Subgroups — C₂×C₅×#5648 #14480467

Order 1920.

3024 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×#237	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₅×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×#123	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#935	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#929	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5648	C₂	1	16	yes	maximal, direct product factor
7	C₂×C₅×#896	C₂	1	2	yes	maximal, complemented
8	C₂×C₅×#888	C₂	1	2	yes	maximal, complemented
9	C₂×C₅×#886	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅×#885	C₂	1	2	yes	maximal, complemented
11	C₂×C₅×#878	C₂	1	2	yes	maximal, complemented
12	C₂×C₅×#877	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₅×#536	—	3	1	no	maximal, Hall
14	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
16	C₂²×C₅×#67	C₂²	1	1	yes	characteristic
17	C₂²×C₅×#67	C₂²	1	1	yes	characteristic
18	C₂³×C₅×Dic₃	C₂²	1	1	yes	characteristic
19	C₂³×C₅×Dic₃	C₂²	1	1	yes	characteristic
20	C₂³×C₅×Dic₃	C₂²	1	1	yes	characteristic
21	C₂×C₅×#237	—	2	8	no	—
22	C₂×C₅×#237	C₂²	1	8	yes	—
23	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
24	C₂²×C₅×Dic₆	—	2	8	no	—
25	C₂²×C₅×Dic₆	C₂²	1	2	yes	—
26	C₂²×C₅×Dic₆	C₂²	1	2	yes	—
27	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
28	C₂²×C₅×Dic₆	C₂²	1	8	yes	complemented
29	C₃×C₅×#123	C₂²	1	8	yes	complemented
30	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
31	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
33	C₂×C₅×#217	C₂²	1	1	yes	characteristic
34	C₂×C₅×#217	C₂²	1	2	yes	—
35	C₅×#935	C₂²	1	8	yes	complemented
36	C₅×#929	C₂²	1	8	yes	complemented
37	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
38	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
39	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
40	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
41	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
42	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
43	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
44	C₅×#896	C₂²	1	16	yes	complemented
45	C₅×#888	C₂²	1	16	yes	complemented
46	C₅×#886	C₂²	1	8	yes	complemented
47	C₅×#885	C₂²	1	16	yes	complemented
48	C₅×#878	C₂²	1	16	yes	complemented
49	C₅×#877	C₂²	1	8	yes	complemented
50	C₂×#5648	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
51	C₂²×C₅×#41	—	3	1	no	—
52	C₂³×C₅×Q₈	—	3	1	no	—
53	C₅×#536	—	3	16	no	—
54	C₂×C₅×C₄⋊Q₈	—	3	2	no	—
55	C₂×C₅×#124	—	3	2	no	—
56	C₂×C₅×#123	—	3	1	no	—
57	C₂×C₅×#123	—	3	1	no	—
58	C₂×C₅×#123	—	3	1	no	—
59	C₂×C₅×#123	D₃	1	1	yes	characteristic, complemented
60	C₂×C₅×C₂²⋊Q₈	—	3	2	no	—
61	C₂×C₅×C₂²⋊Q₈	—	3	2	no	—
62	C₂×C₅×#117	—	3	1	no	—
63	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
64	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
65	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
66	C₂×C₃×C₅×D₄	—	2	4	no	—
67	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
68	C₂²×C₃×C₄×C₅	—	2	4	no	—
