Subgroups — C₂×C₅×#5039 #14427978

Order 1920.

1192 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	C₂×C₃×C₅×#121	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×#213	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#930	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₅×#208	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#832	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5039	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₅×#809	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅×#808	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×#469	—	3	1	no	maximal, Hall
10	C₂²×C₃×C₅×D₄	—	2	1	no	—
11	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
12	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
13	C₂²×C₅×#67	—	2	1	no	—
14	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
15	C₃×C₅×#121	—	2	2	no	—
16	C₃×C₅×#121	C₂²	1	4	yes	complemented
17	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₅×C₂²⋊C₄	—	2	1	no	—
19	C₂×C₅×#213	—	2	4	no	—
20	C₂×C₅×#213	C₂²	1	4	yes	complemented
21	C₅×#930	—	2	2	no	—
22	C₅×#930	C₂²	1	4	yes	complemented
23	C₂×C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
24	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
25	C₂×C₅×#208	—	2	4	no	—
26	C₂×C₅×#208	C₂²	1	4	yes	complemented
27	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
28	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
29	C₅×#832	C₂²	1	4	yes	complemented
30	C₅×#809	C₂²	1	4	yes	complemented
31	C₅×#808	C₂²	1	4	yes	complemented
32	C₂×#5039	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
33	C₂²×C₅×D₈	—	3	1	no	—
34	C₂²×C₅×M₁₆	—	3	1	no	—
35	C₂×C₅×#121	—	3	1	no	—
36	C₂×C₅×#121	D₃	1	1	yes	characteristic, complemented
37	C₅×#469	—	3	8	no	—
38	C₂×C₅×#106	—	3	1	no	—
39	C₂×C₅×#102	—	3	1	no	—
40	C₂×C₅×#102	—	3	1	no	—
41	C₂⁴×C₃×C₅	—	2	1	no	—
42	C₂⁴×C₃×C₅	D₄	1	1	yes	characteristic
43	C₂³×C₅×D₃	—	2	1	no	—
44	C₂×C₃×C₅×D₄	—	2	4	no	—
45	C₂×C₃×C₅×D₄	—	2	2	no	—
46	C₂×C₃×C₅×D₄	—	2	1	no	—
47	C₂×C₃×C₅×D₄	—	2	2	no	—
48	C₂×C₃×C₅×D₄	—	4	4	no	—
49	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
50	C₂²×C₃×C₄×C₅	—	2	2	no	—
51	C₂²×C₃×C₄×C₅	—	2	2	no	—
52	C₂²×C₃×C₄×C₅	—	2	1	no	—
53	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
54	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
55	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
56	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
57	C₂×C₅×#67	—	2	4	no	—
58	C₂×C₅×#67	—	4	4	no	—
59	C₂²×C₅×Dic₃	—	2	1	no	—
60	C₂×C₅×D₁₂	—	2	2	no	—
61	C₂×C₅×D₁₂	—	2	2	no	—
62	C₂×C₅×D₁₂	—	2	1	no	—
63	C₂×C₅×D₁₂	C₂³	1	2	yes	—
64	C₃×C₅×C₄⋊C₄	—	2	1	no	—
65	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
