₂×C₃×C₅	—	2	8	no	—
442	C₂×C₃×C₅	—	4	2	no	—
443	C₂×C₃×C₅	#547	1	4	yes	complemented
444	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
445	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
446	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
447	C₅×D₃	—	4	2	no	—
448	C₂³×C₃	—	2	4	no	—
449	C₂³×C₃	—	2	4	no	—
450	C₂³×C₃	—	2	2	no	—
451	C₂³×C₃	—	2	2	no	—
452	C₂³×C₃	—	2	2	no	—
453	C₂³×C₃	C₂×C₅×D₄	1	8	yes	—
454	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
455	C₂³×C₃	C₂⁴×C₅	1	4	yes	—
456	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
457	C₂²×D₃	—	2	2	no	—
458	C₂²×D₃	—	2	2	no	—
459	C₂²×D₃	—	2	2	no	—
460	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
461	C₃×Q₈	—	2	8	no	—
462	C₃×D₄	—	2	16	no	—
463	C₃×D₄	C₂×C₅×D₄	1	16	yes	complemented
464	C₂×C₃×C₄	—	2	2	no	—
465	C₂×C₃×C₄	—	2	4	no	—
466	C₂×C₃×C₄	—	2	16	no	—
467	C₂×C₃×C₄	—	2	8	no	—
468	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
469	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
470	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
471	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
472	#67	—	2	16	no	—
473	#67	—	2	8	no	—
474	C₂×Dic₃	—	2	4	no	—
475	C₂×Dic₃	—	2	2	no	—
476	C₂×Dic₃	—	2	16	no	—
477	C₂×Dic₃	—	2	4	no	—
478	C₂×Dic₃	—	2	2	no	—
479	C₂×Dic₃	—	2	16	no	—
480	C₂×Dic₃	C₅×#41	1	4	yes	complemented
481	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
482	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
483	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
484	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
485	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
486	C₄×D₃	—	2	8	no	—
487	Dic₆	—	2	8	no	—
488	C₂²×C₅	—	2	4	no	—
489	C₂²×C₅	—	2	4	no	—
490	C₂²×C₅	—	2	16	no	—
491	C₂²×C₅	—	2	2	no	—
492	C₂²×C₅	—	2	2	no	—
493	C₂²×C₅	—	2	2	no	—
494	C₂²×C₅	—	4	4	no	—
495	C₂²×C₅	—	6	2	no	—
496	C₂²×C₅	—	6	2	no	—
497	C₂²×C₅	—	6	2	no	—
498	C₂²×C₅	—	12	4	no	—
499	C₂²×C₅	D₃×#41	1	2	yes	—
500	C₂²×C₅	#1010	1	2	yes	—
501	C₂²×C₅	C₂²×#67	1	8	yes	—
502	C₂²×C₅	C₂²×#67	1	2	yes	—
503	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
504	C₄×C₅	—	2	2	no	—
505	C₄×C₅	—	2	4	no	—
506	C₄×C₅	—	3	4	no	—
507	C₄×C₅	—	6	4	no	—
508	C₄×C₅	—	6	2	no	—
509	C₄×C₅	—	6	2	no	—
510	C₄×C₅	—	6	4	no	—
511	C₄×C₅	C₂²×#67	1	4	yes	—
512	C₂⁴	—	3	1	no	—
513	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