69	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
70	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
71	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
72	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
73	C₂×C₅×#67	—	2	4	no	—
74	C₂×C₅×#67	—	2	4	no	—
75	C₂×C₅×#67	C₂³	1	4	yes	—
76	C₂×C₅×#67	C₂³	1	4	yes	—
77	C₂²×C₅×Dic₃	—	2	4	no	—
78	C₂²×C₅×Dic₃	—	2	4	no	—
79	C₂²×C₅×Dic₃	D₄	1	8	yes	—
80	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
81	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
82	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
83	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
84	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
85	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
86	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
87	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
88	C₅×#237	—	2	32	no	—
89	C₂×C₄×C₅×D₃	—	2	4	no	—
90	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
91	C₂×C₅×Dic₆	—	2	8	no	—
92	C₂×C₅×Dic₆	—	2	8	no	—
93	C₂×C₅×Dic₆	—	2	32	no	—
94	C₂×C₅×Dic₆	—	2	4	no	—
95	C₂×C₅×Dic₆	C₂³	1	8	yes	—
96	C₂×C₅×Dic₆	C₂³	1	8	yes	—
97	C₂×C₅×Dic₆	C₂³	1	4	yes	—
98	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	—
99	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
100	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
101	C₅×#217	C₂³	1	4	yes	—
102	C₅×#217	C₂³	1	8	yes	—
103	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
104	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
105	C₅×C₄⋊Dic₃	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	8	yes	—
110	C₂²×#237	C₂×C₅	1	1	yes	characteristic
111	C₂³×Dic₆	C₂×C₅	1	1	yes	characteristic, complemented
112	C₂×C₃×#123	C₂×C₅	1	1	yes	characteristic, complemented
113	C₂×#935	C₂×C₅	1	1	yes	characteristic, complemented
114	C₂×#929	C₂×C₅	1	1	yes	characteristic, complemented
115	#5648	C₂×C₅	1	16	yes	direct product factor
116	C₂×#896	C₂×C₅	1	2	yes	complemented
117	C₂×#888	C₂×C₅	1	2	yes	complemented
118	C₂×#886	C₂×C₅	1	1	yes	characteristic, complemented
119	C₂×#885	C₂×C₅	1	2	yes	complemented
120	C₂×#878	C₂×C₅	1	2	yes	complemented
121	C₂×#877	C₂×C₅	1	1	yes	characteristic, complemented
122	C₂×C₅×#41	—	3	8	no	—
123	C₂×C₅×#41	—	6	8	no	—
124	C₂²×C₅×Q₈	—	3	2	no	—
125	C₂²×C₅×Q₈	—	3	2	no	—
126	C₂²×C₅×Q₈	—	3	1	no	—
127	C₂²×C₅×Q₈	—	3	8	no	—
128	C₂²×C₅×Q₈	—	6	8	no	—
129	C₂²×C₅×D₄	—	3	1	no	—
130	C₂²×C₅×D₄	—	3	1	no	—
131	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
132	C₂³×C₄×C₅	—	3	1	no	—
133	C₂³×C₄×C₅	—	3	1	no	—
134	C₂³×C₄×C₅	—	3	1	no	—
135	C₂³×C₄×C₅	—	3	1	no	—
136	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
137	C₅×C₄⋊Q₈	—	3	16	no	—
138	C₅×#124	—	3	16	no	—
139	C₅×#123	—	3	8	no	—
140	C₅×#123	—	3	8	no	—
141	C₅×#123	—	3	8	no	—
142	C₅×#123	C₂×D₃	1	8	yes	complemented
143	C₅×C₂²⋊Q₈	—	3	16	no	—
144	C₅×C₂²⋊Q₈	—	3	16	no	—
145	C₅×#117	—	3	8	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	C₂×D₃	1	2	yes	—
151	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
