Subgroups — C₅×D₃×#469 #14427972

Order 1920.

1192 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×D₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₃×#121	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#469	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5159	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5135	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5039	C₂	1	2	yes	maximal, complemented
8	C₅×#4865	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×D₃×#106	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4782	C₂	1	2	yes	maximal, complemented
11	C₅×D₃×#102	C₂	1	2	yes	maximal, complemented
12	C₂×C₅×#469	—	3	1	no	maximal, Hall
13	C₂×C₅×D₃×D₄	—	2	2	no	—
14	C₂×C₅×D₃×D₄	C₂²	1	2	yes	—
15	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic, complemented
17	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic, complemented
18	C₃×C₅×#121	C₂²	1	2	yes	complemented
19	C₅×#939	—	2	2	no	—
20	C₅×#938	C₂²	1	2	yes	complemented
21	C₂×C₅×#213	C₂²	1	2	yes	complemented
22	C₅×#930	C₂²	1	2	yes	complemented
23	C₂×C₅×#208	C₂²	1	1	yes	characteristic, complemented
24	C₅×D₃×D₈	—	2	4	no	—
25	C₅×D₃×M₁₆	—	2	4	no	—
26	C₂×C₅×D₂₄	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
30	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
31	C₅×#895	C₂²	1	2	yes	complemented
32	C₅×D₃×C₄⋊C₄	C₂²	1	2	yes	—
33	C₅×#884	—	2	2	no	—
34	C₅×D₃×C₂²⋊C₄	—	2	2	no	—
35	C₃×C₅×#106	C₂²	1	1	yes	characteristic, complemented
36	C₃×C₅×#102	C₂²	1	2	yes	complemented
37	C₅×#832	C₂²	1	2	yes	complemented
38	C₅×#821	C₂²	1	2	yes	complemented
39	C₅×#817	C₂²	1	1	yes	characteristic, complemented
40	C₅×#809	C₂²	1	2	yes	complemented
41	C₅×#808	C₂²	1	2	yes	complemented
42	D₃×#469	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
43	C₂²×C₅×D₈	—	3	1	no	—
44	C₂²×C₅×M₁₆	—	3	1	no	—
45	C₂×C₅×#121	—	3	2	no	—
46	C₅×#469	—	3	1	no	—
47	C₅×#469	—	3	2	no	—
48	C₅×#469	—	3	1	no	—
49	C₅×#469	—	3	1	no	—
50	C₅×#469	—	3	2	no	—
51	C₅×#469	D₃	1	1	yes	characteristic, direct product factor
52	C₂×C₅×#106	—	3	1	no	—
53	C₂×C₅×#102	—	3	2	no	—
54	C₂³×C₅×D₃	—	2	2	no	—
55	C₂³×C₅×D₃	D₄	1	1	yes	characteristic
56	C₂×C₃×C₅×D₄	—	2	2	no	—
57	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
58	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
59	C₂×C₅×#67	—	2	2	no	—
60	C₂×C₅×#67	—	2	2	no	—
61	C₂×C₅×#67	—	2	2	no	—
62	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
63	C₅×D₃×D₄	—	2	4	no	—
64	C₅×D₃×D₄	—	2	4	no	—
65	C₅×D₃×D₄	—	4	8	no	—
66	C₂×C₅×D₁₂	—	2	2	no	—
67	C₂×C₅×D₁₂	C₂³	1	2	yes	—
68	C₂×C₄×C₅×D₃	—	2	2	no	—
69	C₂×C₄×C₅×D₃	—	2	2	no	—
70	C₂×C₄×C₅×D₃	—	2	2	no	—
71	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
72	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
73	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
74	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
75	C₃×C₅×D₈	—	2	2	no	—
76	C₃×C₅×M₁₆	—	2	2	no	—
77	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
