Subgroups — C₂×C₅×#4823 #14417919

Order 1920.

928 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#950	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#948	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#907	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×C₅×#104	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#822	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×#805	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#803	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4823	C₂	1	8	yes	maximal, direct product factor
9	C₂×C₅×#444	—	3	1	no	maximal, Hall
10	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
11	C₂×C₅×#235	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
14	C₅×#950	C₄	1	4	yes	complemented
15	C₅×#950	C₂²	1	4	yes	—
16	C₅×#948	—	2	2	no	—
17	C₅×#948	C₂²	1	4	yes	complemented
18	C₂×C₅×#216	C₄	1	1	yes	characteristic, complemented
19	C₂×C₅×#215	C₄	1	1	yes	characteristic, complemented
20	C₂×C₅×#214	C₄	1	1	yes	characteristic, complemented
21	C₂×C₅×#213	C₄	1	1	yes	characteristic, complemented
22	C₂×C₅×#208	—	2	1	no	—
23	C₂×C₅×#208	C₂²	1	1	yes	characteristic
24	C₂²×C₅×C₃⋊C₈	—	2	1	no	—
25	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
26	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
27	C₅×#907	—	2	2	no	—
28	C₅×#907	C₂²	1	4	yes	complemented
29	C₂×C₅×ΓL(1,𝔽₂₅)	—	2	1	no	—
30	C₂×C₅×D₃×C₈	—	2	1	no	—
31	C₃×C₅×#104	C₂²	1	4	yes	complemented
32	C₅×#822	C₂²	1	4	yes	complemented
33	C₅×#805	C₂²	1	4	yes	complemented
34	C₅×#803	C₂²	1	4	yes	complemented
35	C₂×#4823	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
36	C₂×C₅×#135	—	3	1	no	—
37	C₂×C₅×#131	—	3	1	no	—
38	C₂×C₅×#131	—	3	1	no	—
39	C₅×#444	—	3	8	no	—
40	C₂×C₅×#108	—	3	1	no	—
41	C₂×C₅×#104	—	3	1	no	—
42	C₂×C₅×#104	D₃	1	1	yes	characteristic, complemented
43	C₂×C₅×#97	—	3	1	no	—
44	C₃×C₅×#41	—	2	1	no	—
45	C₃×C₅×#41	—	2	1	no	—
46	C₃×C₅×#41	C₂×C₄	1	2	yes	—
47	C₃×C₅×#41	C₂³	1	2	yes	—
48	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
49	C₂×C₃×C₅×D₄	—	2	1	no	—
50	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₃×C₄×C₅	—	2	1	no	—
52	C₂²×C₃×C₄×C₅	—	2	1	no	—
53	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
54	C₂×C₅×#67	—	2	1	no	—
55	C₅×#235	—	2	1	no	—
56	C₅×#235	—	2	1	no	—
57	C₅×#235	C₂×C₄	1	2	yes	—
58	C₅×#235	C₂³	1	2	yes	—
59	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄×C₅×D₃	—	2	1	no	—
61	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
62	C₃×C₅×M₁₆	—	2	1	no	—
63	C₃×C₅×M₁₆	C₂³	1	2	yes	—
64	C₂×C₃×C₅×C₈	—	2	1	no	—
65	C₃×C₄²×C₅	—	2	1	no	—
66	C₃×C₄²×C₅	C₂³	1	2	yes	—
67	C₅×#216	C₂×C₄	1	4	yes	complemented
68	C₅×#215	C₂×C₄	1	4	yes	complemented
69	C₅×#214	C₂×C₄	1	4	yes	complemented
70	C₅×#213	C₂×C₄	1	4	yes	complemented
71	C₅×#208	—	2	1	no	—