152	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
153	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
154	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
155	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
156	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	2	yes	—
157	C₂×C₄²×C₅	—	3	2	no	—
158	C₂×#536	—	3	1	no	Sylow
159	C₂³×C₃×C₅	—	2	4	no	—
160	C₂³×C₃×C₅	—	2	2	no	—
161	C₂³×C₃×C₅	—	2	4	no	—
162	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
163	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
164	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
165	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
166	C₂²×C₅×D₃	—	2	2	no	—
167	C₂²×C₅×D₃	—	2	4	no	—
168	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
169	C₃×C₅×D₄	—	2	8	no	—
170	C₂×C₃×C₄×C₅	—	2	8	no	—
171	C₂×C₃×C₄×C₅	—	2	4	no	—
172	C₂×C₃×C₄×C₅	—	2	2	no	—
173	C₂×C₃×C₄×C₅	—	2	4	no	—
174	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
175	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
176	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
177	C₅×#67	—	2	8	no	—
178	C₅×#67	—	2	8	no	—
179	C₂×C₅×Dic₃	—	2	8	no	—
180	C₂×C₅×Dic₃	—	2	4	no	—
181	C₂×C₅×Dic₃	—	2	2	no	—
182	C₂×C₅×Dic₃	—	2	4	no	—
183	C₂×C₅×Dic₃	—	2	8	no	—
184	C₂×C₅×Dic₃	C₂×D₄	1	4	yes	—
185	C₂×C₅×Dic₃	C₂×D₄	1	4	yes	—
186	C₂×C₅×Dic₃	C₂×D₄	1	16	yes	—
187	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
188	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
189	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
190	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
191	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
192	C₄×C₅×D₃	—	2	8	no	—
193	C₅×Dic₆	—	2	16	no	—
194	C₅×Dic₆	—	2	16	no	—
195	C₅×Dic₆	—	2	8	no	—
196	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
197	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
198	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
199	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
200	C₂³×Dic₃	C₂²×C₅	1	1	yes	characteristic
201	C₂³×Dic₃	C₂²×C₅	1	1	yes	characteristic
202	C₂³×Dic₃	C₂²×C₅	1	1	yes	characteristic
203	C₂×#237	—	2	8	no	—
204	C₂×#237	C₂²×C₅	1	8	yes	—
205	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
206	C₂²×Dic₆	—	2	8	no	—
207	C₂²×Dic₆	C₂²×C₅	1	2	yes	—
208	C₂²×Dic₆	C₂²×C₅	1	2	yes	—
209	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
210	C₂²×Dic₆	C₂²×C₅	1	8	yes	complemented
211	C₃×#123	C₂²×C₅	1	8	yes	complemented
212	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
213	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
214	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
215	C₂×#217	C₂²×C₅	1	1	yes	characteristic
216	C₂×#217	C₂²×C₅	1	2	yes	—
217	#935	C₂²×C₅	1	8	yes	complemented
218	#929	C₂²×C₅	1	8	yes	complemented
219	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
220	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
221	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
222	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