514	C₂⁴	C₂²×C₅×D₃	1	2	yes	—
515	#41	—	2	32	no	—
516	#41	—	6	32	no	—
517	C₂×Q₈	—	2	4	no	—
518	C₂×Q₈	—	3	4	no	—
519	C₂×Q₈	—	6	4	no	—
520	C₂×Q₈	C₂²×C₅×D₃	1	4	yes	—
521	C₂×D₄	—	2	8	no	—
522	C₂×D₄	—	3	4	no	—
523	C₂×D₄	—	3	8	no	—
524	C₂×D₄	—	6	4	no	—
525	C₂×D₄	—	6	8	no	—
526	C₂×D₄	C₅×#67	1	8	yes	complemented
527	C₂×D₄	C₂²×C₅×D₃	1	8	yes	—
528	C₂×D₄	C₂²×C₅×D₃	1	4	yes	—
529	C₂²×C₄	—	2	8	no	—
530	C₂²×C₄	—	2	4	no	—
531	C₂²×C₄	—	3	1	no	—
532	C₂²×C₄	—	3	1	no	—
533	C₂²×C₄	—	3	2	no	—
534	C₂²×C₄	—	3	1	no	—
535	C₂²×C₄	—	3	2	no	—
536	C₂²×C₄	—	3	8	no	—
537	C₂²×C₄	—	3	8	no	—
538	C₂²×C₄	—	3	4	no	—
539	C₂²×C₄	—	6	8	no	—
540	C₂²×C₄	—	6	8	no	—
541	C₂²×C₄	—	6	4	no	—
542	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
543	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
544	C₂²×C₄	C₂²×C₅×D₃	1	8	yes	—
545	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
546	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
547	C₄⋊C₄	—	3	4	no	—
548	C₄⋊C₄	—	3	8	no	—
549	C₄⋊C₄	—	3	8	no	—
550	C₄⋊C₄	—	3	8	no	—
551	C₄⋊C₄	—	3	4	no	—
552	C₄⋊C₄	—	3	8	no	—
553	C₂²⋊C₄	—	3	8	no	—
554	C₂²⋊C₄	—	3	4	no	—
555	C₂²⋊C₄	—	3	8	no	—
556	C₂²⋊C₄	—	3	4	no	—
557	C₂²⋊C₄	—	3	8	no	—
558	C₄²	—	3	4	no	—
559	C₃×C₅	C₂×#547	1	1	yes	characteristic, complemented, Hall
560	C₂²×C₃	—	2	16	no	—
561	C₂²×C₃	—	2	4	no	—
562	C₂²×C₃	—	2	4	no	—
563	C₂²×C₃	—	2	2	no	—
564	C₂²×C₃	—	2	2	no	—
565	C₂²×C₃	—	2	2	no	—
566	C₂²×C₃	—	4	4	no	—
567	C₂²×C₃	C₂²×C₅×D₄	1	8	yes	—
568	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
569	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
570	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
571	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
572	C₂×D₃	—	2	2	no	—
573	C₂×D₃	—	2	2	no	—
574	C₂×D₃	—	2	2	no	—
575	C₂×D₃	—	4	4	no	—
576	C₃×C₄	—	2	2	no	—
577	C₃×C₄	—	2	4	no	—
578	C₃×C₄	C₂²×C₅×D₄	1	4	yes	—
579	Dic₃	—	2	4	no	—
580	Dic₃	—	2	2	no	—
581	Dic₃	—	2	4	no	—
582	Dic₃	—	2	2	no	—
583	Dic₃	C₂×C₅×#41	1	4	yes	complemented
584	C₂×C₅	—	2	8	no	—
585	C₂×C₅	—	4	2	no	—
586	C₂×C₅	—	12	2	no	—
587	C₂×C₅	#5824	1	4	yes	direct product factor
588	C₂×C₅	C₂×D₃×#41	1	1	yes	characteristic
589	C₂×C₅	C₂×#1010	1	1	yes	characteristic
590	C₂×C₅	C₂³×#67	1	1	yes	characteristic
591	C₂³	—	2	4	no	—
592	C₂³	—	2	4	no	—
593	C₂³	—	2	2	no	—
594	C₂³	—	2	2	no	—
595	C₂³	—	2	2	no	—
596	C₂³	—	3	2	no	—
597	C₂³	—	6	2	no	—
598	C₂³	—	6	2	no	—
599	C₂³	—	6	2	no	—
