Subgroups — C₂×C₅×#5513 #14483406

Order 1920.

2248 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#929	C₂	1	2	yes	maximal
3	C₂×C₄×C₅×#67	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×#926	C₂	1	2	yes	maximal, complemented
5	C₂×C₅×#924	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5513	C₂	1	16	yes	maximal, direct product factor
7	C₂×C₅×#898	C₂	1	2	yes	maximal, complemented
8	C₂×C₅×#897	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×#892	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅×#890	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅×#889	C₂	1	2	yes	maximal, complemented
12	C₂×C₅×#887	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₅×#552	—	3	1	no	maximal, Hall
14	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
15	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
16	C₂²×C₅×#67	C₂²	1	1	yes	characteristic
17	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
18	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
21	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	8	yes	complemented
23	C₂×C₅×#217	C₂²	1	2	yes	—
24	C₂×C₅×#217	C₂²	1	1	yes	characteristic
25	C₅×#929	C₂²	1	16	yes	—
26	C₄×C₅×#67	C₂²	1	8	yes	—
27	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
28	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
29	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
30	C₅×#926	C₂²	1	16	yes	complemented
31	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
32	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
33	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
34	C₅×#924	C₂²	1	8	yes	complemented
35	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
36	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
37	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
38	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
39	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
41	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
42	C₅×#898	C₂²	1	16	yes	complemented
43	C₅×#897	C₂²	1	8	yes	complemented
44	C₅×#892	C₂²	1	8	yes	complemented
45	C₅×#890	C₂²	1	8	yes	complemented
46	C₅×#889	C₂²	1	16	yes	complemented
47	C₅×#887	C₂²	1	8	yes	complemented
48	C₂×#5513	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
49	C₅×#552	—	3	16	no	—
50	C₂×C₅×#126	—	3	2	no	—
51	C₂×C₅×#125	—	3	2	no	—
52	C₂×C₅×#125	—	3	1	no	—
53	C₂×C₅×#123	—	3	2	no	—
54	C₂×C₅×C₂²⋊Q₈	—	3	1	no	—
55	C₂×C₅×C₂²⋊Q₈	—	3	1	no	—
56	C₂×C₄×C₅×Q₈	—	3	1	no	—
57	C₂×C₄×C₅×D₄	—	3	1	no	—
58	C₂×C₅×#117	—	3	2	no	—
59	C₂×C₅×#117	—	3	1	no	—
60	C₂²×C₅×C₄⋊C₄	D₃	1	1	yes	characteristic, complemented
61	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
62	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
63	C₂²×C₃×C₄×C₅	—	2	8	no	—
64	C₂²×C₃×C₄×C₅	—	2	4	no	—
65	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
66	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
67	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
68	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
69	C₂²×C₃×C₄×C₅	C₂³	1	8	yes	—
70	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
71	C₂×C₅×#67	—	2	4	no	—
72	C₂×C₅×#67	C₂³	1	4	yes	—
73	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
74	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
75	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