223	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
224	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
225	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
226	#896	C₂²×C₅	1	16	yes	complemented
227	#888	C₂²×C₅	1	16	yes	complemented
228	#886	C₂²×C₅	1	8	yes	complemented
229	#885	C₂²×C₅	1	16	yes	complemented
230	#878	C₂²×C₅	1	16	yes	complemented
231	#877	C₂²×C₅	1	8	yes	complemented
232	C₂⁴×C₅	—	3	1	no	—
233	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
234	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
235	C₅×#41	—	6	32	no	—
236	C₂×C₅×Q₈	—	3	8	no	—
237	C₂×C₅×Q₈	—	3	8	no	—
238	C₂×C₅×Q₈	—	3	4	no	—
239	C₂×C₅×Q₈	—	6	8	no	—
240	C₂×C₅×Q₈	—	6	8	no	—
241	C₂×C₅×Q₈	—	6	32	no	—
242	C₂×C₅×Q₈	—	6	4	no	—
243	C₂×C₅×D₄	—	2	4	no	—
244	C₂×C₅×D₄	—	3	4	no	—
245	C₂×C₅×D₄	—	3	4	no	—
246	C₂×C₅×D₄	—	6	4	no	—
247	C₂×C₅×D₄	—	6	4	no	—
248	C₂×C₅×D₄	C₂²×D₃	1	4	yes	—
249	C₂²×C₄×C₅	—	2	4	no	—
250	C₂²×C₄×C₅	—	3	8	no	—
251	C₂²×C₄×C₅	—	3	4	no	—
252	C₂²×C₄×C₅	—	3	1	no	—
253	C₂²×C₄×C₅	—	3	1	no	—
254	C₂²×C₄×C₅	—	3	4	no	—
255	C₂²×C₄×C₅	—	3	4	no	—
256	C₂²×C₄×C₅	—	3	2	no	—
257	C₂²×C₄×C₅	—	3	2	no	—
258	C₂²×C₄×C₅	—	3	1	no	—
259	C₂²×C₄×C₅	—	3	4	no	—
260	C₂²×C₄×C₅	—	6	4	no	—
261	C₂²×C₄×C₅	—	6	4	no	—
262	C₂²×C₄×C₅	—	6	4	no	—
263	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
264	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
265	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
266	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
267	C₅×C₄⋊C₄	—	3	8	no	—
268	C₅×C₄⋊C₄	—	3	8	no	—
269	C₅×C₄⋊C₄	—	3	8	no	—
270	C₅×C₄⋊C₄	—	3	8	no	—
271	C₅×C₄⋊C₄	C₂²×D₃	1	8	yes	—
272	C₅×C₂²⋊C₄	—	3	4	no	—
273	C₅×C₂²⋊C₄	—	3	8	no	—
274	C₅×C₂²⋊C₄	—	3	8	no	—
275	C₅×C₂²⋊C₄	—	3	8	no	—
276	C₅×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
277	C₅×C₂²⋊C₄	C₂²×D₃	1	8	yes	—
278	C₄²×C₅	—	3	8	no	—
279	C₂²×#41	—	3	1	no	—
280	C₂³×Q₈	—	3	1	no	—
281	#536	—	3	16	no	—
282	C₂×C₄⋊Q₈	—	3	2	no	—
283	C₂×#124	—	3	2	no	—
284	C₂×#123	—	3	1	no	—
285	C₂×#123	—	3	1	no	—
286	C₂×#123	—	3	1	no	—
287	C₂×#123	C₅×D₃	1	1	yes	characteristic, complemented
288	C₂×C₂²⋊Q₈	—	3	2	no	—
289	C₂×C₂²⋊Q₈	—	3	2	no	—
290	C₂×#117	—	3	1	no	—
291	C₂²×C₃×C₅	—	2	8	no	—
292	C₂²×C₃×C₅	—	2	4	no	—
293	C₂²×C₃×C₅	—	2	2	no	—
294	C₂²×C₃×C₅	—	2	4	no	—
295	C₂²×C₃×C₅	—	4	4	no	—
296	C₂²×C₃×C₅	C₂²×D₄	1	4	yes	—
297	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
298	C₂²×C₃×C₅	2₋¹⁺⁴	1	4	yes	—
299	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
300	C₂×C₅×D₃	—	2	2	no	—
301	C₂×C₅×D₃	—	2	4	no	—
302	C₂×C₅×D₃	—	4	4	no	—
303	C₃×C₄×C₅	—	2	4	no	—
304	C₃×C₄×C₅	—	2	2	no	—
305	C₃×C₄×C₅	—	2	4	no	—
306	C₅×Dic₃	—	2	4	no	—
307	C₅×Dic₃	—	2	2	no	—
308	C₅×Dic₃	—	2	4	no	—
309	C₅×Dic₃	C₂²×D₄	1	4	yes	—
310	C₅×Dic₃	C₂²×D₄	1	4	yes	—
311	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
312	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
313	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
314	C₂×C₃×D₄	—	2	4	no	—
315	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
316	C₂²×C₃×C₄	—	2	4	no	—