600	C₂³	C₂×C₅×#67	1	8	yes	—
601	C₂³	C₂³×C₅×D₃	1	2	yes	—
602	C₂³	C₂³×C₅×D₃	1	4	yes	—
603	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
604	Q₈	—	2	8	no	—
605	Q₈	—	6	8	no	—
606	D₄	—	2	16	no	—
607	D₄	—	6	8	no	—
608	D₄	—	6	16	no	—
609	D₄	C₂×C₅×#67	1	16	yes	complemented
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	2	4	no	—
612	C₂×C₄	—	2	16	no	—
613	C₂×C₄	—	2	8	no	—
614	C₂×C₄	—	3	4	no	—
615	C₂×C₄	—	3	2	no	—
616	C₂×C₄	—	3	2	no	—
617	C₂×C₄	—	3	4	no	—
618	C₂×C₄	—	3	2	no	—
619	C₂×C₄	—	3	4	no	—
620	C₂×C₄	—	6	16	no	—
621	C₂×C₄	—	6	4	no	—
622	C₂×C₄	—	6	2	no	—
623	C₂×C₄	—	6	2	no	—
624	C₂×C₄	—	6	4	no	—
625	C₂×C₄	—	6	16	no	—
626	C₂×C₄	—	6	8	no	—
627	C₂×C₄	C₂×C₅×#67	1	4	yes	—
628	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
629	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
630	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
631	C₂×C₃	—	2	8	no	—
632	C₂×C₃	—	4	2	no	—
633	C₂×C₃	C₅×#547	1	4	yes	complemented
634	C₂×C₃	C₂³×C₅×D₄	1	1	yes	characteristic
635	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
636	C₂×C₃	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
637	D₃	—	4	2	no	—
638	C₅	C₂×#5824	1	1	yes	characteristic, direct product factor, Sylow
639	C₂²	—	2	4	no	—
640	C₂²	—	2	4	no	—
641	C₂²	—	2	16	no	—
642	C₂²	—	2	2	no	—
643	C₂²	—	2	2	no	—
644	C₂²	—	2	2	no	—
645	C₂²	—	4	4	no	—
646	C₂²	—	6	2	no	—
647	C₂²	—	6	2	no	—
648	C₂²	—	6	2	no	—
649	C₂²	—	12	4	no	—
650	C₂²	C₅×D₃×#41	1	2	yes	—
651	C₂²	C₅×#1010	1	2	yes	—
652	C₂²	C₂²×C₅×#67	1	8	yes	—
653	C₂²	C₂²×C₅×#67	1	2	yes	—
654	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
655	C₄	—	2	2	no	—
656	C₄	—	2	4	no	—
657	C₄	—	3	4	no	—
658	C₄	—	6	4	no	—
659	C₄	—	6	2	no	—
660	C₄	—	6	2	no	—
661	C₄	—	6	4	no	—
662	C₄	C₂²×C₅×#67	1	4	yes	—
663	C₃	C₂×C₅×#547	1	1	yes	characteristic, complemented, Sylow
664	C₂	—	2	8	no	—
665	C₂	—	4	2	no	—
666	C₂	—	12	2	no	—
667	C₂	C₅×#5824	1	4	yes	direct product factor
668	C₂	C₂×C₅×D₃×#41	1	1	yes	characteristic
669	C₂	C₂×C₅×#1010	1	1	yes	characteristic
670	C₂	C₂³×C₅×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₂²×C₃×C₅×#41	C₂
socle	C₂³×C₃×C₅	C₂⁴
hypercenter	C₂²×C₅×#41	D₃
hypocenter	C₃	C₂×C₅×#547
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂²×C₅×#41

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₅×#41	C₂	semidirect
2. C₂²×C₅×#237	C₂	semidirect
3. C₅×#5824	C₂	direct (N × H)
