Subgroups — C₂×C₅×#5804 #14480293

Order 1920.

3968 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₅×#67	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#953	C₂	1	2	yes	maximal, complemented
4	C₂²×C₅×#217	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5804	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₅×#939	C₂	1	4	yes	maximal, complemented
7	C₂×C₅×#937	C₂	1	2	yes	maximal, complemented
8	C₂×C₅×#935	C₂	1	2	yes	maximal, complemented
9	C₂×C₅×#929	C₂	1	2	yes	maximal, complemented
10	C₂×C₅×#534	—	3	1	no	maximal, Hall
11	C₂⁵×C₃×C₅	C₂²	1	1	yes	characteristic
12	C₂⁵×C₃×C₅	C₂²	1	1	yes	characteristic, complemented
13	C₂⁴×C₅×D₃	C₂²	1	1	yes	characteristic, complemented
14	C₂²×C₃×C₅×D₄	—	2	8	no	—
15	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
16	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	complemented
17	C₂²×C₃×C₅×D₄	C₂²	1	8	yes	complemented
18	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic, complemented
19	C₂²×C₅×#67	—	2	8	no	—
20	C₂²×C₅×#67	C₂²	1	2	yes	—
21	C₂²×C₅×#67	C₂²	1	2	yes	complemented
22	C₂²×C₅×#67	C₂²	1	4	yes	complemented
23	C₂²×C₅×#67	C₂²	1	8	yes	complemented
24	C₂³×C₅×Dic₃	C₂²	1	1	yes	characteristic, complemented
25	C₂³×C₅×Dic₃	C₂²	1	2	yes	complemented
26	C₅×#953	C₂²	1	16	yes	complemented
27	C₂×C₅×#217	C₂²	1	2	yes	complemented
28	C₂×C₅×#217	C₂²	1	2	yes	complemented
29	C₂×C₅×#217	C₂²	1	4	yes	complemented
30	C₂×C₅×#217	C₂²	1	8	yes	complemented
31	C₅×#939	C₂²	1	32	yes	complemented
32	C₅×#937	C₂²	1	16	yes	complemented
33	C₅×#935	C₂²	1	16	yes	complemented
34	C₅×#929	C₂²	1	16	yes	complemented
35	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	4	yes	complemented
36	C₂×C₅×Dic₃⋊C₄	C₂²	1	4	yes	complemented
37	C₂×#5804	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
38	C₂³×C₅×D₄	—	3	1	no	—
39	C₂³×C₅×D₄	D₃	1	1	yes	characteristic, complemented
40	C₅×#534	—	3	16	no	—
41	C₂×C₅×#123	—	3	2	no	—
42	C₂×C₅×#123	—	3	2	no	—
43	C₂×C₅×#121	—	3	4	no	—
44	C₂×C₅×#120	—	3	2	no	—
45	C₂×C₅×#120	—	3	2	no	—
46	C₂²×C₅×C₂²⋊C₄	—	3	1	no	—
47	C₂⁴×C₃×C₅	—	2	4	no	—
48	C₂⁴×C₃×C₅	—	4	4	no	—
49	C₂⁴×C₃×C₅	—	4	4	no	—
50	C₂⁴×C₃×C₅	D₄	1	8	yes	complemented
51	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
52	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
53	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
54	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
55	C₂⁴×C₃×C₅	C₂³	1	4	yes	—
56	C₂⁴×C₃×C₅	C₂³	1	4	yes	complemented
57	C₂³×C₅×D₃	—	2	4	no	—
58	C₂³×C₅×D₃	—	4	4	no	—
59	C₂³×C₅×D₃	C₂³	1	2	yes	—
60	C₂³×C₅×D₃	C₂³	1	4	yes	complemented
61	C₂×C₃×C₅×D₄	—	2	8	no	—
62	C₂×C₃×C₅×D₄	—	2	8	no	—
63	C₂×C₃×C₅×D₄	—	2	32	no	—
64	C₂×C₃×C₅×D₄	C₂³	1	8	yes	—
65	C₂×C₃×C₅×D₄	C₂³	1	8	yes	complemented
66	C₂²×C₃×C₄×C₅	—	2	4	no	—
67	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
68	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	complemented
69	C₂×C₅×#67	—	2	8	no	—
70	C₂×C₅×#67	—	2	8	no	—
