Subgroups — C₂×C₅×#5213 #14320284

Order 1920.

3152 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₃×C₄×C₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₅×#67	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₅×#217	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₅×(C₂×D₃)⋊C₄	C₂	1	2	yes	maximal, complemented
5	C₅×#5213	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₅×C₃⋊#95	C₂	1	2	yes	maximal, complemented
7	C₂×C₅×#386	—	3	1	no	maximal, Hall
8	C₂⁵×C₃×C₅	C₂²	1	1	yes	characteristic
9	C₂⁴×C₅×D₃	C₂²	1	1	yes	characteristic
10	C₂³×C₃×C₄×C₅	—	2	4	no	—
11	C₂³×C₃×C₄×C₅	—	2	8	no	—
12	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
13	C₂³×C₃×C₄×C₅	C₂²	1	4	yes	complemented
14	C₂²×C₅×#67	—	2	4	no	—
15	C₂²×C₅×#67	—	2	4	no	—
16	C₂²×C₅×#67	C₄	1	8	yes	complemented
17	C₂²×C₅×#67	C₂²	1	4	yes	—
18	C₂³×C₅×Dic₃	C₂²	1	2	yes	—
19	C₂³×C₅×Dic₃	C₂²	1	1	yes	characteristic
20	C₂×C₅×#217	—	2	4	no	—
21	C₂×C₅×#217	C₂²	1	4	yes	complemented
22	C₂×C₅×(C₂×D₃)⋊C₄	—	2	8	no	—
23	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	8	yes	complemented
24	C₅×C₃⋊#95	C₂²	1	8	yes	complemented
25	C₂×#5213	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
26	C₂³×C₅×D₄	—	3	1	no	—
27	C₂⁴×C₄×C₅	D₃	1	1	yes	characteristic, complemented
28	C₂²×C₅×C₂²⋊C₄	—	3	1	no	—
29	C₂²×C₅×C₂²⋊C₄	—	3	2	no	—
30	C₅×#386	—	3	8	no	—
31	C₂×C₅×#95	—	3	2	no	—
32	C₂⁴×C₃×C₅	—	2	4	no	—
33	C₂⁴×C₃×C₅	—	2	4	no	—
34	C₂⁴×C₃×C₅	C₂×C₄	1	4	yes	—
35	C₂⁴×C₃×C₅	D₄	1	4	yes	—
36	C₂⁴×C₃×C₅	D₄	1	4	yes	—
37	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
38	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
39	C₂³×C₅×D₃	—	2	4	no	—
40	C₂³×C₅×D₃	—	2	2	no	—
41	C₂³×C₅×D₃	—	2	2	no	—
42	C₂³×C₅×D₃	—	2	4	no	—
43	C₂³×C₅×D₃	C₂×C₄	1	4	yes	complemented
44	C₂³×C₅×D₃	C₂³	1	2	yes	—
45	C₂²×C₃×C₄×C₅	—	2	32	no	—
46	C₂²×C₃×C₄×C₅	—	2	4	no	—
47	C₂²×C₃×C₄×C₅	—	2	4	no	—
48	C₂²×C₃×C₄×C₅	—	2	8	no	—
49	C₂²×C₃×C₄×C₅	—	2	16	no	—
50	C₂²×C₃×C₄×C₅	D₄	1	8	yes	complemented
51	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
52	C₂×C₅×#67	—	2	32	no	—
53	C₂×C₅×#67	—	2	8	no	—
54	C₂×C₅×#67	—	2	8	no	—
55	C₂×C₅×#67	C₂×C₄	1	16	yes	complemented
56	C₂²×C₅×Dic₃	—	2	2	no	—
57	C₂²×C₅×Dic₃	—	2	2	no	—
58	C₂²×C₅×Dic₃	—	2	4	no	—
59	C₂²×C₅×Dic₃	—	2	4	no	—
60	C₂²×C₅×Dic₃	—	2	4	no	—
61	C₂²×C₅×Dic₃	C₂×C₄	1	4	yes	complemented
62	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
63	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