66	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
67	C₅×#213	—	2	8	no	—
68	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
69	C₅×C₄⋊Dic₃	—	2	1	no	—
70	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
71	C₅×#208	—	2	8	no	—
72	C₂×C₅×C₃⋊C₈	—	2	2	no	—
73	C₂×C₅×C₃⋊C₈	D₄	1	4	yes	complemented
74	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
75	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
76	C₂×C₃×#121	C₂×C₅	1	1	yes	characteristic, complemented
77	C₂²×#213	C₂×C₅	1	1	yes	characteristic, complemented
78	C₂×#930	C₂×C₅	1	1	yes	characteristic, complemented
79	C₂²×#208	C₂×C₅	1	1	yes	characteristic, complemented
80	C₂×#832	C₂×C₅	1	1	yes	characteristic, complemented
81	#5039	C₂×C₅	1	8	yes	direct product factor
82	C₂×#809	C₂×C₅	1	1	yes	characteristic, complemented
83	C₂×#808	C₂×C₅	1	1	yes	characteristic, complemented
84	C₂²×C₅×D₄	—	2	1	no	—
85	C₂²×C₅×D₄	—	3	1	no	—
86	C₂²×C₅×D₄	—	6	1	no	—
87	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
88	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
89	C₂×C₅×D₈	—	3	4	no	—
90	C₂×C₅×D₈	—	6	4	no	—
91	C₂×C₅×M₁₆	—	3	4	no	—
92	C₂×C₅×M₁₆	—	6	4	no	—
93	C₂²×C₅×C₈	—	3	1	no	—
94	C₂²×C₅×C₈	—	3	1	no	—
95	C₅×#121	—	2	2	no	—
96	C₅×#121	—	3	4	no	—
97	C₅×#121	—	6	2	no	—
98	C₅×#121	C₂×D₃	1	4	yes	complemented
99	C₂×C₅×C₄⋊C₄	—	3	1	no	—
100	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
101	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
102	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
103	C₅×#106	—	3	4	no	—
104	C₅×#102	—	3	4	no	—
105	C₅×#102	—	3	4	no	—
106	C₂×#469	—	3	1	no	Sylow
107	C₂³×C₃×C₅	—	2	2	no	—
108	C₂³×C₃×C₅	—	2	2	no	—
109	C₂³×C₃×C₅	—	2	2	no	—
110	C₂³×C₃×C₅	—	2	2	no	—
111	C₂³×C₃×C₅	—	4	2	no	—
112	C₂³×C₃×C₅	—	4	2	no	—
113	C₂³×C₃×C₅	—	4	2	no	—
114	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
115	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₅×D₃	—	2	2	no	—
117	C₂²×C₅×D₃	—	4	2	no	—
118	C₂²×C₅×D₃	—	4	2	no	—
119	C₂²×C₅×D₃	—	4	2	no	—
120	C₃×C₅×D₄	—	2	2	no	—
121	C₃×C₅×D₄	—	2	2	no	—
122	C₃×C₅×D₄	—	4	8	no	—
123	C₃×C₅×D₄	—	4	2	no	—
124	C₂×C₃×C₄×C₅	—	2	2	no	—
125	C₂×C₃×C₄×C₅	—	2	4	no	—
126	C₂×C₃×C₄×C₅	—	2	2	no	—
127	C₂×C₃×C₄×C₅	—	2	2	no	—
128	C₂×C₃×C₄×C₅	—	2	2	no	—
129	C₂×C₃×C₄×C₅	—	4	2	no	—
130	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
131	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
132	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
133	C₂×C₃×C₄×C₅	#41	1	2	yes	—
134	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
135	C₅×#67	—	4	8	no	—
136	C₂×C₅×Dic₃	—	2	2	no	—
137	C₂×C₅×Dic₃	—	4	2	no	—
138	C₅×D₁₂	—	2	2	no	—
139	C₅×D₁₂	—	2	2	no	—
140	C₅×D₁₂	—	4	2	no	—
141	C₅×C₃⋊C₈	—	2	2	no	—