72	C₅×#208	—	2	4	no	—
73	C₅×#208	C₂³	1	2	yes	—
74	C₂×C₅×C₃⋊C₈	—	2	1	no	—
75	C₂×C₅×C₃⋊C₈	—	2	4	no	—
76	C₂×C₅×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
77	C₂×C₅×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
78	C₂×C₅×C₃⋊C₈	C₂×C₄	1	2	yes	—
79	C₂×C₅×C₃⋊C₈	D₄	1	1	yes	characteristic
80	C₂×C₅×C₃⋊C₈	D₄	1	1	yes	characteristic
81	C₂×C₅×C₃⋊C₈	D₄	1	2	yes	—
82	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
83	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
84	C₅×ΓL(1,𝔽₂₅)	—	2	4	no	—
85	C₅×D₃×C₈	—	2	4	no	—
86	C₂×#950	C₂×C₅	1	1	yes	characteristic
87	C₂×#948	C₂×C₅	1	1	yes	characteristic, complemented
88	C₂×#907	C₂×C₅	1	1	yes	characteristic, complemented
89	C₂×C₃×#104	C₂×C₅	1	1	yes	characteristic, complemented
90	C₂×#822	C₂×C₅	1	1	yes	characteristic, complemented
91	C₂×#805	C₂×C₅	1	1	yes	characteristic, complemented
92	C₂×#803	C₂×C₅	1	1	yes	characteristic, complemented
93	#4823	C₂×C₅	1	8	yes	direct product factor
94	C₂×C₅×#41	—	3	1	no	—
95	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
96	C₅×#135	—	3	4	no	—
97	C₅×#135	—	3	4	no	—
98	C₂×C₅×Q₁₆	—	3	1	no	—
99	C₂×C₅×SD₁₆	—	3	1	no	—
100	C₂×C₅×SD₁₆	—	3	1	no	—
101	C₂×C₅×D₈	—	3	1	no	—
102	C₅×#131	—	3	4	no	—
103	C₅×#131	—	3	4	no	—
104	C₅×#131	—	6	2	no	—
105	C₅×#131	—	6	2	no	—
106	C₂×C₅×M₁₆	—	3	1	no	—
107	C₂×C₅×M₁₆	—	6	1	no	—
108	C₂×C₅×M₁₆	—	6	1	no	—
109	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
110	C₂²×C₅×C₈	—	3	1	no	—
111	C₂²×C₅×C₈	—	3	1	no	—
112	C₂²×C₅×C₈	—	6	1	no	—
113	C₂²×C₅×C₈	—	6	1	no	—
114	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
115	C₅×#108	—	3	4	no	—
116	C₅×#104	—	3	4	no	—
117	C₅×#104	C₂×D₃	1	4	yes	complemented
118	C₅×#97	—	3	4	no	—
119	C₂×#444	—	3	1	no	Sylow
120	C₂³×C₃×C₅	—	2	1	no	—
121	C₂³×C₃×C₅	#41	1	1	yes	characteristic
122	C₂²×C₅×D₃	—	2	1	no	—
123	C₃×C₅×Q₈	—	2	1	no	—
124	C₃×C₅×Q₈	C₂²×C₄	1	2	yes	—
125	C₃×C₅×D₄	—	2	2	no	—
126	C₃×C₅×D₄	—	2	2	no	—
127	C₃×C₅×D₄	—	2	1	no	—
128	C₃×C₅×D₄	C₂²×C₄	1	2	yes	—
129	C₂×C₃×C₄×C₅	—	2	1	no	—
130	C₂×C₃×C₄×C₅	—	2	2	no	—
131	C₂×C₃×C₄×C₅	—	2	2	no	—
132	C₂×C₃×C₄×C₅	—	2	2	no	—
133	C₂×C₃×C₄×C₅	—	4	2	no	—
134	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
137	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
138	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
139	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
140	C₅×#67	—	2	2	no	—
141	C₅×#67	—	2	2	no	—
142	C₂×C₅×Dic₃	—	2	1	no	—
143	C₅×D₁₂	—	2	1	no	—
144	C₅×D₁₂	C₂²×C₄	1	2	yes	—
145	C₄×C₅×D₃	—	2	2	no	—
146	C₄×C₅×D₃	—	2	2	no	—
147	C₅×Dic₆	—	2	1	no	—
148	C₅×Dic₆	C₂²×C₄	1	2	yes	—
149	C₃×C₅×C₈	—	2	2	no	—
150	C₅×C₃⋊C₈	—	2	2	no	—
151	C₅×C₃⋊C₈	C₂²×C₄	1	2	yes	—
152	C₅×C₃⋊C₈	C₂²×C₄	1	2	yes	—
153	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	—
154	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	—