78	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
79	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
80	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
81	C₅×#217	—	2	2	no	—
82	C₅×#213	—	2	4	no	—
83	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
84	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
85	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
86	C₅×Dic₃⋊C₄	—	2	2	no	—
87	C₅×#208	—	2	2	no	—
88	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
89	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
90	C₅×D₂₄	—	2	2	no	—
91	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
92	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
93	C₅×D₃×C₈	—	2	2	no	—
94	C₅×D₃×C₈	D₄	1	4	yes	complemented
95	C₂×D₃×D₈	C₂×C₅	1	1	yes	characteristic, complemented
96	C₂×D₃×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
97	D₃×#121	C₂×C₅	1	2	yes	complemented
98	C₃×#469	C₂×C₅	1	1	yes	characteristic, complemented
99	#5159	C₂×C₅	1	1	yes	characteristic, complemented
100	#5135	C₂×C₅	1	1	yes	characteristic, complemented
101	#5039	C₂×C₅	1	2	yes	complemented
102	#4865	C₂×C₅	1	1	yes	characteristic, complemented
103	D₃×#106	C₂×C₅	1	1	yes	characteristic, complemented
104	#4782	C₂×C₅	1	2	yes	complemented
105	D₃×#102	C₂×C₅	1	2	yes	complemented
106	C₂²×C₅×D₄	—	3	2	no	—
107	C₂²×C₅×D₄	—	6	2	no	—
108	C₂³×C₄×C₅	—	3	1	no	—
109	C₂×C₅×D₈	—	3	2	no	—
110	C₂×C₅×D₈	—	3	1	no	—
111	C₂×C₅×D₈	—	6	4	no	—
112	C₂×C₅×D₈	C₂×D₃	1	1	yes	characteristic, complemented
113	C₂×C₅×M₁₆	—	3	1	no	—
114	C₂×C₅×M₁₆	—	3	1	no	—
115	C₂×C₅×M₁₆	—	3	1	no	—
116	C₂×C₅×M₁₆	—	6	4	no	—
117	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic, complemented
118	C₂²×C₅×C₈	—	3	1	no	—
119	C₂²×C₅×C₈	—	3	1	no	—
120	C₅×#121	—	3	2	no	—
121	C₅×#121	—	3	2	no	—
122	C₅×#121	—	3	2	no	—
123	C₅×#121	—	6	2	no	—
124	C₅×#121	—	6	2	no	—
125	C₅×#121	C₂×D₃	1	2	yes	complemented
126	C₂×C₅×C₄⋊C₄	—	3	2	no	—
127	C₂×C₅×C₂²⋊C₄	—	6	2	no	—
128	C₅×#106	—	3	1	no	—
129	C₅×#106	—	3	2	no	—
130	C₅×#106	C₂×D₃	1	1	yes	characteristic, complemented
131	C₅×#102	—	3	2	no	—
132	C₅×#102	—	3	2	no	—
133	C₅×#102	—	3	2	no	—
134	C₅×#102	C₂×D₃	1	2	yes	complemented
135	C₂×#469	—	3	1	no	Sylow
136	C₂³×C₃×C₅	—	2	2	no	—
137	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₅×D₃	—	2	2	no	—
139	C₂²×C₅×D₃	—	2	4	no	—
140	C₂²×C₅×D₃	—	2	2	no	—
141	C₂²×C₅×D₃	—	4	4	no	—
142	C₂²×C₅×D₃	—	4	4	no	—
143	C₂²×C₅×D₃	—	4	4	no	—
144	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
146	C₃×C₅×D₄	—	2	2	no	—
147	C₃×C₅×D₄	—	2	2	no	—
148	C₃×C₅×D₄	—	4	4	no	—
149	C₂×C₃×C₄×C₅	—	2	1	no	—
150	C₂×C₃×C₄×C₅	—	2	1	no	—
151	C₂×C₃×C₄×C₅	—	2	2	no	—
152	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
153	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
154	C₅×#67	—	4	4	no	—
155	C₅×#67	—	4	4	no	—
156	C₅×#67	—	4	4	no	—
157	C₂×C₅×Dic₃	—	2	2	no	—
158	C₂×C₅×Dic₃	—	2	2	no	—
159	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