317	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
318	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
319	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
320	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
321	C₂×#67	—	2	4	no	—
322	C₂×#67	—	2	4	no	—
323	C₂×#67	C₂³×C₅	1	4	yes	—
324	C₂×#67	C₂³×C₅	1	4	yes	—
325	C₂²×Dic₃	—	2	4	no	—
326	C₂²×Dic₃	—	2	4	no	—
327	C₂²×Dic₃	C₅×D₄	1	8	yes	—
328	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
329	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
330	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
331	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
332	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
333	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
334	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
335	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
336	#237	—	2	32	no	—
337	C₂×C₄×D₃	—	2	4	no	—
338	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
339	C₂×Dic₆	—	2	8	no	—
340	C₂×Dic₆	—	2	8	no	—
341	C₂×Dic₆	—	2	32	no	—
342	C₂×Dic₆	—	2	4	no	—
343	C₂×Dic₆	C₂³×C₅	1	8	yes	—
344	C₂×Dic₆	C₂³×C₅	1	8	yes	—
345	C₂×Dic₆	C₂³×C₅	1	4	yes	—
346	C₃×C₄⋊C₄	C₂³×C₅	1	8	yes	—
347	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
348	C₃×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
349	#217	C₂³×C₅	1	4	yes	—
350	#217	C₂³×C₅	1	8	yes	—
351	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
352	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
353	C₄⋊Dic₃	C₂³×C₅	1	8	yes	—
354	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
355	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
356	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
357	C₄×Dic₃	C₂³×C₅	1	8	yes	—
358	C₂³×C₅	—	2	4	no	—
359	C₂³×C₅	—	2	2	no	—
360	C₂³×C₅	—	2	4	no	—
361	C₂³×C₅	—	3	2	no	—
362	C₂³×C₅	—	6	2	no	—
363	C₂³×C₅	—	6	4	no	—
364	C₂³×C₅	D₃×D₄	1	4	yes	—
365	C₂³×C₅	C₂³×D₃	1	2	yes	—
366	C₂³×C₅	C₂³×D₃	1	2	yes	—
367	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
368	C₅×Q₈	—	6	16	no	—
369	C₅×Q₈	—	6	16	no	—
370	C₅×Q₈	—	6	8	no	—
371	C₅×D₄	—	2	8	no	—
372	C₅×D₄	—	6	8	no	—
373	C₅×D₄	—	6	8	no	—
374	C₂×C₄×C₅	—	2	8	no	—
375	C₂×C₄×C₅	—	2	4	no	—
376	C₂×C₄×C₅	—	2	2	no	—
377	C₂×C₄×C₅	—	2	4	no	—
378	C₂×C₄×C₅	—	3	4	no	—
379	C₂×C₄×C₅	—	3	4	no	—
380	C₂×C₄×C₅	—	3	16	no	—
381	C₂×C₄×C₅	—	3	2	no	—
382	C₂×C₄×C₅	—	3	2	no	—
383	C₂×C₄×C₅	—	3	4	no	—
384	C₂×C₄×C₅	—	3	4	no	—
385	C₂×C₄×C₅	—	3	2	no	—
386	C₂×C₄×C₅	—	6	8	no	—
387	C₂×C₄×C₅	—	6	8	no	—
388	C₂×C₄×C₅	—	6	2	no	—
389	C₂×C₄×C₅	—	6	8	no	—
390	C₂×C₄×C₅	—	6	4	no	—
391	C₂×C₄×C₅	—	6	4	no	—
392	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
393	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
394	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
395	C₂×#41	—	3	8	no	—
396	C₂×#41	—	6	8	no	—
397	C₂²×Q₈	—	3	2	no	—
398	C₂²×Q₈	—	3	2	no	—
399	C₂²×Q₈	—	3	1	no	—
400	C₂²×Q₈	—	3	8	no	—
401	C₂²×Q₈	—	6	8	no	—
402	C₂²×D₄	—	3	1	no	—
403	C₂²×D₄	—	3	1	no	—
404	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
