Subgroups — C₂×C₅×D₃×#124 #14479650

Order 1920.

3760 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×D₃×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×D₃×D₄	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₅×#124	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#947	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#936	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×D₃×#124	C₂	1	16	yes	maximal, direct product factor
7	C₂×C₅×#885	C₂	1	4	yes	maximal, complemented
8	C₂×C₅×D₃×C₂²⋊C₄	C₂	1	4	yes	maximal, complemented
9	C₂×C₅×#875	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₄²×C₅×D₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×C₅×#124	—	3	1	no	maximal, Hall
12	C₂⁴×C₅×D₃	C₂²	1	2	yes	—
13	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
14	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₂²×C₅×#67	C₂²	1	2	yes	—
16	C₂×C₅×D₃×Q₈	—	2	8	no	—
17	C₂×C₅×D₃×Q₈	C₂²	1	8	yes	complemented
18	C₂×C₅×D₃×D₄	—	2	8	no	—
19	C₂×C₅×D₃×D₄	C₂²	1	8	yes	—
20	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
21	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
22	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
23	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
24	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic, complemented
25	C₂²×C₅×Dic₆	C₂²	1	2	yes	complemented
26	C₃×C₅×#124	C₂²	1	8	yes	complemented
27	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	complemented
28	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₅×#217	C₂²	1	4	yes	complemented
30	C₅×#947	C₂²	1	8	yes	complemented
31	C₅×#936	C₂²	1	8	yes	complemented
32	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	4	yes	complemented
33	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	4	yes	complemented
34	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	complemented
35	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic, complemented
36	C₅×#885	C₂²	1	32	yes	complemented
37	C₅×D₃×C₂²⋊C₄	C₂²	1	32	yes	complemented
38	C₅×#875	C₂²	1	8	yes	complemented
39	C₄²×C₅×D₃	C₂²	1	8	yes	complemented
40	C₂×D₃×#124	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
41	C₂³×C₅×Q₈	—	3	1	no	—
42	C₂³×C₅×D₄	—	3	1	no	—
43	C₂×C₅×#124	—	3	1	no	—
44	C₂×C₅×#124	—	3	1	no	—
45	C₂×C₅×#124	—	3	16	no	—
46	C₂×C₅×#124	—	3	4	no	—
47	C₂×C₅×#124	—	3	1	no	—
48	C₂×C₅×#124	D₃	1	1	yes	characteristic, direct product factor
49	C₂²×C₅×C₂²⋊C₄	—	3	4	no	—
50	C₂²×C₄²×C₅	—	3	1	no	—
51	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
52	C₂³×C₅×D₃	—	2	8	no	—
53	C₂³×C₅×D₃	—	2	16	no	—
54	C₂³×C₅×D₃	C₂³	1	8	yes	—
55	C₂³×C₅×D₃	C₂³	1	2	yes	—
56	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
57	C₂×C₃×C₅×Q₈	—	2	4	no	—
58	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	complemented
59	C₂×C₃×C₅×D₄	—	2	4	no	—
60	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