76	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
77	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
78	C₂×C₄×C₅×D₃	—	2	4	no	—
79	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
80	C₂×C₅×Dic₆	—	2	4	no	—
81	C₂×C₅×Dic₆	C₂³	1	4	yes	—
82	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
83	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	—
84	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
85	C₅×#217	C₂³	1	8	yes	—
86	C₅×#217	C₂³	1	4	yes	—
87	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
88	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
89	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
90	C₅×C₄⋊Dic₃	C₂³	1	8	yes	—
91	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
92	C₅×C₄⋊Dic₃	C₂³	1	8	yes	—
93	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
94	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
95	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
96	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
97	C₄×C₅×Dic₃	C₂³	1	4	yes	—
98	C₄×C₅×Dic₃	C₂³	1	8	yes	—
99	C₄×C₅×Dic₃	C₂³	1	8	yes	—
100	C₂²×C₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
101	C₂×#929	C₂×C₅	1	2	yes	—
102	C₂×C₄×#67	C₂×C₅	1	1	yes	characteristic
103	C₂×#926	C₂×C₅	1	2	yes	complemented
104	C₂×#924	C₂×C₅	1	1	yes	characteristic, complemented
105	#5513	C₂×C₅	1	16	yes	direct product factor
106	C₂×#898	C₂×C₅	1	2	yes	complemented
107	C₂×#897	C₂×C₅	1	1	yes	characteristic, complemented
108	C₂×#892	C₂×C₅	1	1	yes	characteristic, complemented
109	C₂×#890	C₂×C₅	1	1	yes	characteristic, complemented
110	C₂×#889	C₂×C₅	1	2	yes	complemented
111	C₂×#887	C₂×C₅	1	1	yes	characteristic, complemented
112	C₂²×C₅×Q₈	—	3	1	no	—
113	C₂²×C₅×D₄	—	3	1	no	—
114	C₂³×C₄×C₅	—	3	1	no	—
115	C₂³×C₄×C₅	C₂×D₃	1	2	yes	—
116	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
117	C₅×#126	—	3	16	no	—
118	C₅×#125	—	3	16	no	—
119	C₅×#125	—	3	8	no	—
120	C₅×#123	—	3	16	no	—
121	C₅×C₂²⋊Q₈	—	3	8	no	—
122	C₅×C₂²⋊Q₈	—	3	8	no	—
123	C₄×C₅×Q₈	—	3	8	no	—
124	C₄×C₅×D₄	—	3	8	no	—
125	C₅×#117	—	3	16	no	—
126	C₅×#117	—	3	8	no	—
127	C₂×C₅×C₄⋊C₄	—	3	1	no	—
128	C₂×C₅×C₄⋊C₄	—	3	2	no	—
129	C₂×C₅×C₄⋊C₄	—	3	2	no	—
130	C₂×C₅×C₄⋊C₄	—	3	2	no	—
131	C₂×C₅×C₄⋊C₄	—	3	2	no	—
132	C₂×C₅×C₄⋊C₄	—	3	1	no	—
133	C₂×C₅×C₄⋊C₄	—	3	2	no	—
134	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
135	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
136	C₂×C₅×C₄⋊C₄	C₂×D₃	1	2	yes	—
137	C₂×C₅×C₄⋊C₄	C₂×D₃	1	8	yes	complemented
138	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
139	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
140	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
141	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
142	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
143	C₂×C₄²×C₅	—	3	2	no	—
144	C₂×C₄²×C₅	—	3	2	no	—
145	C₂×C₄²×C₅	—	3	1	no	—
146	C₂×#552	—	3	1	no	Sylow
147	C₂³×C₃×C₅	—	2	2	no	—
148	C₂³×C₃×C₅	—	2	2	no	—
149	C₂³×C₃×C₅	#41	1	4	yes	—
150	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
151	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
152	C₂²×C₅×D₃	—	2	2	no	—
153	C₂²×C₅×D₃	—	2	2	no	—
154	C₂²×C₅×D₃	—	2	2	no	—
155	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
156	C₂×C₃×C₄×C₅	—	2	2	no	—
157	C₂×C₃×C₄×C₅	—	2	16	no	—
158	C₂×C₃×C₄×C₅	—	2	4	no	—
159	C₂×C₃×C₄×C₅	—	2	4	no	—