142	C₅×C₃⋊C₈	C₂×D₄	1	4	yes	complemented
143	C₂²×C₃×D₄	—	2	1	no	—
144	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
145	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
146	C₂²×#67	—	2	1	no	—
147	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
148	C₃×#121	—	2	2	no	—
149	C₃×#121	C₂²×C₅	1	4	yes	complemented
150	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
151	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
152	C₂×#213	—	2	4	no	—
153	C₂×#213	C₂²×C₅	1	4	yes	complemented
154	#930	—	2	2	no	—
155	#930	C₂²×C₅	1	4	yes	complemented
156	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
157	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
158	C₂×#208	—	2	4	no	—
159	C₂×#208	C₂²×C₅	1	4	yes	complemented
160	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
161	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
162	#832	C₂²×C₅	1	4	yes	complemented
163	#809	C₂²×C₅	1	4	yes	complemented
164	#808	C₂²×C₅	1	4	yes	complemented
165	C₂⁴×C₅	—	2	1	no	—
166	C₂⁴×C₅	—	6	1	no	—
167	C₂⁴×C₅	#67	1	1	yes	characteristic
168	C₂×C₅×D₄	—	2	4	no	—
169	C₂×C₅×D₄	—	2	2	no	—
170	C₂×C₅×D₄	—	2	2	no	—
171	C₂×C₅×D₄	—	2	1	no	—
172	C₂×C₅×D₄	—	3	2	no	—
173	C₂×C₅×D₄	—	4	4	no	—
174	C₂×C₅×D₄	—	6	4	no	—
175	C₂×C₅×D₄	—	6	2	no	—
176	C₂×C₅×D₄	—	6	2	no	—
177	C₂×C₅×D₄	—	6	1	no	—
178	C₂×C₅×D₄	—	12	4	no	—
179	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
180	C₂²×C₄×C₅	—	2	2	no	—
181	C₂²×C₄×C₅	—	2	2	no	—
182	C₂²×C₄×C₅	—	2	1	no	—
183	C₂²×C₄×C₅	—	6	1	no	—
184	C₂²×C₄×C₅	#67	1	2	yes	—
185	C₂²×C₄×C₅	#67	1	1	yes	characteristic
186	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
187	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
188	C₅×D₈	—	6	8	no	—
189	C₅×M₁₆	—	6	8	no	—
190	C₂×C₅×C₈	—	3	4	no	—
191	C₂×C₅×C₈	—	3	2	no	—
192	C₂×C₅×C₈	—	3	2	no	—
193	C₂×C₅×C₈	—	6	2	no	—
194	C₅×C₄⋊C₄	—	2	1	no	—
195	C₅×C₄⋊C₄	—	3	2	no	—
196	C₅×C₄⋊C₄	—	6	1	no	—
197	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
198	C₅×C₂²⋊C₄	—	2	4	no	—
199	C₅×C₂²⋊C₄	—	6	4	no	—
200	C₂²×D₈	—	3	1	no	—
201	C₂²×M₁₆	—	3	1	no	—
202	C₂×#121	—	3	1	no	—
203	C₂×#121	C₅×D₃	1	1	yes	characteristic, complemented
204	#469	—	3	8	no	—
205	C₂×#106	—	3	1	no	—
206	C₂×#102	—	3	1	no	—
207	C₂×#102	—	3	1	no	—
208	C₂²×C₃×C₅	—	2	2	no	—
209	C₂²×C₃×C₅	—	2	2	no	—
210	C₂²×C₃×C₅	—	2	2	no	—
211	C₂²×C₃×C₅	—	4	4	no	—
212	C₂²×C₃×C₅	—	4	2	no	—
213	C₂²×C₃×C₅	—	4	2	no	—
214	C₂²×C₃×C₅	—	4	2	no	—
215	C₂²×C₃×C₅	—	8	4	no	—
216	C₂²×C₃×C₅	#121	1	2	yes	—
217	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	—
218	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	—
219	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
220	C₂×C₅×D₃	—	4	2	no	—
221	C₂×C₅×D₃	—	4	2	no	—
222	C₂×C₅×D₃	—	4	2	no	—