61	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
62	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
63	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
64	C₂×C₅×#67	—	2	8	no	—
65	C₂×C₅×#67	C₂³	1	8	yes	—
66	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
67	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
68	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
69	C₅×D₃×Q₈	—	2	32	no	—
70	C₅×D₃×D₄	—	2	32	no	—
71	C₂×C₅×D₁₂	—	2	4	no	—
72	C₂×C₅×D₁₂	C₂³	1	4	yes	—
73	C₂×C₄×C₅×D₃	—	2	8	no	—
74	C₂×C₄×C₅×D₃	—	2	8	no	—
75	C₂×C₄×C₅×D₃	D₄	1	8	yes	—
76	C₂×C₄×C₅×D₃	C₂³	1	8	yes	—
77	C₂×C₄×C₅×D₃	C₂³	1	8	yes	—
78	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
79	C₂×C₅×Dic₆	—	2	4	no	—
80	C₂×C₅×Dic₆	—	2	8	no	—
81	C₂×C₅×Dic₆	C₂³	1	4	yes	complemented
82	C₂×C₅×Dic₆	C₂³	1	8	yes	complemented
83	C₃×C₅×C₂²⋊C₄	C₂³	1	16	yes	complemented
84	C₃×C₄²×C₅	C₂³	1	4	yes	complemented
85	C₅×#217	C₂³	1	16	yes	complemented
86	C₅×(C₂×D₃)⋊C₄	C₂³	1	16	yes	complemented
87	C₅×(C₂×D₃)⋊C₄	C₂³	1	16	yes	complemented
88	C₄×C₅×Dic₃	C₂³	1	8	yes	complemented
89	C₄×C₅×Dic₃	C₂³	1	4	yes	complemented
90	C₂²×D₃×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
91	C₂²×D₃×D₄	C₂×C₅	1	1	yes	characteristic
92	C₂×C₃×#124	C₂×C₅	1	1	yes	characteristic, complemented
93	C₂×#947	C₂×C₅	1	1	yes	characteristic, complemented
94	C₂×#936	C₂×C₅	1	1	yes	characteristic, complemented
95	D₃×#124	C₂×C₅	1	16	yes	direct product factor
96	C₂×#885	C₂×C₅	1	4	yes	complemented
97	C₂×D₃×C₂²⋊C₄	C₂×C₅	1	4	yes	complemented
98	C₂×#875	C₂×C₅	1	1	yes	characteristic, complemented
99	C₂×C₄²×D₃	C₂×C₅	1	1	yes	characteristic, complemented
100	C₂⁵×C₅	—	3	2	no	—
101	C₂²×C₅×Q₈	—	3	8	no	—
102	C₂²×C₅×Q₈	—	3	2	no	—
103	C₂²×C₅×Q₈	—	3	1	no	—
104	C₂²×C₅×Q₈	—	6	8	no	—
105	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
106	C₂²×C₅×D₄	—	3	2	no	—
107	C₂²×C₅×D₄	—	3	8	no	—
108	C₂²×C₅×D₄	—	3	1	no	—
109	C₂²×C₅×D₄	—	6	8	no	—
110	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
111	C₂³×C₄×C₅	—	3	1	no	—
112	C₂³×C₄×C₅	—	3	2	no	—
113	C₂³×C₄×C₅	—	3	2	no	—
114	C₅×#124	—	3	8	no	—
115	C₅×#124	—	3	8	no	—
116	C₅×#124	—	3	32	no	—
117	C₅×#124	—	3	8	no	—
118	C₅×#124	C₂×D₃	1	8	yes	direct product factor
119	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
120	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
121	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
122	C₂×C₅×C₂²⋊C₄	—	3	32	no	—
123	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	4	yes	complemented
124	C₂×C₄²×C₅	—	3	2	no	—
125	C₂×C₄²×C₅	—	3	1	no	—
126	C₂×C₄²×C₅	—	3	8	no	—
127	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic, complemented
128	C₂²×#124	—	3	1	no	Sylow
129	C₂³×C₃×C₅	—	2	4	no	—
130	C₂³×C₃×C₅	—	2	8	no	—
131	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
132	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
133	C₂²×C₅×D₃	—	2	4	no	—
134	C₂²×C₅×D₃	—	2	8	no	—
