Subgroups — C₂×C₅×#5059 #14438829

Order 1920.

1184 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#124	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×#216	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₅×#215	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₅×#214	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₅×#213	C₂	1	1	yes	maximal, characteristic
6	C₂×C₅×#875	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5059	C₂	1	8	yes	maximal, direct product factor
8	C₂×C₄×C₅×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×#495	—	3	1	no	maximal, Hall
10	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
12	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
13	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
14	C₃×C₅×#124	—	2	2	no	—
15	C₃×C₅×#124	C₂²	1	4	yes	complemented
16	C₂×C₃×C₅×C₂²⋊C₄	—	2	2	no	—
17	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
18	C₂×C₅×#216	—	2	4	no	—
19	C₂×C₅×#216	C₂²	1	4	yes	complemented
20	C₂×C₅×#215	—	2	4	no	—
21	C₂×C₅×#215	C₂²	1	4	yes	complemented
22	C₂×C₅×#214	—	2	4	no	—
23	C₂×C₅×#214	C₂²	1	4	yes	complemented
24	C₂×C₅×#213	—	2	4	no	—
25	C₂×C₅×#213	C₂²	1	4	yes	—
26	C₂×C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
27	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
28	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
29	C₅×#875	—	2	2	no	—
30	C₅×#875	C₂²	1	4	yes	complemented
31	C₄×C₅×C₃⋊C₈	C₂²	1	4	yes	complemented
32	C₂×#5059	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
33	C₂²×C₅×Q₁₆	—	3	1	no	—
34	C₂²×C₅×SD₁₆	—	3	1	no	—
35	C₂²×C₅×SD₁₆	—	3	1	no	—
36	C₂²×C₅×D₈	—	3	1	no	—
37	C₂×C₅×#124	—	3	1	no	—
38	C₂×C₅×#124	D₃	1	1	yes	characteristic, complemented
39	C₅×#495	—	3	8	no	—
40	C₂×C₄×C₅×C₈	—	3	1	no	—
41	C₂⁴×C₃×C₅	—	2	1	no	—
42	C₂³×C₅×D₃	—	2	1	no	—
43	C₂×C₃×C₅×Q₈	—	2	1	no	—
44	C₂×C₃×C₅×Q₈	—	2	2	no	—
45	C₂×C₃×C₅×Q₈	—	2	2	no	—
46	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
47	C₂×C₃×C₅×D₄	—	2	2	no	—
48	C₂×C₃×C₅×D₄	—	2	2	no	—
49	C₂×C₃×C₅×D₄	—	2	1	no	—
50	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
51	C₂²×C₃×C₄×C₅	—	2	1	no	—
52	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
53	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
54	C₂²×C₅×Dic₃	—	2	1	no	—
55	C₂×C₅×D₁₂	—	2	2	no	—
56	C₂×C₅×D₁₂	—	2	2	no	—
57	C₂×C₅×D₁₂	—	2	1	no	—
58	C₂×C₅×D₁₂	C₂³	1	2	yes	—
59	C₂×C₅×Dic₆	—	2	2	no	—
60	C₂×C₅×Dic₆	—	2	2	no	—
61	C₂×C₅×Dic₆	—	2	1	no	—
62	C₂×C₅×Dic₆	C₂³	1	2	yes	—
63	C₃×C₅×C₂²⋊C₄	—	2	8	no	—
64	C₃×C₄²×C₅	D₄	1	2	yes	—
65	C₃×C₄²×C₅	C₂³	1	2	yes	—
66	C₅×#216	—	2	8	no	—
67	C₅×#215	—	2	8	no	—
68	C₅×#214	—	2	8	no	—
69	C₅×#213	—	2	8	no	—
70	C₅×(C₂×D₃)⋊C₄	—	2	8	no	—
71	C₂×C₅×C₃⋊C₈	D₄	1	4	yes	—
72	C₂×C₅×C₃⋊C₈	D₄	1	4	yes	—