64	C₅×#217	—	2	8	no	—
65	C₅×(C₂×D₃)⋊C₄	—	2	16	no	—
66	C₂⁴×C₃×C₄	C₂×C₅	1	1	yes	characteristic, complemented
67	C₂³×#67	C₂×C₅	1	1	yes	characteristic
68	C₂²×#217	C₂×C₅	1	1	yes	characteristic, complemented
69	C₂²×(C₂×D₃)⋊C₄	C₂×C₅	1	2	yes	complemented
70	#5213	C₂×C₅	1	8	yes	direct product factor
71	C₂×C₃⋊#95	C₂×C₅	1	2	yes	complemented
72	C₂⁵×C₅	—	3	1	no	—
73	C₂⁵×C₅	C₂×D₃	1	1	yes	characteristic
74	C₂²×C₅×D₄	—	3	8	no	—
75	C₂²×C₅×D₄	—	3	4	no	—
76	C₂²×C₅×D₄	—	6	4	no	—
77	C₂²×C₅×D₄	—	6	4	no	—
78	C₂³×C₄×C₅	—	2	4	no	—
79	C₂³×C₄×C₅	—	2	8	no	—
80	C₂³×C₄×C₅	—	3	1	no	—
81	C₂³×C₄×C₅	—	3	2	no	—
82	C₂³×C₄×C₅	C₂×D₃	1	2	yes	—
83	C₂³×C₄×C₅	C₂×D₃	1	4	yes	complemented
84	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
85	C₂×C₅×C₂²⋊C₄	—	3	8	no	—
86	C₂×C₅×C₂²⋊C₄	—	6	4	no	—
87	C₂×C₅×C₂²⋊C₄	—	6	8	no	—
88	C₅×#95	—	3	8	no	—
89	C₂×#386	—	3	1	no	Sylow
90	C₂³×C₃×C₅	—	2	16	no	—
91	C₂³×C₃×C₅	—	2	8	no	—
92	C₂³×C₃×C₅	—	2	16	no	—
93	C₂³×C₃×C₅	—	2	8	no	—
94	C₂³×C₃×C₅	—	2	4	no	—
95	C₂³×C₃×C₅	—	2	4	no	—
96	C₂³×C₃×C₅	C₂²⋊C₄	1	16	yes	complemented
97	C₂³×C₃×C₅	C₂²×C₄	1	4	yes	—
98	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
99	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
100	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
101	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
102	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
103	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
104	C₂³×C₃×C₅	#41	1	4	yes	—
105	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
106	C₂²×C₅×D₃	—	2	8	no	—
107	C₂²×C₅×D₃	—	2	16	no	—
108	C₂²×C₅×D₃	—	2	4	no	—
109	C₂²×C₅×D₃	—	2	2	no	—
110	C₂²×C₅×D₃	—	2	2	no	—
111	C₂²×C₅×D₃	—	2	4	no	—
112	C₂²×C₅×D₃	—	4	4	no	—
113	C₂²×C₅×D₃	—	4	8	no	—
114	C₂²×C₅×D₃	—	4	4	no	—
115	C₂²×C₅×D₃	C₂²×C₄	1	4	yes	complemented
116	C₂×C₃×C₄×C₅	—	2	32	no	—
117	C₂×C₃×C₄×C₅	—	2	16	no	—
118	C₂×C₃×C₄×C₅	—	2	4	no	—
119	C₂×C₃×C₄×C₅	—	2	4	no	—
120	C₂×C₃×C₄×C₅	C₂×D₄	1	8	yes	complemented
121	C₅×#67	—	2	32	no	—
122	C₂×C₅×Dic₃	—	2	8	no	—
123	C₂×C₅×Dic₃	—	2	2	no	—
124	C₂×C₅×Dic₃	—	2	2	no	—
125	C₂×C₅×Dic₃	—	2	4	no	—
126	C₂×C₅×Dic₃	—	2	4	no	—
127	C₂×C₅×Dic₃	—	2	4	no	—
128	C₂×C₅×Dic₃	—	4	8	no	—
129	C₂×C₅×Dic₃	C₂²×C₄	1	4	yes	complemented
130	C₂⁵×C₃	C₂²×C₅	1	1	yes	characteristic
131	C₂⁴×D₃	C₂²×C₅	1	1	yes	characteristic
132	C₂³×C₃×C₄	—	2	4	no	—
133	C₂³×C₃×C₄	—	2	8	no	—
134	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