135	C₂²×C₅×D₃	—	2	16	no	—
136	C₂²×C₅×D₃	—	2	32	no	—
137	C₂²×C₅×D₃	—	4	32	no	—
138	C₂²×C₅×D₃	C₂×D₄	1	4	yes	—
139	C₂²×C₅×D₃	#41	1	8	yes	—
140	C₂²×C₅×D₃	C₂⁴	1	4	yes	—
141	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
142	C₃×C₅×Q₈	—	2	8	no	—
143	C₃×C₅×D₄	—	2	8	no	—
144	C₂×C₃×C₄×C₅	—	2	4	no	—
145	C₂×C₃×C₄×C₅	—	2	4	no	—
146	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
147	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
148	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
149	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
150	C₅×#67	—	2	16	no	—
151	C₂×C₅×Dic₃	—	2	4	no	—
152	C₂×C₅×Dic₃	—	2	4	no	—
153	C₂×C₅×Dic₃	C₂×D₄	1	4	yes	—
154	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
155	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
156	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
157	C₅×D₁₂	—	2	8	no	—
158	C₄×C₅×D₃	—	2	16	no	—
159	C₄×C₅×D₃	—	2	16	no	—
160	C₄×C₅×D₃	C₂×D₄	1	16	yes	—
161	C₅×Dic₆	—	2	8	no	—
162	C₅×Dic₆	—	2	16	no	—
163	C₂⁴×D₃	C₂²×C₅	1	2	yes	—
164	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
165	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
166	C₂²×#67	C₂²×C₅	1	2	yes	—
167	C₂×D₃×Q₈	—	2	8	no	—
168	C₂×D₃×Q₈	C₂²×C₅	1	8	yes	complemented
169	C₂×D₃×D₄	—	2	8	no	—
170	C₂×D₃×D₄	C₂²×C₅	1	8	yes	—
171	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
172	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
173	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
174	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
175	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic, complemented
176	C₂²×Dic₆	C₂²×C₅	1	2	yes	complemented
177	C₃×#124	C₂²×C₅	1	8	yes	complemented
178	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	complemented
179	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic, complemented
180	C₂×#217	C₂²×C₅	1	4	yes	complemented
181	#947	C₂²×C₅	1	8	yes	complemented
182	#936	C₂²×C₅	1	8	yes	complemented
183	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	4	yes	complemented
184	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	4	yes	complemented
185	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	complemented
186	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
187	#885	C₂²×C₅	1	32	yes	complemented
188	D₃×C₂²⋊C₄	C₂²×C₅	1	32	yes	complemented
189	#875	C₂²×C₅	1	8	yes	complemented
190	C₄²×D₃	C₂²×C₅	1	8	yes	complemented
191	C₂⁴×C₅	—	3	1	no	—
192	C₂⁴×C₅	—	3	8	no	—
193	C₂⁴×C₅	—	3	2	no	—
194	C₂⁴×C₅	—	6	8	no	—
195	C₂⁴×C₅	—	6	16	no	—
196	C₂⁴×C₅	C₂²×D₃	1	2	yes	—
197	C₂×C₅×Q₈	—	2	4	no	—
198	C₂×C₅×Q₈	—	3	8	no	—
199	C₂×C₅×Q₈	—	3	4	no	—
200	C₂×C₅×Q₈	—	6	8	no	—
201	C₂×C₅×Q₈	—	6	32	no	—
202	C₂×C₅×Q₈	—	6	4	no	—
203	C₂×C₅×Q₈	C₂²×D₃	1	4	yes	complemented
204	C₂×C₅×D₄	—	2	4	no	—
205	C₂×C₅×D₄	—	3	8	no	—
206	C₂×C₅×D₄	—	3	4	no	—
207	C₂×C₅×D₄	—	6	32	no	—
208	C₂×C₅×D₄	—	6	8	no	—