71	C₂×C₅×#67	—	2	32	no	—
72	C₂×C₅×#67	—	4	8	no	—
73	C₂×C₅×#67	C₂³	1	8	yes	—
74	C₂×C₅×#67	C₂³	1	8	yes	complemented
75	C₂×C₅×#67	C₂³	1	16	yes	complemented
76	C₂²×C₅×Dic₃	—	2	4	no	—
77	C₂²×C₅×Dic₃	—	4	4	no	—
78	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
79	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
80	C₂²×C₅×Dic₃	C₂³	1	4	yes	complemented
81	C₂²×C₅×Dic₃	C₂³	1	8	yes	complemented
82	C₅×#217	C₂³	1	8	yes	complemented
83	C₅×#217	C₂³	1	8	yes	complemented
84	C₅×#217	C₂³	1	16	yes	complemented
85	C₅×(C₂×D₃)⋊C₄	C₂³	1	16	yes	complemented
86	C₅×Dic₃⋊C₄	C₂³	1	16	yes	complemented
87	C₂³×C₃×D₄	C₂×C₅	1	1	yes	characteristic, complemented
88	C₂³×#67	C₂×C₅	1	1	yes	characteristic, complemented
89	C₂×#953	C₂×C₅	1	2	yes	complemented
90	C₂²×#217	C₂×C₅	1	1	yes	characteristic, complemented
91	#5804	C₂×C₅	1	16	yes	direct product factor
92	C₂×#939	C₂×C₅	1	4	yes	complemented
93	C₂×#937	C₂×C₅	1	2	yes	complemented
94	C₂×#935	C₂×C₅	1	2	yes	complemented
95	C₂×#929	C₂×C₅	1	2	yes	complemented
96	C₂⁵×C₅	—	3	1	no	—
97	C₂⁵×C₅	C₂×D₃	1	1	yes	characteristic
98	C₂⁵×C₅	C₂×D₃	1	1	yes	characteristic, complemented
99	C₂²×C₅×D₄	—	2	8	no	—
100	C₂²×C₅×D₄	—	3	2	no	—
101	C₂²×C₅×D₄	—	3	2	no	—
102	C₂²×C₅×D₄	—	3	8	no	—
103	C₂²×C₅×D₄	—	3	4	no	—
104	C₂²×C₅×D₄	—	6	8	no	—
105	C₂²×C₅×D₄	C₂×D₃	1	2	yes	—
106	C₂²×C₅×D₄	C₂×D₃	1	2	yes	complemented
107	C₂²×C₅×D₄	C₂×D₃	1	8	yes	complemented
108	C₂³×C₄×C₅	—	3	1	no	—
109	C₂³×C₄×C₅	—	3	2	no	—
110	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic, complemented
111	C₅×#123	—	3	16	no	—
112	C₅×#123	—	3	16	no	—
113	C₅×#121	—	3	32	no	—
114	C₅×#120	—	3	16	no	—
115	C₅×#120	—	3	16	no	—
116	C₂×C₅×C₄⋊C₄	—	3	4	no	—
117	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
118	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
119	C₂×C₅×C₂²⋊C₄	—	3	8	no	—
120	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
121	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
122	C₂×#534	—	3	1	no	Sylow
123	C₂³×C₃×C₅	—	2	4	no	—
124	C₂³×C₃×C₅	—	2	4	no	—
125	C₂³×C₃×C₅	—	2	4	no	—
126	C₂³×C₃×C₅	—	2	4	no	—
127	C₂³×C₃×C₅	—	2	8	no	—
128	C₂³×C₃×C₅	—	2	8	no	—
129	C₂³×C₃×C₅	—	4	16	no	—
130	C₂³×C₃×C₅	—	4	8	no	—
131	C₂³×C₃×C₅	—	4	8	no	—
132	C₂³×C₃×C₅	—	4	16	no	—
133	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
134	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
135	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
136	C₂³×C₃×C₅	C₂×D₄	1	16	yes	complemented
137	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
138	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
139	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
140	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
141	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
142	C₂²×C₅×D₃	—	2	4	no	—
143	C₂²×C₅×D₃	—	2	8	no	—
144	C₂²×C₅×D₃	—	2	8	no	—
145	C₂²×C₅×D₃	—	4	8	no	—
146	C₂²×C₅×D₃	—	4	16	no	—
147	C₂²×C₅×D₃	C₂⁴	1	4	yes	—
148	C₃×C₅×D₄	—	2	16	no	—