155	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
156	C₂×#235	C₂²×C₅	1	1	yes	characteristic
157	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
158	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
159	#950	C₄×C₅	1	4	yes	complemented
160	#950	C₂²×C₅	1	4	yes	—
161	#948	—	2	2	no	—
162	#948	C₂²×C₅	1	4	yes	complemented
163	C₂×#216	C₄×C₅	1	1	yes	characteristic, complemented
164	C₂×#215	C₄×C₅	1	1	yes	characteristic, complemented
165	C₂×#214	C₄×C₅	1	1	yes	characteristic, complemented
166	C₂×#213	C₄×C₅	1	1	yes	characteristic, complemented
167	C₂×#208	—	2	1	no	—
168	C₂×#208	C₂²×C₅	1	1	yes	characteristic
169	C₂²×C₃⋊C₈	—	2	1	no	—
170	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
171	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
172	#907	—	2	2	no	—
173	#907	C₂²×C₅	1	4	yes	complemented
174	C₂×ΓL(1,𝔽₂₅)	—	2	1	no	—
175	C₂×D₃×C₈	—	2	1	no	—
176	C₃×#104	C₂²×C₅	1	4	yes	complemented
177	#822	C₂²×C₅	1	4	yes	complemented
178	#805	C₂²×C₅	1	4	yes	complemented
179	#803	C₂²×C₅	1	4	yes	complemented
180	C₅×#41	—	2	1	no	—
181	C₅×#41	—	2	1	no	—
182	C₅×#41	—	3	2	no	—
183	C₅×#41	—	3	2	no	—
184	C₅×#41	—	6	1	no	—
185	C₅×#41	—	6	1	no	—
186	C₅×#41	C₄×D₃	1	2	yes	—
187	C₅×#41	C₂²×D₃	1	2	yes	—
188	C₂×C₅×Q₈	—	3	1	no	—
189	C₂×C₅×Q₈	C₄×D₃	1	1	yes	characteristic
190	C₂×C₅×D₄	—	2	1	no	—
191	C₂×C₅×D₄	—	3	1	no	—
192	C₂×C₅×D₄	—	6	1	no	—
193	C₂×C₅×D₄	C₄×D₃	1	1	yes	characteristic
194	C₂²×C₄×C₅	—	2	1	no	—
195	C₂²×C₄×C₅	—	2	1	no	—
196	C₂²×C₄×C₅	—	6	1	no	—
197	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
198	C₅×Q₁₆	—	3	4	no	—
199	C₅×SD₁₆	—	3	4	no	—
200	C₅×SD₁₆	—	3	4	no	—
201	C₅×D₈	—	3	4	no	—
202	C₅×M₁₆	—	2	1	no	—
203	C₅×M₁₆	—	3	2	no	—
204	C₅×M₁₆	—	6	4	no	—
205	C₅×M₁₆	—	6	4	no	—
206	C₅×M₁₆	—	6	1	no	—
207	C₅×M₁₆	C₂²×D₃	1	2	yes	—
208	C₂×C₅×C₈	—	2	1	no	—
209	C₂×C₅×C₈	—	3	1	no	—
210	C₂×C₅×C₈	—	3	1	no	—
211	C₂×C₅×C₈	—	3	2	no	—
212	C₂×C₅×C₈	—	3	2	no	—
213	C₂×C₅×C₈	—	3	1	no	—
214	C₂×C₅×C₈	—	3	1	no	—
215	C₂×C₅×C₈	—	3	2	no	—
216	C₂×C₅×C₈	—	3	2	no	—
217	C₂×C₅×C₈	—	6	4	no	—
218	C₂×C₅×C₈	—	6	4	no	—
219	C₂×C₅×C₈	—	6	1	no	—
220	C₄²×C₅	—	2	1	no	—
221	C₄²×C₅	C₂²×D₃	1	2	yes	—
222	C₂×#135	—	3	1	no	—
223	C₂×#131	—	3	1	no	—
224	C₂×#131	—	3	1	no	—
225	#444	—	3	8	no	—
226	C₂×#108	—	3	1	no	—
227	C₂×#104	—	3	1	no	—
228	C₂×#104	C₅×D₃	1	1	yes	characteristic, complemented
229	C₂×#97	—	3	1	no	—
230	C₂²×C₃×C₅	—	2	2	no	—
231	C₂²×C₃×C₅	—	2	2	no	—
232	C₂²×C₃×C₅	—	4	2	no	—
233	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
234	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
235	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
236	C₂×C₅×D₃	—	2	2	no	—
237	C₂×C₅×D₃	—	4	2	no	—
238	C₃×C₄×C₅	—	2	2	no	—
239	C₃×C₄×C₅	—	4	2	no	—
240	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