223	C₂×C₅×D₃	—	8	4	no	—
224	C₃×C₄×C₅	—	2	2	no	—
225	C₃×C₄×C₅	—	4	2	no	—
226	C₃×C₄×C₅	#121	1	2	yes	—
227	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
228	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
229	C₅×Dic₃	—	4	2	no	—
230	C₂⁴×C₃	—	2	1	no	—
231	C₂⁴×C₃	C₅×D₄	1	1	yes	characteristic
232	C₂³×D₃	—	2	1	no	—
233	C₂×C₃×D₄	—	2	4	no	—
234	C₂×C₃×D₄	—	2	2	no	—
235	C₂×C₃×D₄	—	2	1	no	—
236	C₂×C₃×D₄	—	2	2	no	—
237	C₂×C₃×D₄	—	4	4	no	—
238	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
239	C₂²×C₃×C₄	—	2	2	no	—
240	C₂²×C₃×C₄	—	2	2	no	—
241	C₂²×C₃×C₄	—	2	1	no	—
242	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
243	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
244	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
245	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
246	C₂×#67	—	2	4	no	—
247	C₂×#67	—	4	4	no	—
248	C₂²×Dic₃	—	2	1	no	—
249	C₂×D₁₂	—	2	2	no	—
250	C₂×D₁₂	—	2	2	no	—
251	C₂×D₁₂	—	2	1	no	—
252	C₂×D₁₂	C₂³×C₅	1	2	yes	—
253	C₃×C₄⋊C₄	—	2	1	no	—
254	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
255	C₃×C₂²⋊C₄	—	2	4	no	—
256	#213	—	2	8	no	—
257	(C₂×D₃)⋊C₄	—	2	4	no	—
258	C₄⋊Dic₃	—	2	1	no	—
259	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
260	#208	—	2	8	no	—
261	C₂×C₃⋊C₈	—	2	2	no	—
262	C₂×C₃⋊C₈	C₅×D₄	1	4	yes	complemented
263	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
264	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
265	C₂³×C₅	—	2	2	no	—
266	C₂³×C₅	—	2	2	no	—
267	C₂³×C₅	—	2	2	no	—
268	C₂³×C₅	—	2	2	no	—
269	C₂³×C₅	—	4	2	no	—
270	C₂³×C₅	—	4	2	no	—
271	C₂³×C₅	—	4	2	no	—
272	C₂³×C₅	—	6	2	no	—
273	C₂³×C₅	—	12	2	no	—
274	C₂³×C₅	—	12	2	no	—
275	C₂³×C₅	—	12	2	no	—
276	C₂³×C₅	C₂×#67	1	2	yes	—
277	C₂³×C₅	C₂×#67	1	1	yes	characteristic
278	C₅×D₄	—	2	2	no	—
279	C₅×D₄	—	2	2	no	—
280	C₅×D₄	—	4	8	no	—
281	C₅×D₄	—	4	2	no	—
282	C₅×D₄	—	6	2	no	—
283	C₅×D₄	—	6	2	no	—
284	C₅×D₄	—	12	8	no	—
285	C₅×D₄	—	12	2	no	—
286	C₂×C₄×C₅	—	2	2	no	—
287	C₂×C₄×C₅	—	2	4	no	—
288	C₂×C₄×C₅	—	2	2	no	—
289	C₂×C₄×C₅	—	2	2	no	—
290	C₂×C₄×C₅	—	2	2	no	—
291	C₂×C₄×C₅	—	4	2	no	—
292	C₂×C₄×C₅	—	6	2	no	—
293	C₂×C₄×C₅	—	12	2	no	—
294	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
295	C₂×C₄×C₅	#237	1	2	yes	—
296	C₂×C₄×C₅	C₂×#67	1	2	yes	—
297	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
298	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
299	C₅×C₈	—	3	4	no	—
300	C₅×C₈	—	6	2	no	—
301	C₂²×D₄	—	2	1	no	—
302	C₂²×D₄	—	3	1	no	—
303	C₂²×D₄	—	6	1	no	—
304	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
305	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
306	C₂×D₈	—	3	4	no	—
307	C₂×D₈	—	6	4	no	—
308	C₂×M₁₆	—	3	4	no	—
309	C₂×M₁₆	—	6	4	no	—
310	C₂²×C₈	—	3	1	no	—