149	C₃×C₅×D₄	—	2	16	no	—
150	C₂×C₃×C₄×C₅	—	2	4	no	—
151	C₂×C₃×C₄×C₅	—	2	8	no	—
152	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
153	C₅×#67	—	2	16	no	—
154	C₅×#67	—	2	16	no	—
155	C₅×#67	—	4	16	no	—
156	C₂×C₅×Dic₃	—	2	4	no	—
157	C₂×C₅×Dic₃	—	2	8	no	—
158	C₂×C₅×Dic₃	—	2	8	no	—
159	C₂×C₅×Dic₃	—	4	8	no	—
160	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
161	C₂×C₅×Dic₃	C₂⁴	1	8	yes	—
162	C₂⁵×C₃	C₂²×C₅	1	1	yes	characteristic
163	C₂⁵×C₃	C₂²×C₅	1	1	yes	characteristic, complemented
164	C₂⁴×D₃	C₂²×C₅	1	1	yes	characteristic, complemented
165	C₂²×C₃×D₄	—	2	8	no	—
166	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
167	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	complemented
168	C₂²×C₃×D₄	C₂²×C₅	1	8	yes	complemented
169	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic, complemented
170	C₂²×#67	—	2	8	no	—
171	C₂²×#67	C₂²×C₅	1	2	yes	—
172	C₂²×#67	C₂²×C₅	1	2	yes	complemented
173	C₂²×#67	C₂²×C₅	1	4	yes	complemented
174	C₂²×#67	C₂²×C₅	1	8	yes	complemented
175	C₂³×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
176	C₂³×Dic₃	C₂²×C₅	1	2	yes	complemented
177	#953	C₂²×C₅	1	16	yes	complemented
178	C₂×#217	C₂²×C₅	1	2	yes	complemented
179	C₂×#217	C₂²×C₅	1	2	yes	complemented
180	C₂×#217	C₂²×C₅	1	4	yes	complemented
181	C₂×#217	C₂²×C₅	1	8	yes	complemented
182	#939	C₂²×C₅	1	32	yes	complemented
183	#937	C₂²×C₅	1	16	yes	complemented
184	#935	C₂²×C₅	1	16	yes	complemented
185	#929	C₂²×C₅	1	16	yes	complemented
186	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	4	yes	complemented
187	C₂×Dic₃⋊C₄	C₂²×C₅	1	4	yes	complemented
188	C₂⁴×C₅	—	2	4	no	—
189	C₂⁴×C₅	—	3	2	no	—
190	C₂⁴×C₅	—	3	4	no	—
191	C₂⁴×C₅	—	4	4	no	—
192	C₂⁴×C₅	—	4	4	no	—
193	C₂⁴×C₅	—	6	4	no	—
194	C₂⁴×C₅	—	12	4	no	—
195	C₂⁴×C₅	#67	1	8	yes	complemented
196	C₂⁴×C₅	C₂²×D₃	1	2	yes	—
197	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
198	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
199	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
200	C₂⁴×C₅	C₂²×D₃	1	4	yes	—
201	C₂⁴×C₅	C₂²×D₃	1	4	yes	complemented
202	C₂×C₅×D₄	—	2	8	no	—
203	C₂×C₅×D₄	—	2	8	no	—
204	C₂×C₅×D₄	—	2	32	no	—
205	C₂×C₅×D₄	—	3	8	no	—
206	C₂×C₅×D₄	—	3	8	no	—
207	C₂×C₅×D₄	—	3	16	no	—
208	C₂×C₅×D₄	—	6	8	no	—
209	C₂×C₅×D₄	—	6	8	no	—
210	C₂×C₅×D₄	—	6	32	no	—
211	C₂×C₅×D₄	—	12	8	no	—
212	C₂×C₅×D₄	C₂²×D₃	1	8	yes	—
213	C₂×C₅×D₄	C₂²×D₃	1	8	yes	complemented
214	C₂²×C₄×C₅	—	2	4	no	—
215	C₂²×C₄×C₅	—	3	4	no	—
216	C₂²×C₄×C₅	—	3	4	no	—
217	C₂²×C₄×C₅	—	3	2	no	—
218	C₂²×C₄×C₅	—	3	8	no	—
219	C₂²×C₄×C₅	—	6	4	no	—
220	C₂²×C₄×C₅	—	12	4	no	—
221	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
222	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	complemented
223	C₅×C₄⋊C₄	—	3	16	no	—
224	C₅×C₂²⋊C₄	—	3	8	no	—
225	C₅×C₂²⋊C₄	—	3	8	no	—
226	C₅×C₂²⋊C₄	—	3	16	no	—
227	C₅×C₂²⋊C₄	—	3	16	no	—
228	C₂³×D₄	—	3	1	no	—
229	C₂³×D₄	C₅×D₃	1	1	yes	characteristic, complemented
230	#534	—	3	16	no	—