209	C₂×C₅×D₄	—	6	4	no	—
210	C₂×C₅×D₄	C₂²×D₃	1	4	yes	—
211	C₂²×C₄×C₅	—	3	1	no	—
212	C₂²×C₄×C₅	—	3	8	no	—
213	C₂²×C₄×C₅	—	3	4	no	—
214	C₂²×C₄×C₅	—	3	2	no	—
215	C₂²×C₄×C₅	—	3	2	no	—
216	C₂²×C₄×C₅	—	3	8	no	—
217	C₂²×C₄×C₅	—	3	8	no	—
218	C₂²×C₄×C₅	—	6	8	no	—
219	C₂²×C₄×C₅	—	6	8	no	—
220	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
221	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
222	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
223	C₅×C₂²⋊C₄	—	3	16	no	—
224	C₅×C₂²⋊C₄	—	3	16	no	—
225	C₅×C₂²⋊C₄	—	3	16	no	—
226	C₅×C₂²⋊C₄	C₂²×D₃	1	16	yes	complemented
227	C₄²×C₅	—	3	8	no	—
228	C₄²×C₅	—	3	4	no	—
229	C₄²×C₅	C₂²×D₃	1	4	yes	complemented
230	C₂³×Q₈	—	3	1	no	—
231	C₂³×D₄	—	3	1	no	—
232	C₂×#124	—	3	1	no	—
233	C₂×#124	—	3	1	no	—
234	C₂×#124	—	3	16	no	—
235	C₂×#124	—	3	4	no	—
236	C₂×#124	—	3	1	no	—
237	C₂×#124	C₅×D₃	1	1	yes	characteristic, direct product factor
238	C₂²×C₂²⋊C₄	—	3	4	no	—
239	C₂²×C₄²	—	3	1	no	—
240	C₂²×C₃×C₅	—	2	4	no	—
241	C₂²×C₃×C₅	—	2	8	no	—
242	C₂²×C₃×C₅	—	4	8	no	—
243	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
244	C₂²×C₃×C₅	C₂×#41	1	4	yes	—
245	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
246	C₂×C₅×D₃	—	2	4	no	—
247	C₂×C₅×D₃	—	2	8	no	—
248	C₂×C₅×D₃	—	4	8	no	—
249	C₂×C₅×D₃	—	4	32	no	—
250	C₂×C₅×D₃	#124	1	16	yes	direct product factor
251	C₂×C₅×D₃	C₂²×D₄	1	4	yes	—
252	C₂×C₅×D₃	C₂×#41	1	8	yes	—
253	C₃×C₄×C₅	—	2	4	no	—
254	C₃×C₄×C₅	—	2	4	no	—
255	C₃×C₄×C₅	C₂²×D₄	1	4	yes	—
256	C₅×Dic₃	—	2	4	no	—
257	C₅×Dic₃	—	2	4	no	—
258	C₅×Dic₃	C₂²×D₄	1	4	yes	—
259	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
260	C₂³×D₃	—	2	8	no	—
261	C₂³×D₃	—	2	16	no	—
262	C₂³×D₃	C₂³×C₅	1	8	yes	—
263	C₂³×D₃	C₂³×C₅	1	2	yes	—
264	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
265	C₂×C₃×Q₈	—	2	4	no	—
266	C₂×C₃×Q₈	C₂³×C₅	1	4	yes	complemented
267	C₂×C₃×D₄	—	2	4	no	—
268	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
269	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
270	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
271	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
272	C₂×#67	—	2	8	no	—
273	C₂×#67	C₂³×C₅	1	8	yes	—
274	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
275	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
276	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
277	D₃×Q₈	—	2	32	no	—
278	D₃×D₄	—	2	32	no	—
279	C₂×D₁₂	—	2	4	no	—
280	C₂×D₁₂	C₂³×C₅	1	4	yes	—
281	C₂×C₄×D₃	—	2	8	no	—
282	C₂×C₄×D₃	—	2	8	no	—
283	C₂×C₄×D₃	C₅×D₄	1	8	yes	—
284	C₂×C₄×D₃	C₂³×C₅	1	8	yes	—
285	C₂×C₄×D₃	C₂³×C₅	1	8	yes	—
286	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
287	C₂×Dic₆	—	2	4	no	—
288	C₂×Dic₆	—	2	8	no	—
289	C₂×Dic₆	C₂³×C₅	1	4	yes	complemented
290	C₂×Dic₆	C₂³×C₅	1	8	yes	complemented
291	C₃×C₂²⋊C₄	C₂³×C₅	1	16	yes	complemented
292	C₃×C₄²	C₂³×C₅	1	4	yes	complemented
293	#217	C₂³×C₅	1	16	yes	complemented