405	C₂³×C₄	—	3	1	no	—
406	C₂³×C₄	—	3	1	no	—
407	C₂³×C₄	—	3	1	no	—
408	C₂³×C₄	—	3	1	no	—
409	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
410	C₄⋊Q₈	—	3	16	no	—
411	#124	—	3	16	no	—
412	#123	—	3	8	no	—
413	#123	—	3	8	no	—
414	#123	—	3	8	no	—
415	#123	C₂×C₅×D₃	1	8	yes	complemented
416	C₂²⋊Q₈	—	3	16	no	—
417	C₂²⋊Q₈	—	3	16	no	—
418	#117	—	3	8	no	—
419	C₂×C₄⋊C₄	—	3	2	no	—
420	C₂×C₄⋊C₄	—	3	2	no	—
421	C₂×C₄⋊C₄	—	3	2	no	—
422	C₂×C₄⋊C₄	—	3	2	no	—
423	C₂×C₄⋊C₄	C₂×C₅×D₃	1	2	yes	—
424	C₂×C₂²⋊C₄	—	3	1	no	—
425	C₂×C₂²⋊C₄	—	3	2	no	—
426	C₂×C₂²⋊C₄	—	3	2	no	—
427	C₂×C₂²⋊C₄	—	3	2	no	—
428	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
429	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	2	yes	—
430	C₂×C₄²	—	3	2	no	—
431	C₂×C₃×C₅	—	2	4	no	—
432	C₂×C₃×C₅	—	4	2	no	—
433	C₂×C₃×C₅	#536	1	4	yes	complemented
434	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
435	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	2	yes	—
436	C₅×D₃	—	4	2	no	—
437	C₂³×C₃	—	2	4	no	—
438	C₂³×C₃	—	2	2	no	—
439	C₂³×C₃	—	2	4	no	—
440	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
441	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
442	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
443	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
444	C₂²×D₃	—	2	2	no	—
445	C₂²×D₃	—	2	4	no	—
446	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
447	C₃×D₄	—	2	8	no	—
448	C₂×C₃×C₄	—	2	8	no	—
449	C₂×C₃×C₄	—	2	4	no	—
450	C₂×C₃×C₄	—	2	2	no	—
451	C₂×C₃×C₄	—	2	4	no	—
452	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
453	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
454	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
455	#67	—	2	8	no	—
456	#67	—	2	8	no	—
457	C₂×Dic₃	—	2	8	no	—
458	C₂×Dic₃	—	2	4	no	—
459	C₂×Dic₃	—	2	2	no	—
460	C₂×Dic₃	—	2	4	no	—
461	C₂×Dic₃	—	2	8	no	—
462	C₂×Dic₃	C₂×C₅×D₄	1	4	yes	—
463	C₂×Dic₃	C₂×C₅×D₄	1	4	yes	—
464	C₂×Dic₃	C₂×C₅×D₄	1	16	yes	—
465	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
466	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
467	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
468	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
469	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
470	C₄×D₃	—	2	8	no	—
471	Dic₆	—	2	16	no	—
472	Dic₆	—	2	16	no	—
473	Dic₆	—	2	8	no	—
474	C₂²×C₅	—	2	8	no	—
475	C₂²×C₅	—	2	4	no	—
476	C₂²×C₅	—	2	2	no	—
477	C₂²×C₅	—	2	4	no	—
478	C₂²×C₅	—	4	4	no	—
479	C₂²×C₅	—	6	2	no	—
480	C₂²×C₅	—	6	4	no	—
481	C₂²×C₅	—	12	4	no	—
482	C₂²×C₅	C₂×D₃×D₄	1	4	yes	—
483	C₂²×C₅	C₂×D₃×D₄	1	2	yes	—
484	C₂²×C₅	#1010	1	4	yes	—
485	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
486	C₄×C₅	—	2	4	no	—
487	C₄×C₅	—	2	2	no	—
488	C₄×C₅	—	2	4	no	—
489	C₄×C₅	—	3	4	no	—
490	C₄×C₅	—	3	4	no	—
491	C₄×C₅	—	6	2	no	—
492	C₄×C₅	—	6	4	no	—
493	C₄×C₅	—	6	4	no	—
494	C₂⁴	—	3	1	no	—
495	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
496	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
497	#41	—	6	32	no	—
498	C₂×Q₈	—	3	8	no	—