73	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
74	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
75	C₂×C₃×#124	C₂×C₅	1	1	yes	characteristic, complemented
76	C₂²×#216	C₂×C₅	1	1	yes	characteristic, complemented
77	C₂²×#215	C₂×C₅	1	1	yes	characteristic, complemented
78	C₂²×#214	C₂×C₅	1	1	yes	characteristic, complemented
79	C₂²×#213	C₂×C₅	1	1	yes	characteristic
80	C₂×#875	C₂×C₅	1	1	yes	characteristic, complemented
81	#5059	C₂×C₅	1	8	yes	direct product factor
82	C₂×C₄×C₃⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
83	C₂²×C₅×Q₈	—	3	1	no	—
84	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
85	C₂²×C₅×D₄	—	3	1	no	—
86	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
87	C₂×C₅×Q₁₆	—	3	4	no	—
88	C₂×C₅×Q₁₆	—	6	4	no	—
89	C₂×C₅×SD₁₆	—	3	4	no	—
90	C₂×C₅×SD₁₆	—	3	4	no	—
91	C₂×C₅×SD₁₆	—	6	4	no	—
92	C₂×C₅×SD₁₆	—	6	4	no	—
93	C₂×C₅×D₈	—	3	4	no	—
94	C₂×C₅×D₈	—	6	4	no	—
95	C₂²×C₅×C₈	—	3	1	no	—
96	C₂²×C₅×C₈	—	3	1	no	—
97	C₅×#124	—	2	2	no	—
98	C₅×#124	—	3	4	no	—
99	C₅×#124	—	6	2	no	—
100	C₅×#124	C₂×D₃	1	4	yes	complemented
101	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
102	C₂×C₅×C₂²⋊C₄	—	6	2	no	—
103	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
104	C₄×C₅×C₈	—	3	4	no	—
105	C₂×#495	—	3	1	no	Sylow
106	C₂³×C₃×C₅	—	2	2	no	—
107	C₂³×C₃×C₅	—	4	2	no	—
108	C₂³×C₃×C₅	—	4	4	no	—
109	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₅×D₃	—	2	2	no	—
111	C₂²×C₅×D₃	—	4	2	no	—
112	C₂²×C₅×D₃	—	4	4	no	—
113	C₃×C₅×Q₈	—	2	2	no	—
114	C₃×C₅×Q₈	—	2	2	no	—
115	C₃×C₅×Q₈	—	4	2	no	—
116	C₃×C₅×D₄	—	2	2	no	—
117	C₃×C₅×D₄	—	2	2	no	—
118	C₃×C₅×D₄	—	4	2	no	—
119	C₂×C₃×C₄×C₅	—	2	4	no	—
120	C₂×C₃×C₄×C₅	—	2	2	no	—
121	C₂×C₃×C₄×C₅	—	4	2	no	—
122	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
123	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
124	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
125	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
126	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
127	C₂×C₅×Dic₃	—	2	2	no	—
128	C₂×C₅×Dic₃	—	4	2	no	—
129	C₅×D₁₂	—	2	2	no	—
130	C₅×D₁₂	—	2	2	no	—
131	C₅×D₁₂	—	4	2	no	—
132	C₅×Dic₆	—	2	2	no	—
133	C₅×Dic₆	—	2	2	no	—
134	C₅×Dic₆	—	4	2	no	—
135	C₅×C₃⋊C₈	C₂×D₄	1	4	yes	—
136	C₅×C₃⋊C₈	C₂×D₄	1	4	yes	—
137	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
138	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
139	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
140	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
141	C₃×#124	—	2	2	no	—
142	C₃×#124	C₂²×C₅	1	4	yes	complemented
143	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
144	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
145	C₂×#216	—	2	4	no	—
146	C₂×#216	C₂²×C₅	1	4	yes	complemented
147	C₂×#215	—	2	4	no	—