294	(C₂×D₃)⋊C₄	C₂³×C₅	1	16	yes	complemented
295	(C₂×D₃)⋊C₄	C₂³×C₅	1	16	yes	complemented
296	C₄×Dic₃	C₂³×C₅	1	8	yes	complemented
297	C₄×Dic₃	C₂³×C₅	1	4	yes	complemented
298	C₂³×C₅	—	2	4	no	—
299	C₂³×C₅	—	2	8	no	—
300	C₂³×C₅	—	3	4	no	—
301	C₂³×C₅	—	3	8	no	—
302	C₂³×C₅	—	3	2	no	—
303	C₂³×C₅	—	3	4	no	—
304	C₂³×C₅	—	6	16	no	—
305	C₂³×C₅	—	6	32	no	—
306	C₂³×C₅	—	6	4	no	—
307	C₂³×C₅	—	6	8	no	—
308	C₂³×C₅	—	12	32	no	—
309	C₂³×C₅	C₂³×D₃	1	4	yes	—
310	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
311	C₅×Q₈	—	2	8	no	—
312	C₅×Q₈	—	6	16	no	—
313	C₅×Q₈	—	6	8	no	—
314	C₅×D₄	—	2	8	no	—
315	C₅×D₄	—	6	16	no	—
316	C₅×D₄	—	6	8	no	—
317	C₂×C₄×C₅	—	2	4	no	—
318	C₂×C₄×C₅	—	2	4	no	—
319	C₂×C₄×C₅	—	3	4	no	—
320	C₂×C₄×C₅	—	3	2	no	—
321	C₂×C₄×C₅	—	3	16	no	—
322	C₂×C₄×C₅	—	3	4	no	—
323	C₂×C₄×C₅	—	3	4	no	—
324	C₂×C₄×C₅	—	6	16	no	—
325	C₂×C₄×C₅	—	6	16	no	—
326	C₂×C₄×C₅	—	6	4	no	—
327	C₂×C₄×C₅	—	6	4	no	—
328	C₂×C₄×C₅	D₃×D₄	1	4	yes	—
329	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
330	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
331	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
332	C₂⁵	—	3	2	no	—
333	C₂²×Q₈	—	3	8	no	—
334	C₂²×Q₈	—	3	2	no	—
335	C₂²×Q₈	—	3	1	no	—
336	C₂²×Q₈	—	6	8	no	—
337	C₂²×Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
338	C₂²×D₄	—	3	2	no	—
339	C₂²×D₄	—	3	8	no	—
340	C₂²×D₄	—	3	1	no	—
341	C₂²×D₄	—	6	8	no	—
342	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
343	C₂³×C₄	—	3	1	no	—
344	C₂³×C₄	—	3	2	no	—
345	C₂³×C₄	—	3	2	no	—
346	#124	—	3	8	no	—
347	#124	—	3	8	no	—
348	#124	—	3	32	no	—
349	#124	—	3	8	no	—
350	#124	C₂×C₅×D₃	1	8	yes	direct product factor
351	C₂×C₂²⋊C₄	—	3	4	no	—
352	C₂×C₂²⋊C₄	—	3	4	no	—
353	C₂×C₂²⋊C₄	—	3	4	no	—
354	C₂×C₂²⋊C₄	—	3	32	no	—
355	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	4	yes	complemented
356	C₂×C₄²	—	3	2	no	—
357	C₂×C₄²	—	3	1	no	—
358	C₂×C₄²	—	3	8	no	—
359	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic, complemented
360	C₂×C₃×C₅	—	4	4	no	—
361	C₂×C₃×C₅	C₂×#124	1	4	yes	complemented
362	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
363	C₂×C₃×C₅	C₂²×#41	1	2	yes	—
364	C₅×D₃	—	4	4	no	—
365	C₅×D₃	C₂×#124	1	8	yes	direct product factor
366	C₂³×C₃	—	2	4	no	—
367	C₂³×C₃	—	2	8	no	—
368	C₂³×C₃	C₂⁴×C₅	1	4	yes	—
369	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
370	C₂²×D₃	—	2	4	no	—
371	C₂²×D₃	—	2	8	no	—
372	C₂²×D₃	—	2	16	no	—
373	C₂²×D₃	—	2	32	no	—
374	C₂²×D₃	—	4	32	no	—
375	C₂²×D₃	C₂×C₅×D₄	1	4	yes	—
376	C₂²×D₃	C₅×#41	1	8	yes	—
377	C₂²×D₃	C₂⁴×C₅	1	4	yes	—
378	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
379	C₃×Q₈	—	2	8	no	—
380	C₃×D₄	—	2	8	no	—
381	C₂×C₃×C₄	—	2	4	no	—
382	C₂×C₃×C₄	—	2	4	no	—
383	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
384	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
385	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
386	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