499	C₂×Q₈	—	3	8	no	—
500	C₂×Q₈	—	3	4	no	—
501	C₂×Q₈	—	6	8	no	—
502	C₂×Q₈	—	6	8	no	—
503	C₂×Q₈	—	6	32	no	—
504	C₂×Q₈	—	6	4	no	—
505	C₂×D₄	—	2	4	no	—
506	C₂×D₄	—	3	4	no	—
507	C₂×D₄	—	3	4	no	—
508	C₂×D₄	—	6	4	no	—
509	C₂×D₄	—	6	4	no	—
510	C₂×D₄	C₂²×C₅×D₃	1	4	yes	—
511	C₂²×C₄	—	2	4	no	—
512	C₂²×C₄	—	3	8	no	—
513	C₂²×C₄	—	3	1	no	—
514	C₂²×C₄	—	3	1	no	—
515	C₂²×C₄	—	3	4	no	—
516	C₂²×C₄	—	3	2	no	—
517	C₂²×C₄	—	3	2	no	—
518	C₂²×C₄	—	3	1	no	—
519	C₂²×C₄	—	3	4	no	—
520	C₂²×C₄	—	3	4	no	—
521	C₂²×C₄	—	3	4	no	—
522	C₂²×C₄	—	6	4	no	—
523	C₂²×C₄	—	6	4	no	—
524	C₂²×C₄	—	6	4	no	—
525	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
526	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
527	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
528	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
529	C₄⋊C₄	—	3	8	no	—
530	C₄⋊C₄	—	3	8	no	—
531	C₄⋊C₄	—	3	8	no	—
532	C₄⋊C₄	—	3	8	no	—
533	C₄⋊C₄	C₂²×C₅×D₃	1	8	yes	—
534	C₂²⋊C₄	—	3	4	no	—
535	C₂²⋊C₄	—	3	8	no	—
536	C₂²⋊C₄	—	3	8	no	—
537	C₂²⋊C₄	—	3	8	no	—
538	C₂²⋊C₄	C₂²×C₅×D₃	1	4	yes	—
539	C₂²⋊C₄	C₂²×C₅×D₃	1	8	yes	—
540	C₄²	—	3	8	no	—
541	C₃×C₅	C₂×#536	1	1	yes	characteristic, complemented, Hall
542	C₂²×C₃	—	2	8	no	—
543	C₂²×C₃	—	2	4	no	—
544	C₂²×C₃	—	2	2	no	—
545	C₂²×C₃	—	2	4	no	—
546	C₂²×C₃	—	4	4	no	—
547	C₂²×C₃	C₂²×C₅×D₄	1	4	yes	—
548	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
549	C₂²×C₃	C₅×2₋¹⁺⁴	1	4	yes	—
550	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
551	C₂×D₃	—	2	2	no	—
552	C₂×D₃	—	2	4	no	—
553	C₂×D₃	—	4	4	no	—
554	C₃×C₄	—	2	4	no	—
555	C₃×C₄	—	2	2	no	—
556	C₃×C₄	—	2	4	no	—
557	Dic₃	—	2	4	no	—
558	Dic₃	—	2	2	no	—
559	Dic₃	—	2	4	no	—
560	Dic₃	C₂²×C₅×D₄	1	4	yes	—
561	Dic₃	C₂²×C₅×D₄	1	4	yes	—
562	C₂×C₅	—	2	4	no	—
563	C₂×C₅	—	4	2	no	—
564	C₂×C₅	—	12	2	no	—
565	C₂×C₅	#5648	1	4	yes	direct product factor
566	C₂×C₅	C₂²×D₃×D₄	1	1	yes	characteristic
567	C₂×C₅	C₂×#1010	1	2	yes	—
568	C₂³	—	2	4	no	—
569	C₂³	—	2	2	no	—
570	C₂³	—	2	4	no	—
571	C₂³	—	3	2	no	—
572	C₂³	—	6	2	no	—
573	C₂³	—	6	4	no	—
574	C₂³	C₅×D₃×D₄	1	4	yes	—
575	C₂³	C₂³×C₅×D₃	1	2	yes	—
576	C₂³	C₂³×C₅×D₃	1	2	yes	—
577	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
578	Q₈	—	6	16	no	—
579	Q₈	—	6	16	no	—
580	Q₈	—	6	8	no	—
581	D₄	—	2	8	no	—
582	D₄	—	6	8	no	—
583	D₄	—	6	8	no	—
584	C₂×C₄	—	2	8	no	—
585	C₂×C₄	—	2	4	no	—
586	C₂×C₄	—	2	2	no	—
587	C₂×C₄	—	2	4	no	—
588	C₂×C₄	—	3	4	no	—
589	C₂×C₄	—	3	4	no	—
590	C₂×C₄	—	3	16	no	—
591	C₂×C₄	—	3	2	no	—
592	C₂×C₄	—	3	2	no	—
593	C₂×C₄	—	3	4	no	—
594	C₂×C₄	—	3	4	no	—
595	C₂×C₄	—	3	2	no	—
596	C₂×C₄	—	6	8	no	—
597	C₂×C₄	—	6	8	no	—
598	C₂×C₄	—	6	2	no	—
599	C₂×C₄	—	6	8	no	—
600	C₂×C₄	—	6	4	no	—
601	C₂×C₄	—	6	4	no	—
602	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
603	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
604	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
605	C₂×C₃	—	2	4	no	—
606	C₂×C₃	—	4	2	no	—
607	C₂×C₃	C₅×#536	1	4	yes	complemented
608	C₂×C₃	C₂³×C₅×D₄	1	1	yes	characteristic
609	C₂×C₃	C₂×C₅×2₋¹⁺⁴	1	2	yes	—
610	D₃	—	4	2	no	—