148	C₂×#215	C₂²×C₅	1	4	yes	complemented
149	C₂×#214	—	2	4	no	—
150	C₂×#214	C₂²×C₅	1	4	yes	complemented
151	C₂×#213	—	2	4	no	—
152	C₂×#213	C₂²×C₅	1	4	yes	—
153	C₂×(C₂×D₃)⋊C₄	—	2	2	no	—
154	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
155	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
156	#875	—	2	2	no	—
157	#875	C₂²×C₅	1	4	yes	complemented
158	C₄×C₃⋊C₈	C₂²×C₅	1	4	yes	complemented
159	C₂⁴×C₅	—	2	1	no	—
160	C₂⁴×C₅	—	6	1	no	—
161	C₂×C₅×Q₈	—	2	1	no	—
162	C₂×C₅×Q₈	—	2	2	no	—
163	C₂×C₅×Q₈	—	2	2	no	—
164	C₂×C₅×Q₈	—	3	2	no	—
165	C₂×C₅×Q₈	—	6	1	no	—
166	C₂×C₅×Q₈	—	6	2	no	—
167	C₂×C₅×Q₈	—	6	2	no	—
168	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
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	—	6	2	no	—
174	C₂×C₅×D₄	—	6	2	no	—
175	C₂×C₅×D₄	—	6	1	no	—
176	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
177	C₂²×C₄×C₅	—	2	1	no	—
178	C₂²×C₄×C₅	—	6	1	no	—
179	C₂²×C₄×C₅	#67	1	2	yes	—
180	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
181	C₅×Q₁₆	—	6	8	no	—
182	C₅×SD₁₆	—	6	8	no	—
183	C₅×SD₁₆	—	6	8	no	—
184	C₅×D₈	—	6	8	no	—
185	C₂×C₅×C₈	—	3	4	no	—
186	C₂×C₅×C₈	—	3	4	no	—
187	C₂×C₅×C₈	—	3	2	no	—
188	C₂×C₅×C₈	—	3	2	no	—
189	C₅×C₂²⋊C₄	—	2	8	no	—
190	C₅×C₂²⋊C₄	—	6	8	no	—
191	C₄²×C₅	#67	1	2	yes	—
192	C₄²×C₅	C₂²×D₃	1	2	yes	—
193	C₂²×Q₁₆	—	3	1	no	—
194	C₂²×SD₁₆	—	3	1	no	—
195	C₂²×SD₁₆	—	3	1	no	—
196	C₂²×D₈	—	3	1	no	—
197	C₂×#124	—	3	1	no	—
198	C₂×#124	C₅×D₃	1	1	yes	characteristic, complemented
199	#495	—	3	8	no	—
200	C₂×C₄×C₈	—	3	1	no	—
201	C₂²×C₃×C₅	—	4	2	no	—
202	C₂²×C₃×C₅	—	4	4	no	—
203	C₂²×C₃×C₅	—	8	4	no	—
204	C₂²×C₃×C₅	#127	1	2	yes	—
205	C₂²×C₃×C₅	#135	1	4	yes	—
206	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
207	C₂×C₅×D₃	—	4	2	no	—
208	C₂×C₅×D₃	—	4	4	no	—
209	C₂×C₅×D₃	—	8	4	no	—
210	C₃×C₄×C₅	—	2	4	no	—
211	C₃×C₄×C₅	—	4	2	no	—
212	C₃×C₄×C₅	#127	1	2	yes	—
213	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
214	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
215	C₅×Dic₃	—	4	2	no	—
216	C₂⁴×C₃	—	2	1	no	—
217	C₂³×D₃	—	2	1	no	—
218	C₂×C₃×Q₈	—	2	1	no	—
219	C₂×C₃×Q₈	—	2	2	no	—
220	C₂×C₃×Q₈	—	2	2	no	—
221	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
222	C₂×C₃×D₄	—	2	2	no	—
223	C₂×C₃×D₄	—	2	2	no	—
224	C₂×C₃×D₄	—	2	1	no	—
225	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
226	C₂²×C₃×C₄	—	2	1	no	—
227	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
228	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
229	C₂²×Dic₃	—	2	1	no	—
230	C₂×D₁₂	—	2	2	no	—
231	C₂×D₁₂	—	2	2	no	—
232	C₂×D₁₂	—	2	1	no	—
233	C₂×D₁₂	C₂³×C₅	1	2	yes	—
234	C₂×Dic₆	—	2	2	no	—
235	C₂×Dic₆	—	2	2	no	—
236	C₂×Dic₆	—	2	1	no	—
237	C₂×Dic₆	C₂³×C₅	1	2	yes	—
238	C₃×C₂²⋊C₄	—	2	8	no	—
239	C₃×C₄²	C₅×D₄	1	2	yes	—
240	C₃×C₄²	C₂³×C₅	1	2	yes	—
241	#216	—	2	8	no	—