387	#67	—	2	16	no	—
388	C₂×Dic₃	—	2	4	no	—
389	C₂×Dic₃	—	2	4	no	—
390	C₂×Dic₃	C₂×C₅×D₄	1	4	yes	—
391	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
392	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
393	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
394	D₁₂	—	2	8	no	—
395	C₄×D₃	—	2	16	no	—
396	C₄×D₃	—	2	16	no	—
397	C₄×D₃	C₂×C₅×D₄	1	16	yes	—
398	Dic₆	—	2	8	no	—
399	Dic₆	—	2	16	no	—
400	C₂²×C₅	—	2	4	no	—
401	C₂²×C₅	—	2	8	no	—
402	C₂²×C₅	—	3	16	no	—
403	C₂²×C₅	—	3	4	no	—
404	C₂²×C₅	—	3	8	no	—
405	C₂²×C₅	—	4	8	no	—
406	C₂²×C₅	—	6	4	no	—
407	C₂²×C₅	—	6	8	no	—
408	C₂²×C₅	—	12	32	no	—
409	C₂²×C₅	—	12	8	no	—
410	C₂²×C₅	C₂×D₃×D₄	1	2	yes	—
411	C₂²×C₅	D₃×#41	1	4	yes	—
412	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
413	C₄×C₅	—	2	4	no	—
414	C₄×C₅	—	2	4	no	—
415	C₄×C₅	—	3	4	no	—
416	C₄×C₅	—	6	4	no	—
417	C₄×C₅	—	6	4	no	—
418	C₄×C₅	C₂×D₃×D₄	1	4	yes	—
419	C₂⁴	—	3	1	no	—
420	C₂⁴	—	3	8	no	—
421	C₂⁴	—	3	2	no	—
422	C₂⁴	—	6	8	no	—
423	C₂⁴	—	6	16	no	—
424	C₂⁴	C₂²×C₅×D₃	1	2	yes	—
425	C₂×Q₈	—	2	4	no	—
426	C₂×Q₈	—	3	8	no	—
427	C₂×Q₈	—	3	4	no	—
428	C₂×Q₈	—	6	8	no	—
429	C₂×Q₈	—	6	32	no	—
430	C₂×Q₈	—	6	4	no	—
431	C₂×Q₈	C₂²×C₅×D₃	1	4	yes	complemented
432	C₂×D₄	—	2	4	no	—
433	C₂×D₄	—	3	8	no	—
434	C₂×D₄	—	3	4	no	—
435	C₂×D₄	—	6	32	no	—
436	C₂×D₄	—	6	8	no	—
437	C₂×D₄	—	6	4	no	—
438	C₂×D₄	C₂²×C₅×D₃	1	4	yes	—
439	C₂²×C₄	—	3	1	no	—
440	C₂²×C₄	—	3	8	no	—
441	C₂²×C₄	—	3	4	no	—
442	C₂²×C₄	—	3	2	no	—
443	C₂²×C₄	—	3	2	no	—
444	C₂²×C₄	—	3	8	no	—
445	C₂²×C₄	—	3	8	no	—
446	C₂²×C₄	—	6	8	no	—
447	C₂²×C₄	—	6	8	no	—
448	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
449	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
450	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
451	C₂²⋊C₄	—	3	16	no	—
452	C₂²⋊C₄	—	3	16	no	—
453	C₂²⋊C₄	—	3	16	no	—
454	C₂²⋊C₄	C₂²×C₅×D₃	1	16	yes	complemented
455	C₄²	—	3	8	no	—
456	C₄²	—	3	4	no	—
457	C₄²	C₂²×C₅×D₃	1	4	yes	complemented
458	C₃×C₅	C₂²×#124	1	1	yes	characteristic, complemented, Hall
459	C₂²×C₃	—	2	4	no	—
460	C₂²×C₃	—	2	8	no	—
461	C₂²×C₃	—	4	8	no	—
462	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
463	C₂²×C₃	C₂×C₅×#41	1	4	yes	—
464	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
465	C₂×D₃	—	2	4	no	—
466	C₂×D₃	—	2	8	no	—
467	C₂×D₃	—	4	8	no	—
468	C₂×D₃	—	4	32	no	—
469	C₂×D₃	C₅×#124	1	16	yes	direct product factor
470	C₂×D₃	C₂²×C₅×D₄	1	4	yes	—
471	C₂×D₃	C₂×C₅×#41	1	8	yes	—
472	C₃×C₄	—	2	4	no	—
473	C₃×C₄	—	2	4	no	—
474	C₃×C₄	C₂²×C₅×D₄	1	4	yes	—
475	Dic₃	—	2	4	no	—
476	Dic₃	—	2	4	no	—
477	Dic₃	C₂²×C₅×D₄	1	4	yes	—
478	C₂×C₅	—	3	8	no	—
479	C₂×C₅	—	4	4	no	—
480	C₂×C₅	—	12	4	no	—
481	C₂×C₅	D₃×#124	1	4	yes	direct product factor
482	C₂×C₅	C₂²×D₃×D₄	1	1	yes	characteristic
483	C₂×C₅	C₂×D₃×#41	1	2	yes	—
484	C₂³	—	2	4	no	—
485	C₂³	—	2	8	no	—
486	C₂³	—	3	4	no	—
487	C₂³	—	3	8	no	—
488	C₂³	—	3	2	no	—
489	C₂³	—	3	4	no	—