160	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
161	C₅×D₁₂	—	2	2	no	—
162	C₅×D₁₂	—	2	2	no	—
163	C₅×D₁₂	—	4	4	no	—
164	C₄×C₅×D₃	—	2	2	no	—
165	C₄×C₅×D₃	—	2	1	no	—
166	C₄×C₅×D₃	—	2	1	no	—
167	C₄×C₅×D₃	—	2	2	no	—
168	C₄×C₅×D₃	—	4	4	no	—
169	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
170	C₄×C₅×D₃	#41	1	2	yes	—
171	C₃×C₅×C₈	—	2	1	no	—
172	C₃×C₅×C₈	C₂×D₄	1	2	yes	complemented
173	C₅×C₃⋊C₈	—	2	1	no	—
174	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	complemented
175	C₂×D₃×D₄	—	2	2	no	—
176	C₂×D₃×D₄	C₂²×C₅	1	2	yes	—
177	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
178	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic, complemented
179	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
180	C₃×#121	C₂²×C₅	1	2	yes	complemented
181	#939	—	2	2	no	—
182	#938	C₂²×C₅	1	2	yes	complemented
183	C₂×#213	C₂²×C₅	1	2	yes	complemented
184	#930	C₂²×C₅	1	2	yes	complemented
185	C₂×#208	C₂²×C₅	1	1	yes	characteristic, complemented
186	D₃×D₈	—	2	4	no	—
187	D₃×M₁₆	—	2	4	no	—
188	C₂×D₂₄	C₂²×C₅	1	1	yes	characteristic, complemented
189	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	1	yes	characteristic, complemented
190	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	1	yes	characteristic, complemented
191	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
192	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
193	#895	C₂²×C₅	1	2	yes	complemented
194	D₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
195	#884	—	2	2	no	—
196	D₃×C₂²⋊C₄	—	2	2	no	—
197	C₃×#106	C₂²×C₅	1	1	yes	characteristic, complemented
198	C₃×#102	C₂²×C₅	1	2	yes	complemented
199	#832	C₂²×C₅	1	2	yes	complemented
200	#821	C₂²×C₅	1	2	yes	complemented
201	#817	C₂²×C₅	1	1	yes	characteristic, complemented
202	#809	C₂²×C₅	1	2	yes	complemented
203	#808	C₂²×C₅	1	2	yes	complemented
204	C₂⁴×C₅	—	3	1	no	—
205	C₂⁴×C₅	—	6	2	no	—
206	C₂×C₅×D₄	—	2	2	no	—
207	C₂×C₅×D₄	—	3	2	no	—
208	C₂×C₅×D₄	—	6	2	no	—
209	C₂×C₅×D₄	—	6	4	no	—
210	C₂×C₅×D₄	—	6	4	no	—
211	C₂×C₅×D₄	—	6	2	no	—
212	C₂×C₅×D₄	—	6	2	no	—
213	C₂×C₅×D₄	—	6	2	no	—
214	C₂×C₅×D₄	—	12	8	no	—
215	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
216	C₂²×C₄×C₅	—	3	1	no	—
217	C₂²×C₄×C₅	—	3	1	no	—
218	C₂²×C₄×C₅	—	3	1	no	—
219	C₂²×C₄×C₅	—	3	1	no	—
220	C₂²×C₄×C₅	—	3	1	no	—
221	C₂²×C₄×C₅	—	6	2	no	—
222	C₂²×C₄×C₅	—	6	2	no	—
223	C₂²×C₄×C₅	—	6	2	no	—
224	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
225	C₅×D₈	—	2	2	no	—
226	C₅×D₈	—	6	4	no	—
227	C₅×D₈	—	6	2	no	—
228	C₅×M₁₆	—	2	2	no	—
229	C₅×M₁₆	—	6	2	no	—
230	C₅×M₁₆	—	6	2	no	—
231	C₅×M₁₆	—	6	2	no	—
232	C₂×C₅×C₈	—	3	1	no	—
233	C₂×C₅×C₈	—	3	4	no	—
234	C₂×C₅×C₈	—	3	1	no	—
235	C₂×C₅×C₈	—	6	2	no	—
236	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
237	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
238	C₅×C₄⋊C₄	—	3	2	no	—
239	C₅×C₄⋊C₄	—	6	2	no	—
240	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
241	C₅×C₂²⋊C₄	—	2	2	no	—