311	C₂²×C₈	—	3	1	no	—
312	#121	—	2	2	no	—
313	#121	—	3	4	no	—
314	#121	—	6	2	no	—
315	#121	C₂×C₅×D₃	1	4	yes	complemented
316	C₂×C₄⋊C₄	—	3	1	no	—
317	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
318	C₂×C₂²⋊C₄	—	2	1	no	—
319	C₂×C₂²⋊C₄	—	6	1	no	—
320	#106	—	3	4	no	—
321	#102	—	3	4	no	—
322	#102	—	3	4	no	—
323	C₂×C₃×C₅	—	4	2	no	—
324	C₂×C₃×C₅	—	8	2	no	—
325	C₂×C₃×C₅	#469	1	4	yes	complemented
326	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
327	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
328	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
329	C₅×D₃	—	8	2	no	—
330	C₂³×C₃	—	2	2	no	—
331	C₂³×C₃	—	2	2	no	—
332	C₂³×C₃	—	2	2	no	—
333	C₂³×C₃	—	2	2	no	—
334	C₂³×C₃	—	4	2	no	—
335	C₂³×C₃	—	4	2	no	—
336	C₂³×C₃	—	4	2	no	—
337	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
338	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
339	C₂²×D₃	—	2	2	no	—
340	C₂²×D₃	—	4	2	no	—
341	C₂²×D₃	—	4	2	no	—
342	C₂²×D₃	—	4	2	no	—
343	C₃×D₄	—	2	2	no	—
344	C₃×D₄	—	2	2	no	—
345	C₃×D₄	—	4	8	no	—
346	C₃×D₄	—	4	2	no	—
347	C₂×C₃×C₄	—	2	2	no	—
348	C₂×C₃×C₄	—	2	4	no	—
349	C₂×C₃×C₄	—	2	2	no	—
350	C₂×C₃×C₄	—	2	2	no	—
351	C₂×C₃×C₄	—	2	2	no	—
352	C₂×C₃×C₄	—	4	2	no	—
353	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
354	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
355	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
356	C₂×C₃×C₄	C₅×#41	1	2	yes	—
357	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
358	#67	—	4	8	no	—
359	C₂×Dic₃	—	2	2	no	—
360	C₂×Dic₃	—	4	2	no	—
361	D₁₂	—	2	2	no	—
362	D₁₂	—	2	2	no	—
363	D₁₂	—	4	2	no	—
364	C₃⋊C₈	—	2	2	no	—
365	C₃⋊C₈	C₂×C₅×D₄	1	4	yes	complemented
366	C₂²×C₅	—	2	2	no	—
367	C₂²×C₅	—	2	2	no	—
368	C₂²×C₅	—	2	2	no	—
369	C₂²×C₅	—	4	4	no	—
370	C₂²×C₅	—	4	2	no	—
371	C₂²×C₅	—	4	2	no	—
372	C₂²×C₅	—	4	2	no	—
373	C₂²×C₅	—	8	4	no	—
374	C₂²×C₅	—	12	2	no	—
375	C₂²×C₅	—	12	2	no	—
376	C₂²×C₅	—	12	2	no	—
377	C₂²×C₅	—	24	4	no	—
378	C₂²×C₅	#932	1	2	yes	—
379	C₂²×C₅	#939	1	2	yes	—
380	C₂²×C₅	#949	1	2	yes	—
381	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
382	C₄×C₅	—	2	2	no	—
383	C₄×C₅	—	4	2	no	—
384	C₄×C₅	—	12	2	no	—
385	C₄×C₅	#939	1	2	yes	—
386	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
387	C₄×C₅	C₂×#237	1	1	yes	characteristic
388	C₂⁴	—	2	1	no	—
389	C₂⁴	—	6	1	no	—
390	C₂⁴	C₅×#67	1	1	yes	characteristic
391	C₂×D₄	—	2	4	no	—
392	C₂×D₄	—	2	2	no	—
393	C₂×D₄	—	2	2	no	—
394	C₂×D₄	—	2	1	no	—
395	C₂×D₄	—	3	2	no	—
396	C₂×D₄	—	4	4	no	—
397	C₂×D₄	—	6	4	no	—
398	C₂×D₄	—	6	2	no	—
399	C₂×D₄	—	6	2	no	—
400	C₂×D₄	—	6	1	no	—
401	C₂×D₄	—	12	4	no	—
402	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	2	1	no	—
406	C₂²×C₄	—	6	1	no	—
407	C₂²×C₄	C₅×#67	1	1	yes	characteristic