135	C₂³×C₃×C₄	C₂²×C₅	1	4	yes	complemented
136	C₂²×#67	—	2	4	no	—
137	C₂²×#67	—	2	4	no	—
138	C₂²×#67	C₄×C₅	1	8	yes	complemented
139	C₂²×#67	C₂²×C₅	1	4	yes	—
140	C₂³×Dic₃	C₂²×C₅	1	2	yes	—
141	C₂³×Dic₃	C₂²×C₅	1	1	yes	characteristic
142	C₂×#217	—	2	4	no	—
143	C₂×#217	C₂²×C₅	1	4	yes	complemented
144	C₂×(C₂×D₃)⋊C₄	—	2	8	no	—
145	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	8	yes	complemented
146	C₃⋊#95	C₂²×C₅	1	8	yes	complemented
147	C₂⁴×C₅	—	2	4	no	—
148	C₂⁴×C₅	—	2	4	no	—
149	C₂⁴×C₅	—	3	4	no	—
150	C₂⁴×C₅	—	3	2	no	—
151	C₂⁴×C₅	—	6	2	no	—
152	C₂⁴×C₅	—	6	4	no	—
153	C₂⁴×C₅	—	6	4	no	—
154	C₂⁴×C₅	—	6	2	no	—
155	C₂⁴×C₅	C₄×D₃	1	4	yes	—
156	C₂⁴×C₅	D₁₂	1	4	yes	—
157	C₂⁴×C₅	#67	1	4	yes	—
158	C₂⁴×C₅	C₂²×D₃	1	2	yes	—
159	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
160	C₂×C₅×D₄	—	3	16	no	—
161	C₂×C₅×D₄	—	6	32	no	—
162	C₂×C₅×D₄	—	6	8	no	—
163	C₂×C₅×D₄	—	6	8	no	—
164	C₂²×C₄×C₅	—	2	32	no	—
165	C₂²×C₄×C₅	—	2	4	no	—
166	C₂²×C₄×C₅	—	2	4	no	—
167	C₂²×C₄×C₅	—	2	8	no	—
168	C₂²×C₄×C₅	—	2	16	no	—
169	C₂²×C₄×C₅	—	3	4	no	—
170	C₂²×C₄×C₅	—	3	2	no	—
171	C₂²×C₄×C₅	—	3	4	no	—
172	C₂²×C₄×C₅	—	6	2	no	—
173	C₂²×C₄×C₅	—	6	2	no	—
174	C₂²×C₄×C₅	—	6	4	no	—
175	C₂²×C₄×C₅	—	6	4	no	—
176	C₂²×C₄×C₅	—	6	4	no	—
177	C₂²×C₄×C₅	#67	1	8	yes	complemented
178	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
179	C₅×C₂²⋊C₄	—	6	8	no	—
180	C₅×C₂²⋊C₄	—	6	16	no	—
181	C₂³×D₄	—	3	1	no	—
182	C₂⁴×C₄	C₅×D₃	1	1	yes	characteristic, complemented
183	C₂²×C₂²⋊C₄	—	3	1	no	—
184	C₂²×C₂²⋊C₄	—	3	2	no	—
185	#386	—	3	8	no	—
186	C₂×#95	—	3	2	no	—
187	C₂²×C₃×C₅	—	2	8	no	—
188	C₂²×C₃×C₅	—	2	4	no	—
189	C₂²×C₃×C₅	—	2	8	no	—
190	C₂²×C₃×C₅	—	2	4	no	—
191	C₂²×C₃×C₅	—	2	32	no	—
192	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	4	yes	—
193	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	8	yes	complemented
194	C₂²×C₃×C₅	C₄×D₄	1	8	yes	—
195	C₂²×C₃×C₅	#120	1	4	yes	—
196	C₂²×C₃×C₅	#121	1	8	yes	—
197	C₂²×C₃×C₅	#123	1	4	yes	—
198	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
199	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
200	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
201	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
202	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
203	C₂×C₅×D₃	—	2	4	no	—
204	C₂×C₅×D₃	—	2	8	no	—
205	C₂×C₅×D₃	—	4	2	no	—
206	C₂×C₅×D₃	—	4	4	no	—
207	C₂×C₅×D₃	—	4	2	no	—
208	C₂×C₅×D₃	—	4	16	no	—
209	C₃×C₄×C₅	—	2	8	no	—