231	C₂×#123	—	3	2	no	—
232	C₂×#123	—	3	2	no	—
233	C₂×#121	—	3	4	no	—
234	C₂×#120	—	3	2	no	—
235	C₂×#120	—	3	2	no	—
236	C₂²×C₂²⋊C₄	—	3	1	no	—
237	C₂²×C₃×C₅	—	2	8	no	—
238	C₂²×C₃×C₅	—	2	8	no	—
239	C₂²×C₃×C₅	—	2	8	no	—
240	C₂²×C₃×C₅	—	2	4	no	—
241	C₂²×C₃×C₅	—	2	4	no	—
242	C₂²×C₃×C₅	—	2	4	no	—
243	C₂²×C₃×C₅	—	2	4	no	—
244	C₂²×C₃×C₅	—	2	8	no	—
245	C₂²×C₃×C₅	—	4	16	no	—
246	C₂²×C₃×C₅	—	4	16	no	—
247	C₂²×C₃×C₅	—	4	8	no	—
248	C₂²×C₃×C₅	C₂²×D₄	1	4	yes	—
249	C₂²×C₃×C₅	C₂²×D₄	1	4	yes	—
250	C₂²×C₃×C₅	C₂²×D₄	1	4	yes	—
251	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
252	C₂²×C₃×C₅	H(5,𝔽₂)	1	4	yes	—
253	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
254	C₂×C₅×D₃	—	2	4	no	—
255	C₂×C₅×D₃	—	2	8	no	—
256	C₂×C₅×D₃	—	4	16	no	—
257	C₂×C₅×D₃	—	4	8	no	—
258	C₃×C₄×C₅	—	2	4	no	—
259	C₅×Dic₃	—	2	4	no	—
260	C₅×Dic₃	—	2	8	no	—
261	C₂⁴×C₃	—	2	4	no	—
262	C₂⁴×C₃	—	4	4	no	—
263	C₂⁴×C₃	—	4	4	no	—
264	C₂⁴×C₃	C₅×D₄	1	8	yes	complemented
265	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
266	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
267	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
268	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
269	C₂⁴×C₃	C₂³×C₅	1	4	yes	—
270	C₂⁴×C₃	C₂³×C₅	1	4	yes	complemented
271	C₂³×D₃	—	2	4	no	—
272	C₂³×D₃	—	4	4	no	—
273	C₂³×D₃	C₂³×C₅	1	2	yes	—
274	C₂³×D₃	C₂³×C₅	1	4	yes	complemented
275	C₂×C₃×D₄	—	2	8	no	—
276	C₂×C₃×D₄	—	2	8	no	—
277	C₂×C₃×D₄	—	2	32	no	—
278	C₂×C₃×D₄	C₂³×C₅	1	8	yes	—
279	C₂×C₃×D₄	C₂³×C₅	1	8	yes	complemented
280	C₂²×C₃×C₄	—	2	4	no	—
281	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
282	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	complemented
283	C₂×#67	—	2	8	no	—
284	C₂×#67	—	2	8	no	—
285	C₂×#67	—	2	32	no	—
286	C₂×#67	—	4	8	no	—
287	C₂×#67	C₂³×C₅	1	8	yes	—
288	C₂×#67	C₂³×C₅	1	8	yes	complemented
289	C₂×#67	C₂³×C₅	1	16	yes	complemented
290	C₂²×Dic₃	—	2	4	no	—
291	C₂²×Dic₃	—	4	4	no	—
292	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
293	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
294	C₂²×Dic₃	C₂³×C₅	1	4	yes	complemented
295	C₂²×Dic₃	C₂³×C₅	1	8	yes	complemented
296	#217	C₂³×C₅	1	8	yes	complemented
297	#217	C₂³×C₅	1	8	yes	complemented
298	#217	C₂³×C₅	1	16	yes	complemented
299	(C₂×D₃)⋊C₄	C₂³×C₅	1	16	yes	complemented
300	Dic₃⋊C₄	C₂³×C₅	1	16	yes	complemented
301	C₂³×C₅	—	2	4	no	—
302	C₂³×C₅	—	2	4	no	—
303	C₂³×C₅	—	2	4	no	—
304	C₂³×C₅	—	2	8	no	—
305	C₂³×C₅	—	2	4	no	—
306	C₂³×C₅	—	2	8	no	—
307	C₂³×C₅	—	3	4	no	—
308	C₂³×C₅	—	4	16	no	—
309	C₂³×C₅	—	4	8	no	—
310	C₂³×C₅	—	4	8	no	—
311	C₂³×C₅	—	4	16	no	—
312	C₂³×C₅	—	6	8	no	—
313	C₂³×C₅	—	6	8	no	—
314	C₂³×C₅	—	6	4	no	—
315	C₂³×C₅	—	12	8	no	—
316	C₂³×C₅	—	12	16	no	—
317	C₂³×C₅	C₂×#67	1	4	yes	—
318	C₂³×C₅	C₂×#67	1	4	yes	—
319	C₂³×C₅	C₂×#67	1	4	yes	—
320	C₂³×C₅	C₂×#67	1	16	yes	complemented
321	C₂³×C₅	C₂³×D₃	1	4	yes	—
322	C₂³×C₅	C₂³×D₃	1	2	yes	—
323	C₂³×C₅	C₂³×D₃	1	2	yes	—
324	C₂³×C₅	C₂³×D₃	1	2	yes	—