160	C₂×C₃×C₄×C₅	—	2	8	no	—
161	C₂×C₃×C₄×C₅	#41	1	4	yes	—
162	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
163	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
164	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
165	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
166	C₅×#67	—	2	8	no	—
167	C₂×C₅×Dic₃	—	2	4	no	—
168	C₂×C₅×Dic₃	—	2	2	no	—
169	C₂×C₅×Dic₃	—	2	2	no	—
170	C₂×C₅×Dic₃	—	2	2	no	—
171	C₂×C₅×Dic₃	—	2	4	no	—
172	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
173	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
174	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
175	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
176	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
177	C₄×C₅×D₃	—	2	8	no	—
178	C₅×Dic₆	—	2	8	no	—
179	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
180	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
181	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
182	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
183	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
184	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
185	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
186	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
187	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	8	yes	complemented
188	C₂×#217	C₂²×C₅	1	2	yes	—
189	C₂×#217	C₂²×C₅	1	1	yes	characteristic
190	#929	C₂²×C₅	1	16	yes	—
191	C₄×#67	C₂²×C₅	1	8	yes	—
192	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
193	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
194	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
195	#926	C₂²×C₅	1	16	yes	complemented
196	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
197	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
198	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
199	#924	C₂²×C₅	1	8	yes	complemented
200	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
201	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
202	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
203	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
204	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
205	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
206	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
207	#898	C₂²×C₅	1	16	yes	complemented
208	#897	C₂²×C₅	1	8	yes	complemented
209	#892	C₂²×C₅	1	8	yes	complemented
210	#890	C₂²×C₅	1	8	yes	complemented
211	#889	C₂²×C₅	1	16	yes	complemented
212	#887	C₂²×C₅	1	8	yes	complemented
213	C₂⁴×C₅	—	3	1	no	—
214	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
215	C₂×C₅×Q₈	—	3	4	no	—
216	C₂×C₅×Q₈	—	6	4	no	—
217	C₂×C₅×D₄	—	3	4	no	—
218	C₂×C₅×D₄	—	6	4	no	—
219	C₂²×C₄×C₅	—	2	8	no	—
220	C₂²×C₄×C₅	—	2	4	no	—
221	C₂²×C₄×C₅	—	3	1	no	—
222	C₂²×C₄×C₅	—	3	1	no	—
223	C₂²×C₄×C₅	—	3	2	no	—
224	C₂²×C₄×C₅	—	3	2	no	—
225	C₂²×C₄×C₅	—	3	1	no	—
226	C₂²×C₄×C₅	—	3	4	no	—
227	C₂²×C₄×C₅	—	6	4	no	—
228	C₂²×C₄×C₅	C₂²×D₃	1	8	yes	—
229	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
230	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
231	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
232	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
233	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
234	C₅×C₄⋊C₄	—	3	8	no	—
235	C₅×C₄⋊C₄	—	3	4	no	—