242	C₅×C₂²⋊C₄	—	6	2	no	—
243	C₅×C₂²⋊C₄	—	6	2	no	—
244	C₅×C₂²⋊C₄	—	6	2	no	—
245	C₂²×D₈	—	3	1	no	—
246	C₂²×M₁₆	—	3	1	no	—
247	C₂×#121	—	3	2	no	—
248	#469	—	3	1	no	—
249	#469	—	3	1	no	—
250	#469	—	3	2	no	—
251	#469	—	3	1	no	—
252	#469	—	3	2	no	—
253	#469	C₅×D₃	1	1	yes	characteristic, direct product factor
254	C₂×#106	—	3	1	no	—
255	C₂×#102	—	3	2	no	—
256	C₂²×C₃×C₅	—	2	1	no	—
257	C₂²×C₃×C₅	—	2	2	no	—
258	C₂²×C₃×C₅	—	4	2	no	—
259	C₂²×C₃×C₅	—	4	2	no	—
260	C₂²×C₃×C₅	—	4	2	no	—
261	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
262	C₂×C₅×D₃	—	2	1	no	—
263	C₂×C₅×D₃	—	2	2	no	—
264	C₂×C₅×D₃	—	4	4	no	—
265	C₂×C₅×D₃	—	4	2	no	—
266	C₂×C₅×D₃	—	4	2	no	—
267	C₂×C₅×D₃	—	4	2	no	—
268	C₂×C₅×D₃	—	8	8	no	—
269	C₂×C₅×D₃	#121	1	2	yes	—
270	C₂×C₅×D₃	AGL(1,ℤ/8)	1	4	yes	—
271	C₃×C₄×C₅	—	2	1	no	—
272	C₃×C₄×C₅	—	4	2	no	—
273	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
274	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
275	C₅×Dic₃	—	2	1	no	—
276	C₅×Dic₃	—	4	2	no	—
277	C₅×Dic₃	#121	1	2	yes	—
278	C₂³×D₃	—	2	2	no	—
279	C₂³×D₃	C₅×D₄	1	1	yes	characteristic
280	C₂×C₃×D₄	—	2	2	no	—
281	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
282	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
283	C₂×#67	—	2	2	no	—
284	C₂×#67	—	2	2	no	—
285	C₂×#67	—	2	2	no	—
286	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
287	D₃×D₄	—	2	4	no	—
288	D₃×D₄	—	2	4	no	—
289	D₃×D₄	—	4	8	no	—
290	C₂×D₁₂	—	2	2	no	—
291	C₂×D₁₂	C₂³×C₅	1	2	yes	—
292	C₂×C₄×D₃	—	2	2	no	—
293	C₂×C₄×D₃	—	2	2	no	—
294	C₂×C₄×D₃	—	2	2	no	—
295	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
296	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
297	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
298	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
299	C₃×D₈	—	2	2	no	—
300	C₃×M₁₆	—	2	2	no	—
301	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
302	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
303	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
304	C₃×C₂²⋊C₄	—	2	2	no	—
305	#217	—	2	2	no	—
306	#213	—	2	4	no	—
307	(C₂×D₃)⋊C₄	—	2	2	no	—
308	(C₂×D₃)⋊C₄	—	2	2	no	—
309	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
310	Dic₃⋊C₄	—	2	2	no	—
311	#208	—	2	2	no	—
312	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
313	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
314	D₂₄	—	2	2	no	—
315	ΓL(1,𝔽₂₅)	—	2	2	no	—
316	ΓL(1,𝔽₂₅)	—	2	2	no	—
317	D₃×C₈	—	2	2	no	—
318	D₃×C₈	C₅×D₄	1	4	yes	complemented
319	C₂³×C₅	—	2	2	no	—
320	C₂³×C₅	—	3	1	no	—
321	C₂³×C₅	—	3	1	no	—
322	C₂³×C₅	—	6	2	no	—
323	C₂³×C₅	—	6	4	no	—
324	C₂³×C₅	—	6	2	no	—
325	C₂³×C₅	—	12	4	no	—
326	C₂³×C₅	—	12	4	no	—
327	C₂³×C₅	—	12	4	no	—
328	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
329	C₅×D₄	—	2	2	no	—
330	C₅×D₄	—	2	2	no	—
331	C₅×D₄	—	4	4	no	—
332	C₅×D₄	—	6	2	no	—
333	C₅×D₄	—	6	2	no	—
334	C₅×D₄	—	12	4	no	—
335	C₅×D₄	—	12	4	no	—
336	C₅×D₄	—	12	4	no	—
337	C₅×D₄	—	12	4	no	—