490	C₂³	—	6	16	no	—
491	C₂³	—	6	32	no	—
492	C₂³	—	6	4	no	—
493	C₂³	—	6	8	no	—
494	C₂³	—	12	32	no	—
495	C₂³	C₂³×C₅×D₃	1	4	yes	—
496	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
497	Q₈	—	2	8	no	—
498	Q₈	—	6	16	no	—
499	Q₈	—	6	8	no	—
500	D₄	—	2	8	no	—
501	D₄	—	6	16	no	—
502	D₄	—	6	8	no	—
503	C₂×C₄	—	2	4	no	—
504	C₂×C₄	—	2	4	no	—
505	C₂×C₄	—	3	4	no	—
506	C₂×C₄	—	3	2	no	—
507	C₂×C₄	—	3	16	no	—
508	C₂×C₄	—	3	4	no	—
509	C₂×C₄	—	3	4	no	—
510	C₂×C₄	—	6	16	no	—
511	C₂×C₄	—	6	16	no	—
512	C₂×C₄	—	6	4	no	—
513	C₂×C₄	—	6	4	no	—
514	C₂×C₄	C₅×D₃×D₄	1	4	yes	—
515	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
516	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
517	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
518	C₂×C₃	—	4	4	no	—
519	C₂×C₃	C₂×C₅×#124	1	4	yes	complemented
520	C₂×C₃	C₂³×C₅×D₄	1	1	yes	characteristic
521	C₂×C₃	C₂²×C₅×#41	1	2	yes	—
522	D₃	—	4	4	no	—
523	D₃	C₂×C₅×#124	1	8	yes	direct product factor
524	C₅	C₂×D₃×#124	1	1	yes	characteristic, direct product factor, Sylow
525	C₂²	—	2	4	no	—
526	C₂²	—	2	8	no	—
527	C₂²	—	3	16	no	—
528	C₂²	—	3	4	no	—
529	C₂²	—	3	8	no	—
530	C₂²	—	4	8	no	—
531	C₂²	—	6	4	no	—
532	C₂²	—	6	8	no	—
533	C₂²	—	12	32	no	—
534	C₂²	—	12	8	no	—
535	C₂²	C₂×C₅×D₃×D₄	1	2	yes	—
536	C₂²	C₅×D₃×#41	1	4	yes	—
537	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
538	C₄	—	2	4	no	—
539	C₄	—	2	4	no	—
540	C₄	—	3	4	no	—
541	C₄	—	6	4	no	—
542	C₄	—	6	4	no	—
543	C₄	C₂×C₅×D₃×D₄	1	4	yes	—
544	C₃	C₂²×C₅×#124	1	1	yes	characteristic, complemented, Sylow
545	C₂	—	3	8	no	—
546	C₂	—	4	4	no	—
547	C₂	—	12	4	no	—
548	C₂	C₅×D₃×#124	1	4	yes	direct product factor
549	C₂	C₂²×C₅×D₃×D₄	1	1	yes	characteristic
550	C₂	C₂×C₅×D₃×#41	1	2	yes	—

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₂×C₃×C₅×#124	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂²×C₅×D₃×D₄	C₂
hypercenter	C₂×C₅×#124	D₃
hypocenter	C₃	C₂²×C₅×#124
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₅×#124

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×D₃×Q₈	C₂	semidirect
3. C₂×C₃×C₅×#124	C₂	semidirect
4. C₂×C₅×#947	C₂	semidirect
5. C₂×C₅×#936	C₂	semidirect
6. C₅×D₃×#124	C₂	direct (N × H)
7. C₂×C₅×#885	C₂	semidirect
8. C₂×C₅×D₃×C₂²⋊C₄	C₂	semidirect
9. C₂×C₅×#875	C₂	semidirect
10. C₂×C₄²×C₅×D₃	C₂	semidirect
13. C₂²×C₃×C₅×Q₈	C₂²	semidirect
17. C₂×C₅×D₃×Q₈	C₂²	semidirect
24. C₂²×C₅×Dic₆	C₂²	semidirect
25. C₂²×C₅×Dic₆	C₂²	semidirect
26. C₃×C₅×#124	C₂²	semidirect
27. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
28. C₂×C₃×C₄²×C₅	C₂²	semidirect
29. C₂×C₅×#217	C₂²	semidirect
30. C₅×#947	C₂²	semidirect
31. C₅×#936	C₂²	semidirect
32. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
33. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
34. C₂×C₄×C₅×Dic₃	C₂²	semidirect
35. C₂×C₄×C₅×Dic₃	C₂²	semidirect
36. C₅×#885	C₂²	semidirect
37. C₅×D₃×C₂²⋊C₄	C₂²	semidirect