241	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
242	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
243	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
244	C₅×Dic₃	—	2	2	no	—
245	C₃×#41	—	2	1	no	—
246	C₃×#41	—	2	1	no	—
247	C₃×#41	C₂×C₄×C₅	1	2	yes	—
248	C₃×#41	C₂³×C₅	1	2	yes	—
249	C₂×C₃×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
250	C₂×C₃×D₄	—	2	1	no	—
251	C₂×C₃×D₄	C₂×C₄×C₅	1	1	yes	characteristic
252	C₂²×C₃×C₄	—	2	1	no	—
253	C₂²×C₃×C₄	—	2	1	no	—
254	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
255	C₂×#67	—	2	1	no	—
256	#235	—	2	1	no	—
257	#235	—	2	1	no	—
258	#235	C₂×C₄×C₅	1	2	yes	—
259	#235	C₂³×C₅	1	2	yes	—
260	C₂×D₁₂	C₂×C₄×C₅	1	1	yes	characteristic
261	C₂×C₄×D₃	—	2	1	no	—
262	C₂×Dic₆	C₂×C₄×C₅	1	1	yes	characteristic
263	C₃×M₁₆	—	2	1	no	—
264	C₃×M₁₆	C₂³×C₅	1	2	yes	—
265	C₂×C₃×C₈	—	2	1	no	—
266	C₃×C₄²	—	2	1	no	—
267	C₃×C₄²	C₂³×C₅	1	2	yes	—
268	#216	C₂×C₄×C₅	1	4	yes	complemented
269	#215	C₂×C₄×C₅	1	4	yes	complemented
270	#214	C₂×C₄×C₅	1	4	yes	complemented
271	#213	C₂×C₄×C₅	1	4	yes	complemented
272	#208	—	2	1	no	—
273	#208	—	2	4	no	—
274	#208	C₂³×C₅	1	2	yes	—
275	C₂×C₃⋊C₈	—	2	1	no	—
276	C₂×C₃⋊C₈	—	2	4	no	—
277	C₂×C₃⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
278	C₂×C₃⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
279	C₂×C₃⋊C₈	C₂×C₄×C₅	1	2	yes	—
280	C₂×C₃⋊C₈	C₅×D₄	1	1	yes	characteristic
281	C₂×C₃⋊C₈	C₅×D₄	1	1	yes	characteristic
282	C₂×C₃⋊C₈	C₅×D₄	1	2	yes	—
283	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
284	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
285	ΓL(1,𝔽₂₅)	—	2	4	no	—
286	D₃×C₈	—	2	4	no	—
287	C₂³×C₅	—	2	1	no	—
288	C₂³×C₅	—	6	1	no	—
289	C₂³×C₅	#237	1	1	yes	characteristic
290	C₅×Q₈	—	2	1	no	—
291	C₅×Q₈	—	3	2	no	—
292	C₅×Q₈	—	6	1	no	—
293	C₅×Q₈	C₂×C₄×D₃	1	2	yes	—
294	C₅×D₄	—	2	2	no	—
295	C₅×D₄	—	2	2	no	—
296	C₅×D₄	—	2	1	no	—
297	C₅×D₄	—	3	2	no	—
298	C₅×D₄	—	6	2	no	—
299	C₅×D₄	—	6	2	no	—
300	C₅×D₄	—	6	1	no	—
301	C₅×D₄	C₂×C₄×D₃	1	2	yes	—
302	C₂×C₄×C₅	—	2	1	no	—
303	C₂×C₄×C₅	—	2	2	no	—
304	C₂×C₄×C₅	—	2	2	no	—
305	C₂×C₄×C₅	—	2	2	no	—
306	C₂×C₄×C₅	—	4	2	no	—
307	C₂×C₄×C₅	—	6	1	no	—
308	C₂×C₄×C₅	—	6	2	no	—
309	C₂×C₄×C₅	—	6	2	no	—
310	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
311	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
312	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
313	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
314	C₂×C₄×C₅	#237	1	1	yes	characteristic
315	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
316	C₅×C₈	—	2	2	no	—
317	C₅×C₈	—	3	2	no	—
318	C₅×C₈	—	3	2	no	—
319	C₅×C₈	—	3	2	no	—
320	C₅×C₈	—	3	2	no	—
321	C₅×C₈	—	6	2	no	—
322	C₂×#41	—	3	1	no	—
323	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
324	#135	—	3	4	no	—