210	C₅×Dic₃	—	2	4	no	—
211	C₅×Dic₃	—	4	4	no	—
212	C₂⁴×C₃	—	2	4	no	—
213	C₂⁴×C₃	—	2	4	no	—
214	C₂⁴×C₃	C₂×C₄×C₅	1	4	yes	—
215	C₂⁴×C₃	C₅×D₄	1	4	yes	—
216	C₂⁴×C₃	C₅×D₄	1	4	yes	—
217	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
218	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
219	C₂³×D₃	—	2	4	no	—
220	C₂³×D₃	—	2	2	no	—
221	C₂³×D₃	—	2	2	no	—
222	C₂³×D₃	—	2	4	no	—
223	C₂³×D₃	C₂×C₄×C₅	1	4	yes	complemented
224	C₂³×D₃	C₂³×C₅	1	2	yes	—
225	C₂²×C₃×C₄	—	2	32	no	—
226	C₂²×C₃×C₄	—	2	4	no	—
227	C₂²×C₃×C₄	—	2	4	no	—
228	C₂²×C₃×C₄	—	2	8	no	—
229	C₂²×C₃×C₄	—	2	16	no	—
230	C₂²×C₃×C₄	C₅×D₄	1	8	yes	complemented
231	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
232	C₂×#67	—	2	32	no	—
233	C₂×#67	—	2	8	no	—
234	C₂×#67	—	2	8	no	—
235	C₂×#67	C₂×C₄×C₅	1	16	yes	complemented
236	C₂²×Dic₃	—	2	2	no	—
237	C₂²×Dic₃	—	2	2	no	—
238	C₂²×Dic₃	—	2	4	no	—
239	C₂²×Dic₃	—	2	4	no	—
240	C₂²×Dic₃	—	2	4	no	—
241	C₂²×Dic₃	C₂×C₄×C₅	1	4	yes	complemented
242	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
243	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
244	#217	—	2	8	no	—
245	(C₂×D₃)⋊C₄	—	2	16	no	—
246	C₂³×C₅	—	2	16	no	—
247	C₂³×C₅	—	2	8	no	—
248	C₂³×C₅	—	2	16	no	—
249	C₂³×C₅	—	2	8	no	—
250	C₂³×C₅	—	2	4	no	—
251	C₂³×C₅	—	2	4	no	—
252	C₂³×C₅	—	3	4	no	—
253	C₂³×C₅	—	6	8	no	—
254	C₂³×C₅	—	6	16	no	—
255	C₂³×C₅	—	6	2	no	—
256	C₂³×C₅	—	6	4	no	—
257	C₂³×C₅	—	6	4	no	—
258	C₂³×C₅	—	6	2	no	—
259	C₂³×C₅	—	12	4	no	—
260	C₂³×C₅	—	12	8	no	—
261	C₂³×C₅	—	12	4	no	—
262	C₂³×C₅	(C₂×D₃)⋊C₄	1	16	yes	complemented
263	C₂³×C₅	C₂×C₄×D₃	1	4	yes	—
264	C₂³×C₅	C₂×C₄×D₃	1	2	yes	—
265	C₂³×C₅	C₂×D₁₂	1	4	yes	—
266	C₂³×C₅	C₂×D₁₂	1	2	yes	—
267	C₂³×C₅	#235	1	4	yes	—
268	C₂³×C₅	C₂×#67	1	4	yes	—
269	C₂³×C₅	C₂×#67	1	2	yes	—
270	C₂³×C₅	C₂×#67	1	4	yes	—
271	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
272	C₅×D₄	—	6	32	no	—
273	C₂×C₄×C₅	—	2	32	no	—
274	C₂×C₄×C₅	—	2	16	no	—
275	C₂×C₄×C₅	—	2	4	no	—
276	C₂×C₄×C₅	—	2	4	no	—
277	C₂×C₄×C₅	—	3	4	no	—
278	C₂×C₄×C₅	—	6	8	no	—
279	C₂×C₄×C₅	—	6	2	no	—
280	C₂×C₄×C₅	—	6	2	no	—
281	C₂×C₄×C₅	—	6	4	no	—
282	C₂×C₄×C₅	—	6	4	no	—
283	C₂×C₄×C₅	—	6	4	no	—
284	C₂×C₄×C₅	—	12	8	no	—
285	C₂×C₄×C₅	C₂×#67	1	8	yes	complemented
286	C₂⁵	—	3	1	no	—
287	C₂⁵	C₂×C₅×D₃	1	1	yes	characteristic
288	C₂²×D₄	—	3	8	no	—
289	C₂²×D₄	—	3	4	no	—
290	C₂²×D₄	—	6	4	no	—
291	C₂²×D₄	—	6	4	no	—
292	C₂³×C₄	—	2	4	no	—
293	C₂³×C₄	—	2	8	no	—
294	C₂³×C₄	—	3	1	no	—