242	#215	—	2	8	no	—
243	#214	—	2	8	no	—
244	#213	—	2	8	no	—
245	(C₂×D₃)⋊C₄	—	2	8	no	—
246	C₂×C₃⋊C₈	C₅×D₄	1	4	yes	—
247	C₂×C₃⋊C₈	C₅×D₄	1	4	yes	—
248	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
249	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
250	C₂³×C₅	—	2	2	no	—
251	C₂³×C₅	—	4	2	no	—
252	C₂³×C₅	—	4	4	no	—
253	C₂³×C₅	—	6	2	no	—
254	C₂³×C₅	—	12	2	no	—
255	C₂³×C₅	—	12	4	no	—
256	C₂³×C₅	C₂×#67	1	1	yes	characteristic
257	C₅×Q₈	—	2	2	no	—
258	C₅×Q₈	—	2	2	no	—
259	C₅×Q₈	—	4	2	no	—
260	C₅×Q₈	—	6	2	no	—
261	C₅×Q₈	—	6	2	no	—
262	C₅×Q₈	—	12	2	no	—
263	C₅×D₄	—	2	2	no	—
264	C₅×D₄	—	2	2	no	—
265	C₅×D₄	—	4	2	no	—
266	C₅×D₄	—	6	2	no	—
267	C₅×D₄	—	6	2	no	—
268	C₅×D₄	—	12	2	no	—
269	C₂×C₄×C₅	—	2	4	no	—
270	C₂×C₄×C₅	—	2	2	no	—
271	C₂×C₄×C₅	—	4	2	no	—
272	C₂×C₄×C₅	—	6	2	no	—
273	C₂×C₄×C₅	—	12	2	no	—
274	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
275	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
276	C₂×C₄×C₅	C₂×#67	1	4	yes	—
277	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
278	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
279	C₅×C₈	—	3	4	no	—
280	C₅×C₈	—	3	4	no	—
281	C₂²×Q₈	—	3	1	no	—
282	C₂²×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
283	C₂²×D₄	—	3	1	no	—
284	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
285	C₂×Q₁₆	—	3	4	no	—
286	C₂×Q₁₆	—	6	4	no	—
287	C₂×SD₁₆	—	3	4	no	—
288	C₂×SD₁₆	—	3	4	no	—
289	C₂×SD₁₆	—	6	4	no	—
290	C₂×SD₁₆	—	6	4	no	—
291	C₂×D₈	—	3	4	no	—
292	C₂×D₈	—	6	4	no	—
293	C₂²×C₈	—	3	1	no	—
294	C₂²×C₈	—	3	1	no	—
295	#124	—	2	2	no	—
296	#124	—	3	4	no	—
297	#124	—	6	2	no	—
298	#124	C₂×C₅×D₃	1	4	yes	complemented
299	C₂×C₂²⋊C₄	—	2	2	no	—
300	C₂×C₂²⋊C₄	—	6	2	no	—
301	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
302	C₄×C₈	—	3	4	no	—
303	C₂×C₃×C₅	—	8	2	no	—
304	C₂×C₃×C₅	#495	1	4	yes	complemented
305	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
306	C₂×C₃×C₅	C₂×#135	1	2	yes	—
307	C₅×D₃	—	8	2	no	—
308	C₂³×C₃	—	2	2	no	—
309	C₂³×C₃	—	4	2	no	—
310	C₂³×C₃	—	4	4	no	—
311	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
312	C₂²×D₃	—	2	2	no	—
313	C₂²×D₃	—	4	2	no	—
314	C₂²×D₃	—	4	4	no	—
315	C₃×Q₈	—	2	2	no	—
316	C₃×Q₈	—	2	2	no	—
317	C₃×Q₈	—	4	2	no	—
318	C₃×D₄	—	2	2	no	—
319	C₃×D₄	—	2	2	no	—
320	C₃×D₄	—	4	2	no	—
321	C₂×C₃×C₄	—	2	4	no	—
322	C₂×C₃×C₄	—	2	2	no	—
323	C₂×C₃×C₄	—	4	2	no	—
324	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
325	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
326	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
327	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
328	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
329	C₂×Dic₃	—	2	2	no	—
330	C₂×Dic₃	—	4	2	no	—
331	D₁₂	—	2	2	no	—
332	D₁₂	—	2	2	no	—
333	D₁₂	—	4	2	no	—