236	C₅×C₄⋊C₄	—	3	8	no	—
237	C₅×C₄⋊C₄	—	3	4	no	—
238	C₅×C₄⋊C₄	—	3	8	no	—
239	C₅×C₄⋊C₄	—	3	8	no	—
240	C₅×C₄⋊C₄	—	3	8	no	—
241	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
242	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
243	C₅×C₄⋊C₄	C₂²×D₃	1	8	yes	—
244	C₅×C₂²⋊C₄	—	3	4	no	—
245	C₅×C₂²⋊C₄	—	3	8	no	—
246	C₅×C₂²⋊C₄	—	3	8	no	—
247	C₅×C₂²⋊C₄	—	3	4	no	—
248	C₅×C₂²⋊C₄	—	3	8	no	—
249	C₄²×C₅	—	3	8	no	—
250	C₄²×C₅	—	3	8	no	—
251	C₄²×C₅	—	3	4	no	—
252	#552	—	3	16	no	—
253	C₂×#126	—	3	2	no	—
254	C₂×#125	—	3	2	no	—
255	C₂×#125	—	3	1	no	—
256	C₂×#123	—	3	2	no	—
257	C₂×C₂²⋊Q₈	—	3	1	no	—
258	C₂×C₂²⋊Q₈	—	3	1	no	—
259	C₂×C₄×Q₈	—	3	1	no	—
260	C₂×C₄×D₄	—	3	1	no	—
261	C₂×#117	—	3	2	no	—
262	C₂×#117	—	3	1	no	—
263	C₂²×C₄⋊C₄	C₅×D₃	1	1	yes	characteristic, complemented
264	C₂²×C₃×C₅	—	2	8	no	—
265	C₂²×C₃×C₅	—	2	2	no	—
266	C₂²×C₃×C₅	—	2	2	no	—
267	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
268	C₂²×C₃×C₅	C₂×#41	1	4	yes	—
269	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
270	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
271	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
272	C₂×C₅×D₃	—	2	2	no	—
273	C₂×C₅×D₃	—	2	2	no	—
274	C₂×C₅×D₃	—	2	2	no	—
275	C₂×C₅×D₃	—	4	4	no	—
276	C₃×C₄×C₅	—	2	2	no	—
277	C₃×C₄×C₅	—	2	4	no	—
278	C₃×C₄×C₅	—	2	4	no	—
279	C₃×C₄×C₅	C₂×#41	1	4	yes	—
280	C₅×Dic₃	—	2	4	no	—
281	C₅×Dic₃	—	2	2	no	—
282	C₅×Dic₃	—	2	2	no	—
283	C₅×Dic₃	—	2	2	no	—
284	C₅×Dic₃	—	2	4	no	—
285	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
286	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
287	C₂²×C₃×C₄	—	2	8	no	—
288	C₂²×C₃×C₄	—	2	4	no	—
289	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
290	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
291	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
292	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
293	C₂²×C₃×C₄	C₂³×C₅	1	8	yes	—
294	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
295	C₂×#67	—	2	4	no	—
296	C₂×#67	C₂³×C₅	1	4	yes	—
297	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
298	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
299	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
300	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
301	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
302	C₂×C₄×D₃	—	2	4	no	—
303	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
304	C₂×Dic₆	—	2	4	no	—
305	C₂×Dic₆	C₂³×C₅	1	4	yes	—
306	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
307	C₃×C₄⋊C₄	C₂³×C₅	1	8	yes	—
308	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
309	#217	C₂³×C₅	1	8	yes	—
310	#217	C₂³×C₅	1	4	yes	—
311	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
312	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
313	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
314	C₄⋊Dic₃	C₂³×C₅	1	8	yes	—
315	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
316	C₄⋊Dic₃	C₂³×C₅	1	8	yes	—
317	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
318	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
319	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
320	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
321	C₄×Dic₃	C₂³×C₅	1	4	yes	—
322	C₄×Dic₃	C₂³×C₅	1	8	yes	—
323	C₄×Dic₃	C₂³×C₅	1	8	yes	—
324	C₂³×C₅	—	2	2	no	—
325	C₂³×C₅	—	2	2	no	—
326	C₂³×C₅	—	3	2	no	—