611	C₅	C₂×#5648	1	1	yes	characteristic, direct product factor, Sylow
612	C₂²	—	2	8	no	—
613	C₂²	—	2	4	no	—
614	C₂²	—	2	2	no	—
615	C₂²	—	2	4	no	—
616	C₂²	—	4	4	no	—
617	C₂²	—	6	2	no	—
618	C₂²	—	6	4	no	—
619	C₂²	—	12	4	no	—
620	C₂²	C₂×C₅×D₃×D₄	1	4	yes	—
621	C₂²	C₂×C₅×D₃×D₄	1	2	yes	—
622	C₂²	C₅×#1010	1	4	yes	—
623	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
624	C₄	—	2	4	no	—
625	C₄	—	2	2	no	—
626	C₄	—	2	4	no	—
627	C₄	—	3	4	no	—
628	C₄	—	3	4	no	—
629	C₄	—	6	2	no	—
630	C₄	—	6	4	no	—
631	C₄	—	6	4	no	—
632	C₃	C₂×C₅×#536	1	1	yes	characteristic, complemented, Sylow
633	C₂	—	2	4	no	—
634	C₂	—	4	2	no	—
635	C₂	—	12	2	no	—
636	C₂	C₅×#5648	1	4	yes	direct product factor
637	C₂	C₂²×C₅×D₃×D₄	1	1	yes	characteristic
638	C₂	C₂×C₅×#1010	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×#123	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂²×C₅×#237	C₂
hypercenter	C₂×C₅×#123	D₃
hypocenter	C₃	C₂×C₅×#536
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₅×#123

Complements

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

N	H ≅ G/N	type
2. C₂³×C₅×Dic₆	C₂	semidirect
3. C₂×C₃×C₅×#123	C₂	semidirect
4. C₂×C₅×#935	C₂	semidirect
5. C₂×C₅×#929	C₂	semidirect
6. C₅×#5648	C₂	direct (N × H)
7. C₂×C₅×#896	C₂	semidirect
8. C₂×C₅×#888	C₂	semidirect
9. C₂×C₅×#886	C₂	semidirect
10. C₂×C₅×#885	C₂	semidirect
11. C₂×C₅×#878	C₂	semidirect
12. C₂×C₅×#877	C₂	semidirect
28. C₂²×C₅×Dic₆	C₂²	semidirect
29. C₃×C₅×#123	C₂²	semidirect
35. C₅×#935	C₂²	semidirect
36. C₅×#929	C₂²	semidirect
44. C₅×#896	C₂²	semidirect
45. C₅×#888	C₂²	semidirect
46. C₅×#886	C₂²	semidirect
47. C₅×#885	C₂²	semidirect
48. C₅×#878	C₂²	semidirect
49. C₅×#877	C₂²	semidirect
50. C₂×#5648	C₅	direct (N × H)
59. C₂×C₅×#123	D₃	semidirect
111. C₂³×Dic₆	C₂×C₅	semidirect
112. C₂×C₃×#123	C₂×C₅	semidirect
113. C₂×#935	C₂×C₅	semidirect
114. C₂×#929	C₂×C₅	semidirect
115. #5648	C₂×C₅	direct (N × H)
116. C₂×#896	C₂×C₅	semidirect
117. C₂×#888	C₂×C₅	semidirect
118. C₂×#886	C₂×C₅	semidirect
119. C₂×#885	C₂×C₅	semidirect
120. C₂×#878	C₂×C₅	semidirect
121. C₂×#877	C₂×C₅	semidirect
142. C₅×#123	C₂×D₃	semidirect
210. C₂²×Dic₆	C₂²×C₅	semidirect
211. C₃×#123	C₂²×C₅	semidirect
217. #935	C₂²×C₅	semidirect
218. #929	C₂²×C₅	semidirect
226. #896	C₂²×C₅	semidirect
227. #888	C₂²×C₅	semidirect
228. #886	C₂²×C₅	semidirect
229. #885	C₂²×C₅	semidirect
230. #878	C₂²×C₅	semidirect
231. #877	C₂²×C₅	semidirect
287. C₂×#123	C₅×D₃	semidirect
415. #123	C₂×C₅×D₃	semidirect
433. C₂×C₃×C₅	#536	semidirect
541. C₃×C₅	C₂×#536	semidirect
565. C₂×C₅	#5648	direct (N × H)
607. C₂×C₃	C₅×#536	semidirect
611. C₅	C₂×#5648	direct (N × H)
632. C₃	C₂×C₅×#536	semidirect
636. C₂	C₅×#5648	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×#237	2
C₂³×C₅×Dic₆	2
C₂×C₃×C₅×#123	2
C₂×C₅×#935	2
C₂×C₅×#929	2
C₅×#5648	2
C₂×C₅×#896	2
C₂×C₅×#888	2
C₂×C₅×#886	2
C₂×C₅×#885	2
C₂×C₅×#878	2
C₂×C₅×#877	2
C₂×C₅×#536	3
C₂×#5648	5

Subgroups — C2×C5×#5648 #14480467

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5648 #14480467