325	#135	—	3	4	no	—
326	C₂×Q₁₆	—	3	1	no	—
327	C₂×SD₁₆	—	3	1	no	—
328	C₂×SD₁₆	—	3	1	no	—
329	C₂×D₈	—	3	1	no	—
330	#131	—	3	4	no	—
331	#131	—	3	4	no	—
332	#131	—	6	2	no	—
333	#131	—	6	2	no	—
334	C₂×M₁₆	—	3	1	no	—
335	C₂×M₁₆	—	6	1	no	—
336	C₂×M₁₆	—	6	1	no	—
337	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
338	C₂²×C₈	—	3	1	no	—
339	C₂²×C₈	—	3	1	no	—
340	C₂²×C₈	—	6	1	no	—
341	C₂²×C₈	—	6	1	no	—
342	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
343	#108	—	3	4	no	—
344	#104	—	3	4	no	—
345	#104	C₂×C₅×D₃	1	4	yes	complemented
346	#97	—	3	4	no	—
347	C₂×C₃×C₅	—	2	1	no	—
348	C₂×C₃×C₅	—	2	1	no	—
349	C₂×C₃×C₅	—	4	2	no	—
350	C₂×C₃×C₅	#444	1	2	yes	complemented
351	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
352	C₅×D₃	—	4	2	no	—
353	C₂³×C₃	—	2	1	no	—
354	C₂³×C₃	C₅×#41	1	1	yes	characteristic
355	C₂²×D₃	—	2	1	no	—
356	C₃×Q₈	—	2	1	no	—
357	C₃×Q₈	C₂²×C₄×C₅	1	2	yes	—
358	C₃×D₄	—	2	2	no	—
359	C₃×D₄	—	2	2	no	—
360	C₃×D₄	—	2	1	no	—
361	C₃×D₄	C₂²×C₄×C₅	1	2	yes	—
362	C₂×C₃×C₄	—	2	1	no	—
363	C₂×C₃×C₄	—	2	2	no	—
364	C₂×C₃×C₄	—	2	2	no	—
365	C₂×C₃×C₄	—	2	2	no	—
366	C₂×C₃×C₄	—	4	2	no	—
367	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
368	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
369	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
370	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
371	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
372	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
373	#67	—	2	2	no	—
374	#67	—	2	2	no	—
375	C₂×Dic₃	—	2	1	no	—
376	D₁₂	—	2	1	no	—
377	D₁₂	C₂²×C₄×C₅	1	2	yes	—
378	C₄×D₃	—	2	2	no	—
379	C₄×D₃	—	2	2	no	—
380	Dic₆	—	2	1	no	—
381	Dic₆	C₂²×C₄×C₅	1	2	yes	—
382	C₃×C₈	—	2	2	no	—
383	C₃⋊C₈	—	2	2	no	—
384	C₃⋊C₈	C₂²×C₄×C₅	1	2	yes	—
385	C₃⋊C₈	C₂²×C₄×C₅	1	2	yes	—
386	C₃⋊C₈	C₂×C₅×D₄	1	2	yes	—
387	C₃⋊C₈	C₂×C₅×D₄	1	2	yes	—
388	C₂²×C₅	—	2	2	no	—
389	C₂²×C₅	—	2	2	no	—
390	C₂²×C₅	—	4	2	no	—
391	C₂²×C₅	—	6	2	no	—
392	C₂²×C₅	—	12	2	no	—
393	C₂²×C₅	#67⋊C₄	1	1	yes	characteristic
394	C₂²×C₅	#67⋊C₄	1	1	yes	characteristic
395	C₂²×C₅	C₂×#237	1	1	yes	characteristic
396	C₄×C₅	—	2	2	no	—
397	C₄×C₅	—	4	2	no	—
398	C₄×C₅	—	6	2	no	—
399	C₄×C₅	#67⋊C₄	1	1	yes	characteristic
400	C₄×C₅	#67⋊C₄	1	1	yes	characteristic
401	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
402	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
403	#41	—	2	1	no	—
404	#41	—	2	1	no	—
405	#41	—	3	2	no	—
406	#41	—	3	2	no	—
407	#41	—	6	1	no	—
408	#41	—	6	1	no	—
409	#41	C₄×C₅×D₃	1	2	yes	—
410	#41	C₂²×C₅×D₃	1	2	yes	—
411	C₂×Q₈	—	3	1	no	—
412	C₂×Q₈	C₄×C₅×D₃	1	1	yes	characteristic
413	C₂×D₄	—	2	1	no	—
414	C₂×D₄	—	3	1	no	—
415	C₂×D₄	—	6	1	no	—
416	C₂×D₄	C₄×C₅×D₃	1	1	yes	characteristic
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	2	1	no	—
419	C₂²×C₄	—	6	1	no	—