327	C₂³×C₅	—	6	2	no	—
328	C₂³×C₅	—	6	2	no	—
329	C₂³×C₅	—	6	2	no	—
330	C₂³×C₅	#237	1	4	yes	—
331	C₂³×C₅	C₂³×D₃	1	2	yes	—
332	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
333	C₅×Q₈	—	6	8	no	—
334	C₅×D₄	—	6	8	no	—
335	C₂×C₄×C₅	—	2	2	no	—
336	C₂×C₄×C₅	—	2	16	no	—
337	C₂×C₄×C₅	—	2	4	no	—
338	C₂×C₄×C₅	—	2	4	no	—
339	C₂×C₄×C₅	—	2	8	no	—
340	C₂×C₄×C₅	—	3	2	no	—
341	C₂×C₄×C₅	—	3	2	no	—
342	C₂×C₄×C₅	—	3	4	no	—
343	C₂×C₄×C₅	—	3	4	no	—
344	C₂×C₄×C₅	—	3	2	no	—
345	C₂×C₄×C₅	—	6	2	no	—
346	C₂×C₄×C₅	—	6	4	no	—
347	C₂×C₄×C₅	—	6	2	no	—
348	C₂×C₄×C₅	—	6	2	no	—
349	C₂×C₄×C₅	—	6	4	no	—
350	C₂×C₄×C₅	—	6	8	no	—
351	C₂×C₄×C₅	#235	1	4	yes	—
352	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
353	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
354	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
355	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
356	C₂²×Q₈	—	3	1	no	—
357	C₂²×D₄	—	3	1	no	—
358	C₂³×C₄	—	3	1	no	—
359	C₂³×C₄	C₂×C₅×D₃	1	2	yes	—
360	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
361	#126	—	3	16	no	—
362	#125	—	3	16	no	—
363	#125	—	3	8	no	—
364	#123	—	3	16	no	—
365	C₂²⋊Q₈	—	3	8	no	—
366	C₂²⋊Q₈	—	3	8	no	—
367	C₄×Q₈	—	3	8	no	—
368	C₄×D₄	—	3	8	no	—
369	#117	—	3	16	no	—
370	#117	—	3	8	no	—
371	C₂×C₄⋊C₄	—	3	2	no	—
372	C₂×C₄⋊C₄	—	3	1	no	—
373	C₂×C₄⋊C₄	—	3	2	no	—
374	C₂×C₄⋊C₄	—	3	1	no	—
375	C₂×C₄⋊C₄	—	3	2	no	—
376	C₂×C₄⋊C₄	—	3	2	no	—
377	C₂×C₄⋊C₄	—	3	2	no	—
378	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
379	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
380	C₂×C₄⋊C₄	C₂×C₅×D₃	1	2	yes	—
381	C₂×C₄⋊C₄	C₂×C₅×D₃	1	8	yes	complemented
382	C₂×C₂²⋊C₄	—	3	1	no	—
383	C₂×C₂²⋊C₄	—	3	2	no	—
384	C₂×C₂²⋊C₄	—	3	2	no	—
385	C₂×C₂²⋊C₄	—	3	1	no	—
386	C₂×C₂²⋊C₄	—	3	2	no	—
387	C₂×C₄²	—	3	2	no	—
388	C₂×C₄²	—	3	2	no	—
389	C₂×C₄²	—	3	1	no	—
390	C₂×C₃×C₅	—	2	4	no	—
391	C₂×C₃×C₅	#552	1	4	yes	complemented
392	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
393	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
394	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
395	C₅×D₃	—	4	2	no	—
396	C₂³×C₃	—	2	2	no	—
397	C₂³×C₃	—	2	2	no	—
398	C₂³×C₃	C₅×#41	1	4	yes	—
399	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
400	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
401	C₂²×D₃	—	2	2	no	—
402	C₂²×D₃	—	2	2	no	—
403	C₂²×D₃	—	2	2	no	—
404	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
405	C₂×C₃×C₄	—	2	2	no	—
406	C₂×C₃×C₄	—	2	16	no	—
407	C₂×C₃×C₄	—	2	4	no	—
408	C₂×C₃×C₄	—	2	4	no	—
409	C₂×C₃×C₄	—	2	8	no	—
410	C₂×C₃×C₄	C₅×#41	1	4	yes	—
411	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
412	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
413	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
414	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
415	#67	—	2	8	no	—
416	C₂×Dic₃	—	2	4	no	—
417	C₂×Dic₃	—	2	2	no	—
418	C₂×Dic₃	—	2	2	no	—
419	C₂×Dic₃	—	2	2	no	—
420	C₂×Dic₃	—	2	4	no	—
421	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
422	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
423	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
424	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
425	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
426	C₄×D₃	—	2	8	no	—
427	Dic₆	—	2	8	no	—
428	C₂²×C₅	—	2	2	no	—
429	C₂²×C₅	—	2	2	no	—
430	C₂²×C₅	—	2	8	no	—