334	Dic₆	—	2	2	no	—
335	Dic₆	—	2	2	no	—
336	Dic₆	—	4	2	no	—
337	C₃⋊C₈	C₂×C₅×D₄	1	4	yes	—
338	C₃⋊C₈	C₂×C₅×D₄	1	4	yes	—
339	C₂²×C₅	—	4	2	no	—
340	C₂²×C₅	—	4	4	no	—
341	C₂²×C₅	—	8	4	no	—
342	C₂²×C₅	—	12	2	no	—
343	C₂²×C₅	—	12	4	no	—
344	C₂²×C₅	—	24	4	no	—
345	C₂²×C₅	#940	1	2	yes	—
346	C₂²×C₅	#950	1	4	yes	—
347	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
348	C₄×C₅	—	2	4	no	—
349	C₄×C₅	—	4	2	no	—
350	C₄×C₅	—	12	2	no	—
351	C₄×C₅	#940	1	2	yes	—
352	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
353	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
354	C₂⁴	—	2	1	no	—
355	C₂⁴	—	6	1	no	—
356	C₂×Q₈	—	2	1	no	—
357	C₂×Q₈	—	2	2	no	—
358	C₂×Q₈	—	2	2	no	—
359	C₂×Q₈	—	3	2	no	—
360	C₂×Q₈	—	6	1	no	—
361	C₂×Q₈	—	6	2	no	—
362	C₂×Q₈	—	6	2	no	—
363	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
364	C₂×D₄	—	2	2	no	—
365	C₂×D₄	—	2	2	no	—
366	C₂×D₄	—	2	1	no	—
367	C₂×D₄	—	3	2	no	—
368	C₂×D₄	—	6	2	no	—
369	C₂×D₄	—	6	2	no	—
370	C₂×D₄	—	6	1	no	—
371	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	6	1	no	—
374	C₂²×C₄	C₅×#67	1	2	yes	—
375	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
376	Q₁₆	—	6	8	no	—
377	SD₁₆	—	6	8	no	—
378	SD₁₆	—	6	8	no	—
379	D₈	—	6	8	no	—
380	C₂×C₈	—	3	4	no	—
381	C₂×C₈	—	3	4	no	—
382	C₂×C₈	—	3	2	no	—
383	C₂×C₈	—	3	2	no	—
384	C₂²⋊C₄	—	2	8	no	—
385	C₂²⋊C₄	—	6	8	no	—
386	C₄²	C₅×#67	1	2	yes	—
387	C₄²	C₂²×C₅×D₃	1	2	yes	—
388	C₃×C₅	C₂×#495	1	1	yes	characteristic, complemented, Hall
389	C₂²×C₃	—	4	2	no	—
390	C₂²×C₃	—	4	4	no	—
391	C₂²×C₃	—	8	4	no	—
392	C₂²×C₃	C₅×#127	1	2	yes	—
393	C₂²×C₃	C₅×#135	1	4	yes	—
394	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
395	C₂×D₃	—	4	2	no	—
396	C₂×D₃	—	4	4	no	—
397	C₂×D₃	—	8	4	no	—
398	C₃×C₄	—	2	4	no	—
399	C₃×C₄	—	4	2	no	—
400	C₃×C₄	C₅×#127	1	2	yes	—
401	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
402	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
403	Dic₃	—	4	2	no	—
404	C₂×C₅	—	8	2	no	—
405	C₂×C₅	—	24	2	no	—
406	C₂×C₅	#5059	1	4	yes	direct product factor
407	C₂×C₅	C₂×#940	1	1	yes	characteristic
408	C₂×C₅	C₂×#950	1	2	yes	—
409	C₂³	—	2	2	no	—
410	C₂³	—	4	2	no	—
411	C₂³	—	4	4	no	—
412	C₂³	—	6	2	no	—
413	C₂³	—	12	2	no	—
414	C₂³	—	12	4	no	—
415	C₂³	C₂×C₅×#67	1	1	yes	characteristic
416	Q₈	—	2	2	no	—
417	Q₈	—	2	2	no	—
418	Q₈	—	4	2	no	—
419	Q₈	—	6	2	no	—
420	Q₈	—	6	2	no	—
421	Q₈	—	12	2	no	—
422	D₄	—	2	2	no	—
423	D₄	—	2	2	no	—
424	D₄	—	4	2	no	—
425	D₄	—	6	2	no	—
426	D₄	—	6	2	no	—
427	D₄	—	12	2	no	—
428	C₂×C₄	—	2	4	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	6	2	no	—
432	C₂×C₄	—	12	2	no	—
433	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
434	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
435	C₂×C₄	C₂×C₅×#67	1	4	yes	—
436	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