325	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
326	C₅×D₄	—	2	16	no	—
327	C₅×D₄	—	2	16	no	—
328	C₅×D₄	—	6	16	no	—
329	C₅×D₄	—	6	16	no	—
330	C₅×D₄	—	12	16	no	—
331	C₂×C₄×C₅	—	2	4	no	—
332	C₂×C₄×C₅	—	2	8	no	—
333	C₂×C₄×C₅	—	3	8	no	—
334	C₂×C₄×C₅	—	3	4	no	—
335	C₂×C₄×C₅	—	6	8	no	—
336	C₂×C₄×C₅	—	6	8	no	—
337	C₂×C₄×C₅	—	6	4	no	—
338	C₂×C₄×C₅	—	12	8	no	—
339	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
340	C₂⁵	—	3	1	no	—
341	C₂⁵	C₂×C₅×D₃	1	1	yes	characteristic
342	C₂⁵	C₂×C₅×D₃	1	1	yes	characteristic, complemented
343	C₂²×D₄	—	2	8	no	—
344	C₂²×D₄	—	3	2	no	—
345	C₂²×D₄	—	3	2	no	—
346	C₂²×D₄	—	3	8	no	—
347	C₂²×D₄	—	3	4	no	—
348	C₂²×D₄	—	6	8	no	—
349	C₂²×D₄	C₂×C₅×D₃	1	2	yes	—
350	C₂²×D₄	C₂×C₅×D₃	1	2	yes	complemented
351	C₂²×D₄	C₂×C₅×D₃	1	8	yes	complemented
352	C₂³×C₄	—	3	1	no	—
353	C₂³×C₄	—	3	2	no	—
354	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
355	#123	—	3	16	no	—
356	#123	—	3	16	no	—
357	#121	—	3	32	no	—
358	#120	—	3	16	no	—
359	#120	—	3	16	no	—
360	C₂×C₄⋊C₄	—	3	4	no	—
361	C₂×C₂²⋊C₄	—	3	2	no	—
362	C₂×C₂²⋊C₄	—	3	2	no	—
363	C₂×C₂²⋊C₄	—	3	8	no	—
364	C₂×C₂²⋊C₄	—	3	4	no	—
365	C₂×C₂²⋊C₄	—	3	4	no	—
366	C₂×C₃×C₅	—	2	4	no	—
367	C₂×C₃×C₅	—	2	4	no	—
368	C₂×C₃×C₅	—	2	4	no	—
369	C₂×C₃×C₅	—	4	4	no	—
370	C₂×C₃×C₅	#534	1	4	yes	complemented
371	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
372	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
373	C₅×D₃	—	4	4	no	—
374	C₂³×C₃	—	2	4	no	—
375	C₂³×C₃	—	2	4	no	—
376	C₂³×C₃	—	2	4	no	—
377	C₂³×C₃	—	2	4	no	—
378	C₂³×C₃	—	2	8	no	—
379	C₂³×C₃	—	2	8	no	—
380	C₂³×C₃	—	4	16	no	—
381	C₂³×C₃	—	4	8	no	—
382	C₂³×C₃	—	4	8	no	—
383	C₂³×C₃	—	4	16	no	—
384	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
385	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
386	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
387	C₂³×C₃	C₂×C₅×D₄	1	16	yes	complemented
388	C₂³×C₃	C₂⁴×C₅	1	4	yes	—
389	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
390	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
391	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
392	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
393	C₂²×D₃	—	2	4	no	—
394	C₂²×D₃	—	2	8	no	—
395	C₂²×D₃	—	2	8	no	—
396	C₂²×D₃	—	4	8	no	—
397	C₂²×D₃	—	4	16	no	—
398	C₂²×D₃	C₂⁴×C₅	1	4	yes	—
399	C₃×D₄	—	2	16	no	—
400	C₃×D₄	—	2	16	no	—
401	C₂×C₃×C₄	—	2	4	no	—
402	C₂×C₃×C₄	—	2	8	no	—
403	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
404	#67	—	2	16	no	—
405	#67	—	2	16	no	—
406	#67	—	4	16	no	—
407	C₂×Dic₃	—	2	4	no	—
408	C₂×Dic₃	—	2	8	no	—
409	C₂×Dic₃	—	2	8	no	—
410	C₂×Dic₃	—	4	8	no	—
411	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
412	C₂×Dic₃	C₂⁴×C₅	1	8	yes	—
413	C₂²×C₅	—	2	4	no	—
414	C₂²×C₅	—	2	4	no	—
415	C₂²×C₅	—	2	4	no	—
416	C₂²×C₅	—	2	8	no	—
417	C₂²×C₅	—	2	8	no	—
418	C₂²×C₅	—	2	8	no	—
419	C₂²×C₅	—	2	8	no	—
420	C₂²×C₅	—	2	4	no	—
421	C₂²×C₅	—	4	16	no	—
422	C₂²×C₅	—	4	16	no	—