295	C₂³×C₄	—	3	2	no	—
296	C₂³×C₄	C₂×C₅×D₃	1	2	yes	—
297	C₂³×C₄	C₂×C₅×D₃	1	4	yes	complemented
298	C₂×C₂²⋊C₄	—	3	4	no	—
299	C₂×C₂²⋊C₄	—	3	8	no	—
300	C₂×C₂²⋊C₄	—	6	4	no	—
301	C₂×C₂²⋊C₄	—	6	8	no	—
302	#95	—	3	8	no	—
303	C₂×C₃×C₅	—	2	8	no	—
304	C₂×C₃×C₅	#386	1	8	yes	complemented
305	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
306	C₂×C₃×C₅	C₂×C₄×D₄	1	2	yes	—
307	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
308	C₂×C₃×C₅	C₂×#121	1	2	yes	—
309	C₂×C₃×C₅	C₂×#123	1	1	yes	characteristic
310	C₅×D₃	—	4	4	no	—
311	C₂³×C₃	—	2	16	no	—
312	C₂³×C₃	—	2	8	no	—
313	C₂³×C₃	—	2	16	no	—
314	C₂³×C₃	—	2	8	no	—
315	C₂³×C₃	—	2	4	no	—
316	C₂³×C₃	—	2	4	no	—
317	C₂³×C₃	C₅×C₂²⋊C₄	1	16	yes	complemented
318	C₂³×C₃	C₂²×C₄×C₅	1	4	yes	—
319	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
320	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
321	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
322	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
323	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
324	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
325	C₂³×C₃	C₅×#41	1	4	yes	—
326	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
327	C₂²×D₃	—	2	8	no	—
328	C₂²×D₃	—	2	16	no	—
329	C₂²×D₃	—	2	4	no	—
330	C₂²×D₃	—	2	2	no	—
331	C₂²×D₃	—	2	2	no	—
332	C₂²×D₃	—	2	4	no	—
333	C₂²×D₃	—	4	4	no	—
334	C₂²×D₃	—	4	8	no	—
335	C₂²×D₃	—	4	4	no	—
336	C₂²×D₃	C₂²×C₄×C₅	1	4	yes	complemented
337	C₂×C₃×C₄	—	2	32	no	—
338	C₂×C₃×C₄	—	2	16	no	—
339	C₂×C₃×C₄	—	2	4	no	—
340	C₂×C₃×C₄	—	2	4	no	—
341	C₂×C₃×C₄	C₂×C₅×D₄	1	8	yes	complemented
342	#67	—	2	32	no	—
343	C₂×Dic₃	—	2	8	no	—
344	C₂×Dic₃	—	2	2	no	—
345	C₂×Dic₃	—	2	2	no	—
346	C₂×Dic₃	—	2	4	no	—
347	C₂×Dic₃	—	2	4	no	—
348	C₂×Dic₃	—	2	4	no	—
349	C₂×Dic₃	—	4	8	no	—
350	C₂×Dic₃	C₂²×C₄×C₅	1	4	yes	complemented
351	C₂²×C₅	—	2	32	no	—
352	C₂²×C₅	—	2	8	no	—
353	C₂²×C₅	—	2	4	no	—
354	C₂²×C₅	—	2	8	no	—
355	C₂²×C₅	—	2	4	no	—
356	C₂²×C₅	—	6	4	no	—
357	C₂²×C₅	—	6	8	no	—
358	C₂²×C₅	—	12	16	no	—
359	C₂²×C₅	—	12	2	no	—
360	C₂²×C₅	—	12	4	no	—
361	C₂²×C₅	—	12	2	no	—
362	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	4	yes	—
363	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	8	yes	complemented
364	C₂²×C₅	C₄×#67	1	8	yes	—
365	C₂²×C₅	#929	1	4	yes	—
366	C₂²×C₅	#930	1	8	yes	—
367	C₂²×C₅	#953	1	4	yes	—
368	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
369	C₂²×C₅	C₂²×D₁₂	1	1	yes	characteristic