408	C₂²×C₄	C₅×#67	1	2	yes	—
409	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
410	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
411	D₈	—	6	8	no	—
412	M₁₆	—	6	8	no	—
413	C₂×C₈	—	3	4	no	—
414	C₂×C₈	—	3	2	no	—
415	C₂×C₈	—	3	2	no	—
416	C₂×C₈	—	6	2	no	—
417	C₄⋊C₄	—	2	1	no	—
418	C₄⋊C₄	—	3	2	no	—
419	C₄⋊C₄	—	6	1	no	—
420	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
421	C₂²⋊C₄	—	2	4	no	—
422	C₂²⋊C₄	—	6	4	no	—
423	C₃×C₅	C₂×#469	1	1	yes	characteristic, complemented, Hall
424	C₂²×C₃	—	2	2	no	—
425	C₂²×C₃	—	2	2	no	—
426	C₂²×C₃	—	2	2	no	—
427	C₂²×C₃	—	4	4	no	—
428	C₂²×C₃	—	4	2	no	—
429	C₂²×C₃	—	4	2	no	—
430	C₂²×C₃	—	4	2	no	—
431	C₂²×C₃	—	8	4	no	—
432	C₂²×C₃	C₅×#121	1	2	yes	—
433	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	2	yes	—
434	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	2	yes	—
435	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
436	C₂×D₃	—	4	2	no	—
437	C₂×D₃	—	4	2	no	—
438	C₂×D₃	—	4	2	no	—
439	C₂×D₃	—	8	4	no	—
440	C₃×C₄	—	2	2	no	—
441	C₃×C₄	—	4	2	no	—
442	C₃×C₄	C₅×#121	1	2	yes	—
443	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
444	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
445	Dic₃	—	4	2	no	—
446	C₂×C₅	—	4	2	no	—
447	C₂×C₅	—	8	2	no	—
448	C₂×C₅	—	24	2	no	—
449	C₂×C₅	#5039	1	4	yes	direct product factor
450	C₂×C₅	C₂×#932	1	1	yes	characteristic
451	C₂×C₅	C₂×#939	1	1	yes	characteristic
452	C₂×C₅	C₂×#949	1	1	yes	characteristic
453	C₂³	—	2	2	no	—
454	C₂³	—	2	2	no	—
455	C₂³	—	2	2	no	—
456	C₂³	—	2	2	no	—
457	C₂³	—	4	2	no	—
458	C₂³	—	4	2	no	—
459	C₂³	—	4	2	no	—
460	C₂³	—	6	2	no	—
461	C₂³	—	12	2	no	—
462	C₂³	—	12	2	no	—
463	C₂³	—	12	2	no	—
464	C₂³	C₂×C₅×#67	1	2	yes	—
465	C₂³	C₂×C₅×#67	1	1	yes	characteristic
466	D₄	—	2	2	no	—
467	D₄	—	2	2	no	—
468	D₄	—	4	8	no	—
469	D₄	—	4	2	no	—
470	D₄	—	6	2	no	—
471	D₄	—	6	2	no	—
472	D₄	—	12	8	no	—
473	D₄	—	12	2	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	6	2	no	—
481	C₂×C₄	—	12	2	no	—
482	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
483	C₂×C₄	C₅×#237	1	2	yes	—
484	C₂×C₄	C₂×C₅×#67	1	2	yes	—
485	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
486	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
487	C₈	—	3	4	no	—
488	C₈	—	6	2	no	—
489	C₂×C₃	—	4	2	no	—
490	C₂×C₃	—	8	2	no	—
491	C₂×C₃	C₅×#469	1	4	yes	complemented
492	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
493	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
494	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
495	D₃	—	8	2	no	—
496	C₅	C₂×#5039	1	1	yes	characteristic, direct product factor, Sylow
497	C₂²	—	2	2	no	—
498	C₂²	—	2	2	no	—
499	C₂²	—	2	2	no	—
500	C₂²	—	4	4	no	—
501	C₂²	—	4	2	no	—
502	C₂²	—	4	2	no	—