423	C₂²×C₅	—	4	8	no	—
424	C₂²×C₅	—	6	8	no	—
425	C₂²×C₅	—	6	4	no	—
426	C₂²×C₅	—	12	16	no	—
427	C₂²×C₅	—	12	8	no	—
428	C₂²×C₅	#1004	1	4	yes	—
429	C₂²×C₅	C₂²×#67	1	4	yes	—
430	C₂²×C₅	C₂²×#67	1	4	yes	—
431	C₂²×C₅	C₂²×#67	1	4	yes	—
432	C₂²×C₅	C₂²×#67	1	2	yes	—
433	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
434	C₄×C₅	—	2	4	no	—
435	C₄×C₅	—	6	8	no	—
436	C₄×C₅	—	6	4	no	—
437	C₂⁴	—	2	4	no	—
438	C₂⁴	—	3	2	no	—
439	C₂⁴	—	3	4	no	—
440	C₂⁴	—	4	4	no	—
441	C₂⁴	—	4	4	no	—
442	C₂⁴	—	6	4	no	—
443	C₂⁴	—	12	4	no	—
444	C₂⁴	C₅×#67	1	8	yes	complemented
445	C₂⁴	C₂²×C₅×D₃	1	2	yes	—
446	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
447	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
448	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
449	C₂⁴	C₂²×C₅×D₃	1	4	yes	—
450	C₂⁴	C₂²×C₅×D₃	1	4	yes	complemented
451	C₂×D₄	—	2	8	no	—
452	C₂×D₄	—	2	8	no	—
453	C₂×D₄	—	2	32	no	—
454	C₂×D₄	—	3	8	no	—
455	C₂×D₄	—	3	8	no	—
456	C₂×D₄	—	3	16	no	—
457	C₂×D₄	—	6	8	no	—
458	C₂×D₄	—	6	8	no	—
459	C₂×D₄	—	6	32	no	—
460	C₂×D₄	—	12	8	no	—
461	C₂×D₄	C₂²×C₅×D₃	1	8	yes	—
462	C₂×D₄	C₂²×C₅×D₃	1	8	yes	complemented
463	C₂²×C₄	—	2	4	no	—
464	C₂²×C₄	—	3	4	no	—
465	C₂²×C₄	—	3	2	no	—
466	C₂²×C₄	—	3	4	no	—
467	C₂²×C₄	—	3	8	no	—
468	C₂²×C₄	—	6	4	no	—
469	C₂²×C₄	—	12	4	no	—
470	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
471	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	complemented
472	C₄⋊C₄	—	3	16	no	—
473	C₂²⋊C₄	—	3	8	no	—
474	C₂²⋊C₄	—	3	8	no	—
475	C₂²⋊C₄	—	3	16	no	—
476	C₂²⋊C₄	—	3	16	no	—
477	C₃×C₅	C₂×#534	1	1	yes	characteristic, complemented, Hall
478	C₂²×C₃	—	2	8	no	—
479	C₂²×C₃	—	2	8	no	—
480	C₂²×C₃	—	2	8	no	—
481	C₂²×C₃	—	2	4	no	—
482	C₂²×C₃	—	2	4	no	—
483	C₂²×C₃	—	2	4	no	—
484	C₂²×C₃	—	2	4	no	—
485	C₂²×C₃	—	2	8	no	—
486	C₂²×C₃	—	4	16	no	—
487	C₂²×C₃	—	4	16	no	—
488	C₂²×C₃	—	4	8	no	—
489	C₂²×C₃	C₂²×C₅×D₄	1	4	yes	—
490	C₂²×C₃	C₂²×C₅×D₄	1	4	yes	—
491	C₂²×C₃	C₂²×C₅×D₄	1	4	yes	—
492	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
493	C₂²×C₃	C₅×H(5,𝔽₂)	1	4	yes	—
494	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
495	C₂×D₃	—	2	4	no	—
496	C₂×D₃	—	2	8	no	—
497	C₂×D₃	—	4	16	no	—
498	C₂×D₃	—	4	8	no	—
499	C₃×C₄	—	2	4	no	—
500	Dic₃	—	2	4	no	—
501	Dic₃	—	2	8	no	—
502	C₂×C₅	—	2	4	no	—
503	C₂×C₅	—	2	4	no	—
504	C₂×C₅	—	2	4	no	—
505	C₂×C₅	—	4	4	no	—
506	C₂×C₅	—	12	4	no	—
507	C₂×C₅	#5804	1	4	yes	direct product factor
508	C₂×C₅	C₂×#1004	1	2	yes	—
509	C₂×C₅	C₂³×#67	1	1	yes	characteristic
510	C₂³	—	2	4	no	—
511	C₂³	—	2	4	no	—
512	C₂³	—	2	4	no	—
513	C₂³	—	2	8	no	—
514	C₂³	—	2	4	no	—
515	C₂³	—	2	8	no	—
516	C₂³	—	3	4	no	—
517	C₂³	—	4	16	no	—
518	C₂³	—	4	8	no	—
519	C₂³	—	4	8	no	—
520	C₂³	—	4	16	no	—
521	C₂³	—	6	8	no	—
522	C₂³	—	6	8	no	—
523	C₂³	—	6	4	no	—
524	C₂³	—	12	8	no	—
525	C₂³	—	12	16	no	—
526	C₂³	C₂×C₅×#67	1	4	yes	—
527	C₂³	C₂×C₅×#67	1	4	yes	—
528	C₂³	C₂×C₅×#67	1	4	yes	—
529	C₂³	C₂×C₅×#67	1	16	yes	complemented
530	C₂³	C₂³×C₅×D₃	1	4	yes	—