437	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
438	C₈	—	3	4	no	—
439	C₈	—	3	4	no	—
440	C₂×C₃	—	8	2	no	—
441	C₂×C₃	C₅×#495	1	4	yes	complemented
442	C₂×C₃	C₂×C₅×#127	1	1	yes	characteristic
443	C₂×C₃	C₂×C₅×#135	1	2	yes	—
444	D₃	—	8	2	no	—
445	C₅	C₂×#5059	1	1	yes	characteristic, direct product factor, Sylow
446	C₂²	—	4	2	no	—
447	C₂²	—	4	4	no	—
448	C₂²	—	8	4	no	—
449	C₂²	—	12	2	no	—
450	C₂²	—	12	4	no	—
451	C₂²	—	24	4	no	—
452	C₂²	C₅×#940	1	2	yes	—
453	C₂²	C₅×#950	1	4	yes	—
454	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
455	C₄	—	2	4	no	—
456	C₄	—	4	2	no	—
457	C₄	—	12	2	no	—
458	C₄	C₅×#940	1	2	yes	—
459	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
460	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
461	C₃	C₂×C₅×#495	1	1	yes	characteristic, complemented, Sylow
462	C₂	—	8	2	no	—
463	C₂	—	24	2	no	—
464	C₂	C₅×#5059	1	4	yes	direct product factor
465	C₂	C₂×C₅×#940	1	1	yes	characteristic
466	C₂	C₂×C₅×#950	1	2	yes	—

	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×#124	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂²×C₅×#213	C₂
hypercenter	C₂×C₅×#124	D₃
hypocenter	C₃	C₂×C₅×#495
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₄²×C₅ ◁ C₂×C₅×#124

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#124	C₂	semidirect
2. C₂²×C₅×#216	C₂	semidirect
3. C₂²×C₅×#215	C₂	semidirect
4. C₂²×C₅×#214	C₂	semidirect
6. C₂×C₅×#875	C₂	semidirect
7. C₅×#5059	C₂	direct (N × H)
8. C₂×C₄×C₅×C₃⋊C₈	C₂	semidirect
15. C₃×C₅×#124	C₂²	semidirect
19. C₂×C₅×#216	C₂²	semidirect
21. C₂×C₅×#215	C₂²	semidirect
23. C₂×C₅×#214	C₂²	semidirect
30. C₅×#875	C₂²	semidirect
31. C₄×C₅×C₃⋊C₈	C₂²	semidirect
32. C₂×#5059	C₅	direct (N × H)
38. C₂×C₅×#124	D₃	semidirect
75. C₂×C₃×#124	C₂×C₅	semidirect
76. C₂²×#216	C₂×C₅	semidirect
77. C₂²×#215	C₂×C₅	semidirect
78. C₂²×#214	C₂×C₅	semidirect
80. C₂×#875	C₂×C₅	semidirect
81. #5059	C₂×C₅	direct (N × H)
82. C₂×C₄×C₃⋊C₈	C₂×C₅	semidirect
100. C₅×#124	C₂×D₃	semidirect
142. C₃×#124	C₂²×C₅	semidirect
146. C₂×#216	C₂²×C₅	semidirect
148. C₂×#215	C₂²×C₅	semidirect
150. C₂×#214	C₂²×C₅	semidirect
157. #875	C₂²×C₅	semidirect
158. C₄×C₃⋊C₈	C₂²×C₅	semidirect
198. C₂×#124	C₅×D₃	semidirect
298. #124	C₂×C₅×D₃	semidirect
304. C₂×C₃×C₅	#495	semidirect
388. C₃×C₅	C₂×#495	semidirect
406. C₂×C₅	#5059	direct (N × H)
441. C₂×C₃	C₅×#495	semidirect
445. C₅	C₂×#5059	direct (N × H)
461. C₃	C₂×C₅×#495	semidirect
464. C₂	C₅×#5059	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×#124	2
C₂²×C₅×#216	2
C₂²×C₅×#215	2
C₂²×C₅×#214	2
C₂²×C₅×#213	2
C₂×C₅×#875	2
C₅×#5059	2
C₂×C₄×C₅×C₃⋊C₈	2
C₂×C₅×#495	3
C₂×#5059	5

Subgroups — C2×C5×#5059 #14438829

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5059 #14438829