370	C₂²×C₅	C₂×#235	1	2	yes	—
371	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
372	C₂²×C₅	C₂²×#67	1	2	yes	—
373	C₄×C₅	—	2	8	no	—
374	C₄×C₅	—	6	4	no	—
375	C₄×C₅	—	12	4	no	—
376	C₂⁴	—	2	4	no	—
377	C₂⁴	—	2	4	no	—
378	C₂⁴	—	3	4	no	—
379	C₂⁴	—	3	2	no	—
380	C₂⁴	—	6	2	no	—
381	C₂⁴	—	6	4	no	—
382	C₂⁴	—	6	4	no	—
383	C₂⁴	—	6	2	no	—
384	C₂⁴	C₄×C₅×D₃	1	4	yes	—
385	C₂⁴	C₅×D₁₂	1	4	yes	—
386	C₂⁴	C₅×#67	1	4	yes	—
387	C₂⁴	C₂²×C₅×D₃	1	2	yes	—
388	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
389	C₂×D₄	—	3	16	no	—
390	C₂×D₄	—	6	32	no	—
391	C₂×D₄	—	6	8	no	—
392	C₂×D₄	—	6	8	no	—
393	C₂²×C₄	—	2	32	no	—
394	C₂²×C₄	—	2	4	no	—
395	C₂²×C₄	—	2	4	no	—
396	C₂²×C₄	—	2	8	no	—
397	C₂²×C₄	—	2	16	no	—
398	C₂²×C₄	—	3	4	no	—
399	C₂²×C₄	—	3	2	no	—
400	C₂²×C₄	—	3	4	no	—
401	C₂²×C₄	—	6	2	no	—
402	C₂²×C₄	—	6	2	no	—
403	C₂²×C₄	—	6	4	no	—
404	C₂²×C₄	—	6	4	no	—
405	C₂²×C₄	—	6	4	no	—
406	C₂²×C₄	C₅×#67	1	8	yes	complemented
407	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
408	C₂²⋊C₄	—	6	8	no	—
409	C₂²⋊C₄	—	6	16	no	—
410	C₃×C₅	C₂×#386	1	1	yes	characteristic, complemented, Hall
411	C₂²×C₃	—	2	32	no	—
412	C₂²×C₃	—	2	8	no	—
413	C₂²×C₃	—	2	4	no	—
414	C₂²×C₃	—	2	8	no	—
415	C₂²×C₃	—	2	4	no	—
416	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	4	yes	—
417	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	8	yes	complemented
418	C₂²×C₃	C₄×C₅×D₄	1	8	yes	—
419	C₂²×C₃	C₅×#120	1	4	yes	—
420	C₂²×C₃	C₅×#121	1	8	yes	—
421	C₂²×C₃	C₅×#123	1	4	yes	—
422	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
423	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
424	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
425	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
426	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
427	C₂×D₃	—	2	4	no	—
428	C₂×D₃	—	2	8	no	—
429	C₂×D₃	—	4	16	no	—
430	C₂×D₃	—	4	2	no	—
431	C₂×D₃	—	4	4	no	—
432	C₂×D₃	—	4	2	no	—
433	C₃×C₄	—	2	8	no	—
434	Dic₃	—	2	4	no	—
435	Dic₃	—	4	4	no	—
436	C₂×C₅	—	2	8	no	—
437	C₂×C₅	—	12	4	no	—
438	C₂×C₅	#5213	1	8	yes	direct product factor
439	C₂×C₅	C₂²×(C₂×D₃)⋊C₄	1	1	yes	characteristic
440	C₂×C₅	C₂×C₄×#67	1	2	yes	—
441	C₂×C₅	C₂×#929	1	1	yes	characteristic
442	C₂×C₅	C₂×#930	1	2	yes	—
443	C₂×C₅	C₂×#953	1	1	yes	characteristic
444	C₂³	—	2	16	no	—
445	C₂³	—	2	8	no	—
446	C₂³	—	2	16	no	—
447	C₂³	—	2	8	no	—
448	C₂³	—	2	4	no	—
449	C₂³	—	2	4	no	—
450	C₂³	—	3	4	no	—
451	C₂³	—	6	8	no	—
452	C₂³	—	6	16	no	—