503	C₂²	—	4	2	no	—
504	C₂²	—	8	4	no	—
505	C₂²	—	12	2	no	—
506	C₂²	—	12	2	no	—
507	C₂²	—	12	2	no	—
508	C₂²	—	24	4	no	—
509	C₂²	C₅×#932	1	2	yes	—
510	C₂²	C₅×#939	1	2	yes	—
511	C₂²	C₅×#949	1	2	yes	—
512	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
513	C₄	—	2	2	no	—
514	C₄	—	4	2	no	—
515	C₄	—	12	2	no	—
516	C₄	C₅×#939	1	2	yes	—
517	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
518	C₄	C₂×C₅×#237	1	1	yes	characteristic
519	C₃	C₂×C₅×#469	1	1	yes	characteristic, complemented, Sylow
520	C₂	—	4	2	no	—
521	C₂	—	8	2	no	—
522	C₂	—	24	2	no	—
523	C₂	C₅×#5039	1	4	yes	direct product factor
524	C₂	C₂×C₅×#932	1	1	yes	characteristic
525	C₂	C₂×C₅×#939	1	1	yes	characteristic
526	C₂	C₂×C₅×#949	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂×#67
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂×C₃×C₅×#121	C₂
socle	C₂³×C₃×C₅	C₂×D₄
hypercenter	C₂×C₅×#121	D₃
hypocenter	C₃	C₂×C₅×#469
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂³×C₄×C₅ ◁ C₂×C₅×#121

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#121	C₂	semidirect
2. C₂²×C₅×#213	C₂	semidirect
3. C₂×C₅×#930	C₂	semidirect
4. C₂²×C₅×#208	C₂	semidirect
5. C₂×C₅×#832	C₂	semidirect
6. C₅×#5039	C₂	direct (N × H)
7. C₂×C₅×#809	C₂	semidirect
8. C₂×C₅×#808	C₂	semidirect
16. C₃×C₅×#121	C₂²	semidirect
20. C₂×C₅×#213	C₂²	semidirect
22. C₅×#930	C₂²	semidirect
26. C₂×C₅×#208	C₂²	semidirect
29. C₅×#832	C₂²	semidirect
30. C₅×#809	C₂²	semidirect
31. C₅×#808	C₂²	semidirect
32. C₂×#5039	C₅	direct (N × H)
36. C₂×C₅×#121	D₃	semidirect
73. C₂×C₅×C₃⋊C₈	D₄	semidirect
76. C₂×C₃×#121	C₂×C₅	semidirect
77. C₂²×#213	C₂×C₅	semidirect
78. C₂×#930	C₂×C₅	semidirect
79. C₂²×#208	C₂×C₅	semidirect
80. C₂×#832	C₂×C₅	semidirect
81. #5039	C₂×C₅	direct (N × H)
82. C₂×#809	C₂×C₅	semidirect
83. C₂×#808	C₂×C₅	semidirect
98. C₅×#121	C₂×D₃	semidirect
142. C₅×C₃⋊C₈	C₂×D₄	semidirect
149. C₃×#121	C₂²×C₅	semidirect
153. C₂×#213	C₂²×C₅	semidirect
155. #930	C₂²×C₅	semidirect
159. C₂×#208	C₂²×C₅	semidirect
162. #832	C₂²×C₅	semidirect
163. #809	C₂²×C₅	semidirect
164. #808	C₂²×C₅	semidirect
203. C₂×#121	C₅×D₃	semidirect
262. C₂×C₃⋊C₈	C₅×D₄	semidirect
315. #121	C₂×C₅×D₃	semidirect
325. C₂×C₃×C₅	#469	semidirect
365. C₃⋊C₈	C₂×C₅×D₄	semidirect
423. C₃×C₅	C₂×#469	semidirect
449. C₂×C₅	#5039	direct (N × H)
491. C₂×C₃	C₅×#469	semidirect
496. C₅	C₂×#5039	direct (N × H)
519. C₃	C₂×C₅×#469	semidirect
523. C₂	C₅×#5039	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×#121	2
C₂²×C₅×#213	2
C₂×C₅×#930	2
C₂²×C₅×#208	2
C₂×C₅×#832	2
C₅×#5039	2
C₂×C₅×#809	2
C₂×C₅×#808	2
C₂×C₅×#469	3
C₂×#5039	5

Subgroups — C2×C5×#5039 #14427978

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5039 #14427978