431	C₂²×C₅	—	6	2	no	—
432	C₂²×C₅	—	6	2	no	—
433	C₂²×C₅	—	6	2	no	—
434	C₂²×C₅	—	12	4	no	—
435	C₂²×C₅	C₂×#235	1	2	yes	—
436	C₂²×C₅	C₂×#237	1	4	yes	—
437	C₂²×C₅	C₂×#237	1	2	yes	—
438	C₂²×C₅	#1007	1	2	yes	—
439	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
440	C₄×C₅	—	2	2	no	—
441	C₄×C₅	—	2	4	no	—
442	C₄×C₅	—	2	4	no	—
443	C₄×C₅	—	6	2	no	—
444	C₄×C₅	—	6	4	no	—
445	C₄×C₅	—	6	2	no	—
446	C₄×C₅	—	6	2	no	—
447	C₄×C₅	—	6	4	no	—
448	C₄×C₅	C₂×#235	1	4	yes	—
449	C₂⁴	—	3	1	no	—
450	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
451	C₂×Q₈	—	3	4	no	—
452	C₂×Q₈	—	6	4	no	—
453	C₂×D₄	—	3	4	no	—
454	C₂×D₄	—	6	4	no	—
455	C₂²×C₄	—	2	8	no	—
456	C₂²×C₄	—	2	4	no	—
457	C₂²×C₄	—	3	1	no	—
458	C₂²×C₄	—	3	1	no	—
459	C₂²×C₄	—	3	2	no	—
460	C₂²×C₄	—	3	2	no	—
461	C₂²×C₄	—	3	1	no	—
462	C₂²×C₄	—	3	4	no	—
463	C₂²×C₄	—	6	4	no	—
464	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
465	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
466	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
467	C₂²×C₄	C₂²×C₅×D₃	1	8	yes	—
468	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
469	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
470	C₄⋊C₄	—	3	8	no	—
471	C₄⋊C₄	—	3	4	no	—
472	C₄⋊C₄	—	3	8	no	—
473	C₄⋊C₄	—	3	4	no	—
474	C₄⋊C₄	—	3	8	no	—
475	C₄⋊C₄	—	3	8	no	—
476	C₄⋊C₄	—	3	8	no	—
477	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
478	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
479	C₄⋊C₄	C₂²×C₅×D₃	1	8	yes	—
480	C₂²⋊C₄	—	3	4	no	—
481	C₂²⋊C₄	—	3	8	no	—
482	C₂²⋊C₄	—	3	8	no	—
483	C₂²⋊C₄	—	3	4	no	—
484	C₂²⋊C₄	—	3	8	no	—
485	C₄²	—	3	8	no	—
486	C₄²	—	3	8	no	—
487	C₄²	—	3	4	no	—
488	C₃×C₅	C₂×#552	1	1	yes	characteristic, complemented, Hall
489	C₂²×C₃	—	2	8	no	—
490	C₂²×C₃	—	2	2	no	—
491	C₂²×C₃	—	2	2	no	—
492	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
493	C₂²×C₃	C₂×C₅×#41	1	4	yes	—
494	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
495	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
496	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
497	C₂×D₃	—	2	2	no	—
498	C₂×D₃	—	2	2	no	—
499	C₂×D₃	—	2	2	no	—
500	C₂×D₃	—	4	4	no	—
501	C₃×C₄	—	2	2	no	—
502	C₃×C₄	—	2	4	no	—
503	C₃×C₄	—	2	4	no	—
504	C₃×C₄	C₂×C₅×#41	1	4	yes	—
505	Dic₃	—	2	4	no	—
506	Dic₃	—	2	2	no	—
507	Dic₃	—	2	2	no	—
508	Dic₃	—	2	2	no	—
509	Dic₃	—	2	4	no	—
510	C₂×C₅	—	2	4	no	—
511	C₂×C₅	—	12	2	no	—
512	C₂×C₅	#5513	1	4	yes	direct product factor
513	C₂×C₅	C₂²×#235	1	1	yes	characteristic
514	C₂×C₅	C₂²×#237	1	1	yes	characteristic
515	C₂×C₅	C₂×#1007	1	1	yes	characteristic
516	C₂³	—	2	2	no	—
517	C₂³	—	2	2	no	—
518	C₂³	—	3	2	no	—
519	C₂³	—	6	2	no	—
520	C₂³	—	6	2	no	—
521	C₂³	—	6	2	no	—
522	C₂³	C₅×#237	1	4	yes	—
523	C₂³	C₂³×C₅×D₃	1	2	yes	—
524	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
525	Q₈	—	6	8	no	—
526	D₄	—	6	8	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	16	no	—
529	C₂×C₄	—	2	4	no	—
530	C₂×C₄	—	2	4	no	—
531	C₂×C₄	—	2	8	no	—
532	C₂×C₄	—	3	2	no	—
533	C₂×C₄	—	3	2	no	—
534	C₂×C₄	—	3	4	no	—
535	C₂×C₄	—	3	4	no	—
536	C₂×C₄	—	3	2	no	—
537	C₂×C₄	—	6	2	no	—
538	C₂×C₄	—	6	4	no	—
539	C₂×C₄	—	6	2	no	—
540	C₂×C₄	—	6	2	no	—
541	C₂×C₄	—	6	4	no	—
542	C₂×C₄	—	6	8	no	—
543	C₂×C₄	C₅×#235	1	4	yes	—
544	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
545	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
546	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