453	C₂³	—	6	2	no	—
454	C₂³	—	6	4	no	—
455	C₂³	—	6	4	no	—
456	C₂³	—	6	2	no	—
457	C₂³	—	12	4	no	—
458	C₂³	—	12	8	no	—
459	C₂³	—	12	4	no	—
460	C₂³	C₅×(C₂×D₃)⋊C₄	1	16	yes	complemented
461	C₂³	C₂×C₄×C₅×D₃	1	4	yes	—
462	C₂³	C₂×C₄×C₅×D₃	1	2	yes	—
463	C₂³	C₂×C₅×D₁₂	1	4	yes	—
464	C₂³	C₂×C₅×D₁₂	1	2	yes	—
465	C₂³	C₅×#235	1	4	yes	—
466	C₂³	C₂×C₅×#67	1	4	yes	—
467	C₂³	C₂×C₅×#67	1	2	yes	—
468	C₂³	C₂×C₅×#67	1	4	yes	—
469	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
470	D₄	—	6	32	no	—
471	C₂×C₄	—	2	32	no	—
472	C₂×C₄	—	2	16	no	—
473	C₂×C₄	—	2	4	no	—
474	C₂×C₄	—	2	4	no	—
475	C₂×C₄	—	3	4	no	—
476	C₂×C₄	—	6	8	no	—
477	C₂×C₄	—	6	2	no	—
478	C₂×C₄	—	6	2	no	—
479	C₂×C₄	—	6	4	no	—
480	C₂×C₄	—	6	4	no	—
481	C₂×C₄	—	6	4	no	—
482	C₂×C₄	—	12	8	no	—
483	C₂×C₄	C₂×C₅×#67	1	8	yes	complemented
484	C₂×C₃	—	2	8	no	—
485	C₂×C₃	C₅×#386	1	8	yes	complemented
486	C₂×C₃	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
487	C₂×C₃	C₂×C₄×C₅×D₄	1	2	yes	—
488	C₂×C₃	C₂×C₅×#120	1	1	yes	characteristic
489	C₂×C₃	C₂×C₅×#121	1	2	yes	—
490	C₂×C₃	C₂×C₅×#123	1	1	yes	characteristic
491	D₃	—	4	4	no	—
492	C₅	C₂×#5213	1	1	yes	characteristic, direct product factor, Sylow
493	C₂²	—	2	32	no	—
494	C₂²	—	2	8	no	—
495	C₂²	—	2	4	no	—
496	C₂²	—	2	8	no	—
497	C₂²	—	2	4	no	—
498	C₂²	—	6	4	no	—
499	C₂²	—	6	8	no	—
500	C₂²	—	12	16	no	—
501	C₂²	—	12	2	no	—
502	C₂²	—	12	4	no	—
503	C₂²	—	12	2	no	—
504	C₂²	C₂×C₅×(C₂×D₃)⋊C₄	1	4	yes	—
505	C₂²	C₂×C₅×(C₂×D₃)⋊C₄	1	8	yes	complemented
506	C₂²	C₄×C₅×#67	1	8	yes	—
507	C₂²	C₅×#929	1	4	yes	—
508	C₂²	C₅×#930	1	8	yes	—
509	C₂²	C₅×#953	1	4	yes	—
510	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
511	C₂²	C₂²×C₅×D₁₂	1	1	yes	characteristic
512	C₂²	C₂×C₅×#235	1	2	yes	—
513	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
514	C₂²	C₂²×C₅×#67	1	2	yes	—
515	C₄	—	2	8	no	—
516	C₄	—	6	4	no	—
517	C₄	—	12	4	no	—
518	C₃	C₂×C₅×#386	1	1	yes	characteristic, complemented, Sylow
519	C₂	—	2	8	no	—
520	C₂	—	12	4	no	—
521	C₂	C₅×#5213	1	8	yes	direct product factor
522	C₂	C₂²×C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
523	C₂	C₂×C₄×C₅×#67	1	2	yes	—
524	C₂	C₂×C₅×#929	1	1	yes	characteristic
525	C₂	C₂×C₅×#930	1	2	yes	—
526	C₂	C₂×C₅×#953	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴×C₅	C₂²×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂³	C₂³×C₅×D₃
Fitting	C₂⁴×C₃×C₄×C₅	C₂
socle	C₂⁴×C₃×C₅	C₂³
prime radical	C₂³×C₅×#67	C₂