420	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
421	Q₁₆	—	3	4	no	—
422	SD₁₆	—	3	4	no	—
423	SD₁₆	—	3	4	no	—
424	D₈	—	3	4	no	—
425	M₁₆	—	2	1	no	—
426	M₁₆	—	3	2	no	—
427	M₁₆	—	6	4	no	—
428	M₁₆	—	6	4	no	—
429	M₁₆	—	6	1	no	—
430	M₁₆	C₂²×C₅×D₃	1	2	yes	—
431	C₂×C₈	—	2	1	no	—
432	C₂×C₈	—	3	1	no	—
433	C₂×C₈	—	3	1	no	—
434	C₂×C₈	—	3	2	no	—
435	C₂×C₈	—	3	1	no	—
436	C₂×C₈	—	3	1	no	—
437	C₂×C₈	—	3	2	no	—
438	C₂×C₈	—	3	2	no	—
439	C₂×C₈	—	3	2	no	—
440	C₂×C₈	—	6	4	no	—
441	C₂×C₈	—	6	4	no	—
442	C₂×C₈	—	6	1	no	—
443	C₄²	—	2	1	no	—
444	C₄²	C₂²×C₅×D₃	1	2	yes	—
445	C₃×C₅	C₂×#444	1	1	yes	characteristic, complemented, Hall
446	C₂²×C₃	—	2	2	no	—
447	C₂²×C₃	—	2	2	no	—
448	C₂²×C₃	—	4	2	no	—
449	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
450	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
451	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
452	C₂×D₃	—	2	2	no	—
453	C₂×D₃	—	4	2	no	—
454	C₃×C₄	—	2	2	no	—
455	C₃×C₄	—	4	2	no	—
456	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
457	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
458	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
459	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
460	Dic₃	—	2	2	no	—
461	C₂×C₅	—	2	1	no	—
462	C₂×C₅	—	2	1	no	—
463	C₂×C₅	—	4	2	no	—
464	C₂×C₅	—	12	2	no	—
465	C₂×C₅	#4823	1	2	yes	direct product factor
466	C₂×C₅	C₂×#67⋊C₄	1	1	yes	characteristic
467	C₂³	—	2	1	no	—
468	C₂³	—	6	1	no	—
469	C₂³	C₅×#237	1	1	yes	characteristic
470	Q₈	—	2	1	no	—
471	Q₈	—	3	2	no	—
472	Q₈	—	6	1	no	—
473	Q₈	C₂×C₄×C₅×D₃	1	2	yes	—
474	D₄	—	2	2	no	—
475	D₄	—	2	2	no	—
476	D₄	—	2	1	no	—
477	D₄	—	3	2	no	—
478	D₄	—	6	2	no	—
479	D₄	—	6	2	no	—
480	D₄	—	6	1	no	—
481	D₄	C₂×C₄×C₅×D₃	1	2	yes	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	6	1	no	—
488	C₂×C₄	—	6	2	no	—
489	C₂×C₄	—	6	2	no	—
490	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
491	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
492	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
493	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
494	C₂×C₄	C₅×#237	1	1	yes	characteristic
495	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
496	C₈	—	2	2	no	—
497	C₈	—	3	2	no	—
498	C₈	—	3	2	no	—
499	C₈	—	3	2	no	—
500	C₈	—	3	2	no	—
501	C₈	—	6	2	no	—
502	C₂×C₃	—	2	1	no	—
503	C₂×C₃	—	2	1	no	—
504	C₂×C₃	—	4	2	no	—
505	C₂×C₃	C₅×#444	1	2	yes	complemented
506	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
507	D₃	—	4	2	no	—
508	C₅	C₂×#4823	1	1	yes	characteristic, direct product factor, Sylow
509	C₂²	—	2	2	no	—
510	C₂²	—	2	2	no	—
511	C₂²	—	4	2	no	—
512	C₂²	—	6	2	no	—
513	C₂²	—	12	2	no	—
514	C₂²	C₅×#67⋊C₄	1	1	yes	characteristic
515	C₂²	C₅×#67⋊C₄	1	1	yes	characteristic
516	C₂²	C₂×C₅×#237	1	1	yes	characteristic
517	C₄	—	2	2	no	—
518	C₄	—	4	2	no	—