547	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
548	C₂×C₃	—	2	4	no	—
549	C₂×C₃	C₅×#552	1	4	yes	complemented
550	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
551	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
552	C₂×C₃	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
553	D₃	—	4	2	no	—
554	C₅	C₂×#5513	1	1	yes	characteristic, direct product factor, Sylow
555	C₂²	—	2	2	no	—
556	C₂²	—	2	2	no	—
557	C₂²	—	2	8	no	—
558	C₂²	—	6	2	no	—
559	C₂²	—	6	2	no	—
560	C₂²	—	6	2	no	—
561	C₂²	—	12	4	no	—
562	C₂²	C₂×C₅×#235	1	2	yes	—
563	C₂²	C₂×C₅×#237	1	4	yes	—
564	C₂²	C₂×C₅×#237	1	2	yes	—
565	C₂²	C₅×#1007	1	2	yes	—
566	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
567	C₄	—	2	2	no	—
568	C₄	—	2	4	no	—
569	C₄	—	2	4	no	—
570	C₄	—	6	2	no	—
571	C₄	—	6	4	no	—
572	C₄	—	6	2	no	—
573	C₄	—	6	2	no	—
574	C₄	—	6	4	no	—
575	C₄	C₂×C₅×#235	1	4	yes	—
576	C₃	C₂×C₅×#552	1	1	yes	characteristic, complemented, Sylow
577	C₂	—	2	4	no	—
578	C₂	—	12	2	no	—
579	C₂	C₅×#5513	1	4	yes	direct product factor
580	C₂	C₂²×C₅×#235	1	1	yes	characteristic
581	C₂	C₂²×C₅×#237	1	1	yes	characteristic
582	C₂	C₂×C₅×#1007	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×C₄⋊C₄	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂²×C₅×#67	C₂²
hypercenter	C₂²×C₅×C₄⋊C₄	D₃
hypocenter	C₃	C₂×C₅×#552
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂²×C₅×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₅×C₄⋊C₄	C₂	semidirect
4. C₂×C₅×#926	C₂	semidirect
5. C₂×C₅×#924	C₂	semidirect
6. C₅×#5513	C₂	direct (N × H)
7. C₂×C₅×#898	C₂	semidirect
8. C₂×C₅×#897	C₂	semidirect
9. C₂×C₅×#892	C₂	semidirect
10. C₂×C₅×#890	C₂	semidirect
11. C₂×C₅×#889	C₂	semidirect
12. C₂×C₅×#887	C₂	semidirect
22. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
30. C₅×#926	C₂²	semidirect
34. C₅×#924	C₂²	semidirect
42. C₅×#898	C₂²	semidirect
43. C₅×#897	C₂²	semidirect
44. C₅×#892	C₂²	semidirect
45. C₅×#890	C₂²	semidirect
46. C₅×#889	C₂²	semidirect
47. C₅×#887	C₂²	semidirect
48. C₂×#5513	C₅	direct (N × H)
60. C₂²×C₅×C₄⋊C₄	D₃	semidirect
100. C₂²×C₃×C₄⋊C₄	C₂×C₅	semidirect
103. C₂×#926	C₂×C₅	semidirect
104. C₂×#924	C₂×C₅	semidirect
105. #5513	C₂×C₅	direct (N × H)
106. C₂×#898	C₂×C₅	semidirect
107. C₂×#897	C₂×C₅	semidirect
108. C₂×#892	C₂×C₅	semidirect
109. C₂×#890	C₂×C₅	semidirect
110. C₂×#889	C₂×C₅	semidirect
111. C₂×#887	C₂×C₅	semidirect
137. C₂×C₅×C₄⋊C₄	C₂×D₃	semidirect
187. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
195. #926	C₂²×C₅	semidirect
199. #924	C₂²×C₅	semidirect
207. #898	C₂²×C₅	semidirect
208. #897	C₂²×C₅	semidirect
209. #892	C₂²×C₅	semidirect
210. #890	C₂²×C₅	semidirect
211. #889	C₂²×C₅	semidirect
212. #887	C₂²×C₅	semidirect
263. C₂²×C₄⋊C₄	C₅×D₃	semidirect
381. C₂×C₄⋊C₄	C₂×C₅×D₃	semidirect
391. C₂×C₃×C₅	#552	semidirect
488. C₃×C₅	C₂×#552	semidirect
512. C₂×C₅	#5513	direct (N × H)
549. C₂×C₃	C₅×#552	semidirect
554. C₅	C₂×#5513	direct (N × H)
576. C₃	C₂×C₅×#552	semidirect
579. C₂	C₅×#5513	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×C₄⋊C₄	2
C₂×C₅×#929	2
C₂×C₄×C₅×#67	2
C₂×C₅×#926	2
C₂×C₅×#924	2
C₅×#5513	2
C₂×C₅×#898	2
C₂×C₅×#897	2
C₂×C₅×#892	2
C₂×C₅×#890	2
C₂×C₅×#889	2
C₂×C₅×#887	2
C₂×C₅×#552	3
C₂×#5513	5

Subgroups — C2×C5×#5513 #14483406

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5513 #14483406