4. C₂×C₅×#946	C₂	semidirect
5. C₂×C₅×#944	C₂	semidirect
6. C₂×C₅×#939	C₂	semidirect
7. C₂×C₅×#935	C₂	semidirect
8. C₂×C₅×D₄×Dic₃	C₂	semidirect
9. C₂×C₅×#929	C₂	semidirect
10. C₂×C₄×C₅×#67	C₂	semidirect
11. C₂×C₅×#924	C₂	semidirect
12. C₂²×C₅×Dic₃⋊C₄	C₂	semidirect
15. C₂×C₃×C₅×#41	C₂²	semidirect
26. C₂×C₅×#237	C₂²	semidirect
32. C₅×#946	C₂²	semidirect
33. C₅×#944	C₂²	semidirect
34. C₅×#939	C₂²	semidirect
35. C₅×#935	C₂²	semidirect
36. C₅×D₄×Dic₃	C₂²	semidirect
37. C₅×#929	C₂²	semidirect
38. C₄×C₅×#67	C₂²	semidirect
42. C₅×#924	C₂²	semidirect
48. C₂×C₅×Dic₃⋊C₄	C₂²	semidirect
50. C₂×#5824	C₅	direct (N × H)
52. C₂²×C₅×#41	D₃	semidirect
70. C₂×C₃×C₅×D₄	D₄	semidirect
110. C₂²×C₃×#41	C₂×C₅	semidirect
111. C₂²×#237	C₂×C₅	semidirect
112. #5824	C₂×C₅	direct (N × H)
113. C₂×#946	C₂×C₅	semidirect
114. C₂×#944	C₂×C₅	semidirect
115. C₂×#939	C₂×C₅	semidirect
116. C₂×#935	C₂×C₅	semidirect
117. C₂×D₄×Dic₃	C₂×C₅	semidirect
118. C₂×#929	C₂×C₅	semidirect
119. C₂×C₄×#67	C₂×C₅	semidirect
120. C₂×#924	C₂×C₅	semidirect
121. C₂²×Dic₃⋊C₄	C₂×C₅	semidirect
125. C₂×C₅×#41	C₂×D₃	semidirect
174. C₃×C₅×D₄	C₂×D₄	semidirect
191. C₂×C₅×Dic₃	#41	semidirect
200. C₂×C₃×#41	C₂²×C₅	semidirect
211. C₂×#237	C₂²×C₅	semidirect
217. #946	C₂²×C₅	semidirect
218. #944	C₂²×C₅	semidirect
219. #939	C₂²×C₅	semidirect
220. #935	C₂²×C₅	semidirect
221. D₄×Dic₃	C₂²×C₅	semidirect
222. #929	C₂²×C₅	semidirect
223. C₄×#67	C₂²×C₅	semidirect
227. #924	C₂²×C₅	semidirect
233. C₂×Dic₃⋊C₄	C₂²×C₅	semidirect
249. C₂×C₅×D₄	#67	semidirect
283. C₂²×#41	C₅×D₃	semidirect
317. C₅×Dic₃	C₂×#41	semidirect
325. C₂×C₃×D₄	C₅×D₄	semidirect
383. C₅×D₄	C₂×#67	semidirect
408. C₂×#41	C₂×C₅×D₃	semidirect
443. C₂×C₃×C₅	#547	semidirect
463. C₃×D₄	C₂×C₅×D₄	semidirect
480. C₂×Dic₃	C₅×#41	semidirect
526. C₂×D₄	C₅×#67	semidirect
559. C₃×C₅	C₂×#547	semidirect
583. Dic₃	C₂×C₅×#41	semidirect
587. C₂×C₅	#5824	direct (N × H)
609. D₄	C₂×C₅×#67	semidirect
633. C₂×C₃	C₅×#547	semidirect
638. C₅	C₂×#5824	direct (N × H)
663. C₃	C₂×C₅×#547	semidirect
667. C₂	C₅×#5824	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×#41	2
C₂²×C₅×#237	2
C₅×#5824	2
C₂×C₅×#946	2
C₂×C₅×#944	2
C₂×C₅×#939	2
C₂×C₅×#935	2
C₂×C₅×D₄×Dic₃	2
C₂×C₅×#929	2
C₂×C₄×C₅×#67	2
C₂×C₅×#924	2
C₂²×C₅×Dic₃⋊C₄	2
C₂×C₅×#547	3
C₂×#5824	5

Subgroups — C2×C5×#5824 #14482673

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5824 #14482673