531	C₂³	C₂³×C₅×D₃	1	2	yes	—
532	C₂³	C₂³×C₅×D₃	1	2	yes	—
533	C₂³	C₂³×C₅×D₃	1	2	yes	—
534	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
535	D₄	—	2	16	no	—
536	D₄	—	2	16	no	—
537	D₄	—	6	16	no	—
538	D₄	—	6	16	no	—
539	D₄	—	12	16	no	—
540	C₂×C₄	—	2	4	no	—
541	C₂×C₄	—	2	8	no	—
542	C₂×C₄	—	3	8	no	—
543	C₂×C₄	—	3	4	no	—
544	C₂×C₄	—	6	8	no	—
545	C₂×C₄	—	6	8	no	—
546	C₂×C₄	—	6	4	no	—
547	C₂×C₄	—	12	8	no	—
548	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
549	C₂×C₃	—	2	4	no	—
550	C₂×C₃	—	2	4	no	—
551	C₂×C₃	—	2	4	no	—
552	C₂×C₃	—	4	4	no	—
553	C₂×C₃	C₅×#534	1	4	yes	complemented
554	C₂×C₃	C₂³×C₅×D₄	1	1	yes	characteristic
555	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	2	yes	—
556	D₃	—	4	4	no	—
557	C₅	C₂×#5804	1	1	yes	characteristic, direct product factor, Sylow
558	C₂²	—	2	4	no	—
559	C₂²	—	2	4	no	—
560	C₂²	—	2	4	no	—
561	C₂²	—	2	8	no	—
562	C₂²	—	2	8	no	—
563	C₂²	—	2	8	no	—
564	C₂²	—	2	8	no	—
565	C₂²	—	2	4	no	—
566	C₂²	—	4	16	no	—
567	C₂²	—	4	16	no	—
568	C₂²	—	4	8	no	—
569	C₂²	—	6	8	no	—
570	C₂²	—	6	4	no	—
571	C₂²	—	12	16	no	—
572	C₂²	—	12	8	no	—
573	C₂²	C₅×#1004	1	4	yes	—
574	C₂²	C₂²×C₅×#67	1	4	yes	—
575	C₂²	C₂²×C₅×#67	1	4	yes	—
576	C₂²	C₂²×C₅×#67	1	4	yes	—
577	C₂²	C₂²×C₅×#67	1	2	yes	—
578	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
579	C₄	—	2	4	no	—
580	C₄	—	6	8	no	—
581	C₄	—	6	4	no	—
582	C₃	C₂×C₅×#534	1	1	yes	characteristic, complemented, Sylow
583	C₂	—	2	4	no	—
584	C₂	—	2	4	no	—
585	C₂	—	2	4	no	—
586	C₂	—	4	4	no	—
587	C₂	—	12	4	no	—
588	C₂	C₅×#5804	1	4	yes	direct product factor
589	C₂	C₂×C₅×#1004	1	2	yes	—
590	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	C₂³×C₃×C₅×D₄	C₂
socle	C₂³×C₃×C₅	C₂⁴
hypercenter	C₂³×C₅×D₄	D₃
hypocenter	C₃	C₂×C₅×#534
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂³×C₅×D₄

Complements

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

N	H ≅ G/N	type
1. C₂³×C₃×C₅×D₄	C₂	semidirect
2. C₂³×C₅×#67	C₂	semidirect
3. C₂×C₅×#953	C₂	semidirect
4. C₂²×C₅×#217	C₂	semidirect
5. C₅×#5804	C₂	direct (N × H)
6. C₂×C₅×#939	C₂	semidirect
7. C₂×C₅×#937	C₂	semidirect
8. C₂×C₅×#935	C₂	semidirect
9. C₂×C₅×#929	C₂	semidirect
12. C₂⁵×C₃×C₅	C₂²	semidirect
13. C₂⁴×C₅×D₃	C₂²	semidirect
16. C₂²×C₃×C₅×D₄	C₂²	semidirect
17. C₂²×C₃×C₅×D₄	C₂²	semidirect
18. C₂³×C₃×C₄×C₅	C₂²	semidirect
21. C₂²×C₅×#67	C₂²	semidirect
22. C₂²×C₅×#67	C₂²	semidirect
23. C₂²×C₅×#67	C₂²	semidirect
24. C₂³×C₅×Dic₃	C₂²	semidirect
25. C₂³×C₅×Dic₃	C₂²	semidirect
26. C₅×#953	C₂²	semidirect
27. C₂×C₅×#217	C₂²	semidirect
28. C₂×C₅×#217	C₂²	semidirect
29. C₂×C₅×#217	C₂²	semidirect
30. C₂×C₅×#217	C₂²	semidirect
31. C₅×#939	C₂²	semidirect
32. C₅×#937	C₂²	semidirect
33. C₅×#935	C₂²	semidirect
34. C₅×#929	C₂²	semidirect
35. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
36. C₂×C₅×Dic₃⋊C₄	C₂²	semidirect
37. C₂×#5804	C₅	direct (N × H)
39. C₂³×C₅×D₄	D₃	semidirect
50. C₂⁴×C₃×C₅	D₄	semidirect
56. C₂⁴×C₃×C₅	C₂³	semidirect