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₂⁴×C₄×C₅	D₃
hypocenter	C₃	C₂×C₅×#386
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂⁴×C₅ ◁ C₂⁴×C₄×C₅

Complements

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

N	H ≅ G/N	type
1. C₂⁴×C₃×C₄×C₅	C₂	semidirect
3. C₂²×C₅×#217	C₂	semidirect
4. C₂²×C₅×(C₂×D₃)⋊C₄	C₂	semidirect
5. C₅×#5213	C₂	direct (N × H)
6. C₂×C₅×C₃⋊#95	C₂	semidirect
13. C₂³×C₃×C₄×C₅	C₂²	semidirect
16. C₂²×C₅×#67	C₄	semidirect
21. C₂×C₅×#217	C₂²	semidirect
23. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
24. C₅×C₃⋊#95	C₂²	semidirect
25. C₂×#5213	C₅	direct (N × H)
27. C₂⁴×C₄×C₅	D₃	semidirect
43. C₂³×C₅×D₃	C₂×C₄	semidirect
50. C₂²×C₃×C₄×C₅	D₄	semidirect
55. C₂×C₅×#67	C₂×C₄	semidirect
61. C₂²×C₅×Dic₃	C₂×C₄	semidirect
66. C₂⁴×C₃×C₄	C₂×C₅	semidirect
68. C₂²×#217	C₂×C₅	semidirect
69. C₂²×(C₂×D₃)⋊C₄	C₂×C₅	semidirect
70. #5213	C₂×C₅	direct (N × H)
71. C₂×C₃⋊#95	C₂×C₅	semidirect
83. C₂³×C₄×C₅	C₂×D₃	semidirect
96. C₂³×C₃×C₅	C₂²⋊C₄	semidirect
115. C₂²×C₅×D₃	C₂²×C₄	semidirect
120. C₂×C₃×C₄×C₅	C₂×D₄	semidirect
129. C₂×C₅×Dic₃	C₂²×C₄	semidirect
135. C₂³×C₃×C₄	C₂²×C₅	semidirect
138. C₂²×#67	C₄×C₅	semidirect
143. C₂×#217	C₂²×C₅	semidirect
145. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
146. C₃⋊#95	C₂²×C₅	semidirect
177. C₂²×C₄×C₅	#67	semidirect
182. C₂⁴×C₄	C₅×D₃	semidirect
193. C₂²×C₃×C₅	C₂×C₂²⋊C₄	semidirect
223. C₂³×D₃	C₂×C₄×C₅	semidirect
230. C₂²×C₃×C₄	C₅×D₄	semidirect
235. C₂×#67	C₂×C₄×C₅	semidirect
241. C₂²×Dic₃	C₂×C₄×C₅	semidirect
262. C₂³×C₅	(C₂×D₃)⋊C₄	semidirect
285. C₂×C₄×C₅	C₂×#67	semidirect
297. C₂³×C₄	C₂×C₅×D₃	semidirect
304. C₂×C₃×C₅	#386	semidirect
317. C₂³×C₃	C₅×C₂²⋊C₄	semidirect
336. C₂²×D₃	C₂²×C₄×C₅	semidirect
341. C₂×C₃×C₄	C₂×C₅×D₄	semidirect
350. C₂×Dic₃	C₂²×C₄×C₅	semidirect
363. C₂²×C₅	C₂×(C₂×D₃)⋊C₄	semidirect
406. C₂²×C₄	C₅×#67	semidirect
410. C₃×C₅	C₂×#386	semidirect
417. C₂²×C₃	C₂×C₅×C₂²⋊C₄	semidirect
438. C₂×C₅	#5213	direct (N × H)
460. C₂³	C₅×(C₂×D₃)⋊C₄	semidirect
483. C₂×C₄	C₂×C₅×#67	semidirect
485. C₂×C₃	C₅×#386	semidirect
492. C₅	C₂×#5213	direct (N × H)
505. C₂²	C₂×C₅×(C₂×D₃)⋊C₄	semidirect
518. C₃	C₂×C₅×#386	semidirect
521. C₂	C₅×#5213	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×C₃×C₄×C₅	2
C₂³×C₅×#67	2
C₂²×C₅×#217	2
C₂²×C₅×(C₂×D₃)⋊C₄	2
C₅×#5213	2
C₂×C₅×C₃⋊#95	2
C₂×C₅×#386	3
C₂×#5213	5

Subgroups — C2×C5×#5213 #14320284

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5213 #14320284