38. C₅×#875	C₂²	semidirect
39. C₄²×C₅×D₃	C₂²	semidirect
40. C₂×D₃×#124	C₅	direct (N × H)
48. C₂×C₅×#124	D₃	direct (N × H)
58. C₂×C₃×C₅×Q₈	C₂³	semidirect
81. C₂×C₅×Dic₆	C₂³	semidirect
82. C₂×C₅×Dic₆	C₂³	semidirect
83. C₃×C₅×C₂²⋊C₄	C₂³	semidirect
84. C₃×C₄²×C₅	C₂³	semidirect
85. C₅×#217	C₂³	semidirect
86. C₅×(C₂×D₃)⋊C₄	C₂³	semidirect
87. C₅×(C₂×D₃)⋊C₄	C₂³	semidirect
88. C₄×C₅×Dic₃	C₂³	semidirect
89. C₄×C₅×Dic₃	C₂³	semidirect
90. C₂²×D₃×Q₈	C₂×C₅	semidirect
92. C₂×C₃×#124	C₂×C₅	semidirect
93. C₂×#947	C₂×C₅	semidirect
94. C₂×#936	C₂×C₅	semidirect
95. D₃×#124	C₂×C₅	direct (N × H)
96. C₂×#885	C₂×C₅	semidirect
97. C₂×D₃×C₂²⋊C₄	C₂×C₅	semidirect
98. C₂×#875	C₂×C₅	semidirect
99. C₂×C₄²×D₃	C₂×C₅	semidirect
105. C₂²×C₅×Q₈	C₂×D₃	semidirect
118. C₅×#124	C₂×D₃	direct (N × H)
123. C₂×C₅×C₂²⋊C₄	C₂×D₃	semidirect
127. C₂×C₄²×C₅	C₂×D₃	semidirect
164. C₂²×C₃×Q₈	C₂²×C₅	semidirect
168. C₂×D₃×Q₈	C₂²×C₅	semidirect
175. C₂²×Dic₆	C₂²×C₅	semidirect
176. C₂²×Dic₆	C₂²×C₅	semidirect
177. C₃×#124	C₂²×C₅	semidirect
178. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
179. C₂×C₃×C₄²	C₂²×C₅	semidirect
180. C₂×#217	C₂²×C₅	semidirect
181. #947	C₂²×C₅	semidirect
182. #936	C₂²×C₅	semidirect
183. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
184. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
185. C₂×C₄×Dic₃	C₂²×C₅	semidirect
186. C₂×C₄×Dic₃	C₂²×C₅	semidirect
187. #885	C₂²×C₅	semidirect
188. D₃×C₂²⋊C₄	C₂²×C₅	semidirect
189. #875	C₂²×C₅	semidirect
190. C₄²×D₃	C₂²×C₅	semidirect
203. C₂×C₅×Q₈	C₂²×D₃	semidirect
226. C₅×C₂²⋊C₄	C₂²×D₃	semidirect
229. C₄²×C₅	C₂²×D₃	semidirect
237. C₂×#124	C₅×D₃	direct (N × H)
250. C₂×C₅×D₃	#124	direct (N × H)
266. C₂×C₃×Q₈	C₂³×C₅	semidirect
289. C₂×Dic₆	C₂³×C₅	semidirect
290. C₂×Dic₆	C₂³×C₅	semidirect
291. C₃×C₂²⋊C₄	C₂³×C₅	semidirect
292. C₃×C₄²	C₂³×C₅	semidirect
293. #217	C₂³×C₅	semidirect
294. (C₂×D₃)⋊C₄	C₂³×C₅	semidirect
295. (C₂×D₃)⋊C₄	C₂³×C₅	semidirect
296. C₄×Dic₃	C₂³×C₅	semidirect
297. C₄×Dic₃	C₂³×C₅	semidirect
337. C₂²×Q₈	C₂×C₅×D₃	semidirect
350. #124	C₂×C₅×D₃	direct (N × H)
355. C₂×C₂²⋊C₄	C₂×C₅×D₃	semidirect
359. C₂×C₄²	C₂×C₅×D₃	semidirect
361. C₂×C₃×C₅	C₂×#124	semidirect
365. C₅×D₃	C₂×#124	direct (N × H)
431. C₂×Q₈	C₂²×C₅×D₃	semidirect
454. C₂²⋊C₄	C₂²×C₅×D₃	semidirect
457. C₄²	C₂²×C₅×D₃	semidirect
458. C₃×C₅	C₂²×#124	semidirect
469. C₂×D₃	C₅×#124	direct (N × H)
481. C₂×C₅	D₃×#124	direct (N × H)
519. C₂×C₃	C₂×C₅×#124	semidirect
523. D₃	C₂×C₅×#124	direct (N × H)
524. C₅	C₂×D₃×#124	direct (N × H)
544. C₃	C₂²×C₅×#124	semidirect
548. C₂	C₅×D₃×#124	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×C₅×D₃×Q₈	2
C₂²×C₅×D₃×D₄	2
C₂×C₃×C₅×#124	2
C₂×C₅×#947	2
C₂×C₅×#936	2
C₅×D₃×#124	2
C₂×C₅×#885	2
C₂×C₅×D₃×C₂²⋊C₄	2
C₂×C₅×#875	2
C₂×C₄²×C₅×D₃	2
C₂²×C₅×#124	3
C₂×D₃×#124	5

Subgroups — C2×C5×D3×#124 #14479650

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×D₃×#124 #14479650