60. C₂³×C₅×D₃	C₂³	semidirect
65. C₂×C₃×C₅×D₄	C₂³	semidirect
68. C₂²×C₃×C₄×C₅	C₂³	semidirect
74. C₂×C₅×#67	C₂³	semidirect
75. C₂×C₅×#67	C₂³	semidirect
80. C₂²×C₅×Dic₃	C₂³	semidirect
81. C₂²×C₅×Dic₃	C₂³	semidirect
82. C₅×#217	C₂³	semidirect
83. C₅×#217	C₂³	semidirect
84. C₅×#217	C₂³	semidirect
85. C₅×(C₂×D₃)⋊C₄	C₂³	semidirect
86. C₅×Dic₃⋊C₄	C₂³	semidirect
87. C₂³×C₃×D₄	C₂×C₅	semidirect
88. C₂³×#67	C₂×C₅	semidirect
89. C₂×#953	C₂×C₅	semidirect
90. C₂²×#217	C₂×C₅	semidirect
91. #5804	C₂×C₅	direct (N × H)
92. C₂×#939	C₂×C₅	semidirect
93. C₂×#937	C₂×C₅	semidirect
94. C₂×#935	C₂×C₅	semidirect
95. C₂×#929	C₂×C₅	semidirect
98. C₂⁵×C₅	C₂×D₃	semidirect
106. C₂²×C₅×D₄	C₂×D₃	semidirect
107. C₂²×C₅×D₄	C₂×D₃	semidirect
110. C₂³×C₄×C₅	C₂×D₃	semidirect
136. C₂³×C₃×C₅	C₂×D₄	semidirect
163. C₂⁵×C₃	C₂²×C₅	semidirect
164. C₂⁴×D₃	C₂²×C₅	semidirect
167. C₂²×C₃×D₄	C₂²×C₅	semidirect
168. C₂²×C₃×D₄	C₂²×C₅	semidirect
169. C₂³×C₃×C₄	C₂²×C₅	semidirect
172. C₂²×#67	C₂²×C₅	semidirect
173. C₂²×#67	C₂²×C₅	semidirect
174. C₂²×#67	C₂²×C₅	semidirect
175. C₂³×Dic₃	C₂²×C₅	semidirect
176. C₂³×Dic₃	C₂²×C₅	semidirect
177. #953	C₂²×C₅	semidirect
178. C₂×#217	C₂²×C₅	semidirect
179. C₂×#217	C₂²×C₅	semidirect
180. C₂×#217	C₂²×C₅	semidirect
181. C₂×#217	C₂²×C₅	semidirect
182. #939	C₂²×C₅	semidirect
183. #937	C₂²×C₅	semidirect
184. #935	C₂²×C₅	semidirect
185. #929	C₂²×C₅	semidirect
186. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
187. C₂×Dic₃⋊C₄	C₂²×C₅	semidirect
195. C₂⁴×C₅	#67	semidirect
201. C₂⁴×C₅	C₂²×D₃	semidirect
213. C₂×C₅×D₄	C₂²×D₃	semidirect
222. C₂²×C₄×C₅	C₂²×D₃	semidirect
229. C₂³×D₄	C₅×D₃	semidirect
264. C₂⁴×C₃	C₅×D₄	semidirect
270. C₂⁴×C₃	C₂³×C₅	semidirect
274. C₂³×D₃	C₂³×C₅	semidirect
279. C₂×C₃×D₄	C₂³×C₅	semidirect
282. C₂²×C₃×C₄	C₂³×C₅	semidirect
288. C₂×#67	C₂³×C₅	semidirect
289. C₂×#67	C₂³×C₅	semidirect
294. C₂²×Dic₃	C₂³×C₅	semidirect
295. C₂²×Dic₃	C₂³×C₅	semidirect
296. #217	C₂³×C₅	semidirect
297. #217	C₂³×C₅	semidirect
298. #217	C₂³×C₅	semidirect
299. (C₂×D₃)⋊C₄	C₂³×C₅	semidirect
300. Dic₃⋊C₄	C₂³×C₅	semidirect
320. C₂³×C₅	C₂×#67	semidirect
342. C₂⁵	C₂×C₅×D₃	semidirect
350. C₂²×D₄	C₂×C₅×D₃	semidirect
351. C₂²×D₄	C₂×C₅×D₃	semidirect
354. C₂³×C₄	C₂×C₅×D₃	semidirect
370. C₂×C₃×C₅	#534	semidirect
387. C₂³×C₃	C₂×C₅×D₄	semidirect
444. C₂⁴	C₅×#67	semidirect
450. C₂⁴	C₂²×C₅×D₃	semidirect
462. C₂×D₄	C₂²×C₅×D₃	semidirect
471. C₂²×C₄	C₂²×C₅×D₃	semidirect
477. C₃×C₅	C₂×#534	semidirect
507. C₂×C₅	#5804	direct (N × H)
529. C₂³	C₂×C₅×#67	semidirect
553. C₂×C₃	C₅×#534	semidirect
557. C₅	C₂×#5804	direct (N × H)
582. C₃	C₂×C₅×#534	semidirect
588. C₂	C₅×#5804	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂³×C₃×C₅×D₄	2
C₂³×C₅×#67	2
C₂×C₅×#953	2
C₂²×C₅×#217	2
C₅×#5804	2
C₂×C₅×#939	2
C₂×C₅×#937	2
C₂×C₅×#935	2
C₂×C₅×#929	2
C₂×C₅×#534	3
C₂×#5804	5

Subgroups — C2×C5×#5804 #14480293

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5804 #14480293