519	C₄	—	6	2	no	—
520	C₄	C₅×#67⋊C₄	1	1	yes	characteristic
521	C₄	C₅×#67⋊C₄	1	1	yes	characteristic
522	C₄	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
523	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
524	C₃	C₂×C₅×#444	1	1	yes	characteristic, complemented, Sylow
525	C₂	—	2	1	no	—
526	C₂	—	2	1	no	—
527	C₂	—	4	2	no	—
528	C₂	—	12	2	no	—
529	C₂	C₅×#4823	1	2	yes	direct product factor
530	C₂	C₂×C₅×#67⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	D₃×D₄
commutator	C₃×C₄	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂×C₃×C₅×#104	C₂
socle	C₂²×C₃×C₅	C₄×D₄
prime radical	C₂×C₅×#950	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₂×C₅×#104	D₃
hypocenter	C₃	C₂×C₅×#444
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×#104

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#948	C₂	semidirect
3. C₂×C₅×#907	C₂	semidirect
4. C₂×C₃×C₅×#104	C₂	semidirect
5. C₂×C₅×#822	C₂	semidirect
6. C₂×C₅×#805	C₂	semidirect
7. C₂×C₅×#803	C₂	semidirect
8. C₅×#4823	C₂	direct (N × H)
14. C₅×#950	C₄	semidirect
17. C₅×#948	C₂²	semidirect
18. C₂×C₅×#216	C₄	semidirect
19. C₂×C₅×#215	C₄	semidirect
20. C₂×C₅×#214	C₄	semidirect
21. C₂×C₅×#213	C₄	semidirect
28. C₅×#907	C₂²	semidirect
31. C₃×C₅×#104	C₂²	semidirect
32. C₅×#822	C₂²	semidirect
33. C₅×#805	C₂²	semidirect
34. C₅×#803	C₂²	semidirect
35. C₂×#4823	C₅	direct (N × H)
42. C₂×C₅×#104	D₃	semidirect
67. C₅×#216	C₂×C₄	semidirect
68. C₅×#215	C₂×C₄	semidirect
69. C₅×#214	C₂×C₄	semidirect
70. C₅×#213	C₂×C₄	semidirect
87. C₂×#948	C₂×C₅	semidirect
88. C₂×#907	C₂×C₅	semidirect
89. C₂×C₃×#104	C₂×C₅	semidirect
90. C₂×#822	C₂×C₅	semidirect
91. C₂×#805	C₂×C₅	semidirect
92. C₂×#803	C₂×C₅	semidirect
93. #4823	C₂×C₅	direct (N × H)
117. C₅×#104	C₂×D₃	semidirect
159. #950	C₄×C₅	semidirect
162. #948	C₂²×C₅	semidirect
163. C₂×#216	C₄×C₅	semidirect
164. C₂×#215	C₄×C₅	semidirect
165. C₂×#214	C₄×C₅	semidirect
166. C₂×#213	C₄×C₅	semidirect
173. #907	C₂²×C₅	semidirect
176. C₃×#104	C₂²×C₅	semidirect
177. #822	C₂²×C₅	semidirect
178. #805	C₂²×C₅	semidirect
179. #803	C₂²×C₅	semidirect
228. C₂×#104	C₅×D₃	semidirect
268. #216	C₂×C₄×C₅	semidirect
269. #215	C₂×C₄×C₅	semidirect
270. #214	C₂×C₄×C₅	semidirect
271. #213	C₂×C₄×C₅	semidirect
345. #104	C₂×C₅×D₃	semidirect
350. C₂×C₃×C₅	#444	semidirect
445. C₃×C₅	C₂×#444	semidirect
465. C₂×C₅	#4823	direct (N × H)
505. C₂×C₃	C₅×#444	semidirect
508. C₅	C₂×#4823	direct (N × H)
524. C₃	C₂×C₅×#444	semidirect
529. C₂	C₅×#4823	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×C₅×#950	2
C₂×C₅×#948	2
C₂×C₅×#907	2
C₂×C₃×C₅×#104	2
C₂×C₅×#822	2
C₂×C₅×#805	2
C₂×C₅×#803	2
C₅×#4823	2
C₂×C₅×#444	3
C₂×#4823	5

Subgroups — C2×C5×#4823 #14417919

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#4823 #14417919