338	C₂×C₄×C₅	—	2	1	no	—
339	C₂×C₄×C₅	—	2	1	no	—
340	C₂×C₄×C₅	—	2	2	no	—
341	C₂×C₄×C₅	—	3	1	no	—
342	C₂×C₄×C₅	—	3	2	no	—
343	C₂×C₄×C₅	—	3	2	no	—
344	C₂×C₄×C₅	—	3	1	no	—
345	C₂×C₄×C₅	—	6	2	no	—
346	C₂×C₄×C₅	—	6	2	no	—
347	C₂×C₄×C₅	—	6	2	no	—
348	C₂×C₄×C₅	—	6	1	no	—
349	C₂×C₄×C₅	—	6	1	no	—
350	C₂×C₄×C₅	—	6	2	no	—
351	C₂×C₄×C₅	—	12	4	no	—
352	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
353	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
354	C₅×C₈	—	2	1	no	—
355	C₅×C₈	—	3	2	no	—
356	C₅×C₈	—	6	1	no	—
357	C₅×C₈	D₃×D₄	1	2	yes	complemented
358	C₂²×D₄	—	3	2	no	—
359	C₂²×D₄	—	6	2	no	—
360	C₂³×C₄	—	3	1	no	—
361	C₂×D₈	—	3	2	no	—
362	C₂×D₈	—	3	1	no	—
363	C₂×D₈	—	6	4	no	—
364	C₂×D₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
365	C₂×M₁₆	—	3	1	no	—
366	C₂×M₁₆	—	3	1	no	—
367	C₂×M₁₆	—	3	1	no	—
368	C₂×M₁₆	—	6	4	no	—
369	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic, complemented
370	C₂²×C₈	—	3	1	no	—
371	C₂²×C₈	—	3	1	no	—
372	#121	—	3	2	no	—
373	#121	—	3	2	no	—
374	#121	—	3	2	no	—
375	#121	—	6	2	no	—
376	#121	—	6	2	no	—
377	#121	C₂×C₅×D₃	1	2	yes	complemented
378	C₂×C₄⋊C₄	—	3	2	no	—
379	C₂×C₂²⋊C₄	—	6	2	no	—
380	#106	—	3	1	no	—
381	#106	—	3	2	no	—
382	#106	C₂×C₅×D₃	1	1	yes	characteristic, complemented
383	#102	—	3	2	no	—
384	#102	—	3	2	no	—
385	#102	—	3	2	no	—
386	#102	C₂×C₅×D₃	1	2	yes	complemented
387	C₂×C₃×C₅	—	4	1	no	—
388	C₂×C₃×C₅	—	8	2	no	—
389	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
390	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	2	yes	—
391	C₅×D₃	—	4	1	no	—
392	C₅×D₃	—	8	2	no	—
393	C₅×D₃	#469	1	4	yes	direct product factor
394	C₂³×C₃	—	2	2	no	—
395	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
396	C₂²×D₃	—	2	2	no	—
397	C₂²×D₃	—	2	4	no	—
398	C₂²×D₃	—	2	2	no	—
399	C₂²×D₃	—	4	4	no	—
400	C₂²×D₃	—	4	4	no	—
401	C₂²×D₃	—	4	4	no	—
402	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
403	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
404	C₃×D₄	—	2	2	no	—
405	C₃×D₄	—	2	2	no	—
406	C₃×D₄	—	4	4	no	—
407	C₂×C₃×C₄	—	2	1	no	—
408	C₂×C₃×C₄	—	2	1	no	—
409	C₂×C₃×C₄	—	2	2	no	—
410	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
411	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
412	#67	—	4	4	no	—
413	#67	—	4	4	no	—
414	#67	—	4	4	no	—
415	C₂×Dic₃	—	2	2	no	—
416	C₂×Dic₃	—	2	2	no	—
417	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
418	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
419	D₁₂	—	2	2	no	—
420	D₁₂	—	2	2	no	—
421	D₁₂	—	4	4	no	—
422	C₄×D₃	—	2	2	no	—
423	C₄×D₃	—	2	1	no	—
424	C₄×D₃	—	2	1	no	—
425	C₄×D₃	—	2	2	no	—
426	C₄×D₃	—	4	4	no	—
427	C₄×D₃	C₂×C₅×D₄	1	2	yes	—
428	C₄×D₃	C₅×#41	1	2	yes	—
429	C₃×C₈	—	2	1	no	—
430	C₃×C₈	C₂×C₅×D₄	1	2	yes	complemented
431	C₃⋊C₈	—	2	1	no	—
432	C₃⋊C₈	C₂×C₅×D₄	1	2	yes	complemented
433	C₂²×C₅	—	2	2	no	—
434	C₂²×C₅	—	2	1	no	—
435	C₂²×C₅	—	3	4	no	—
436	C₂²×C₅	—	3	2	no	—
437	C₂²×C₅	—	4	2	no	—
438	C₂²×C₅	—	4	2	no	—
439	C₂²×C₅	—	4	2	no	—
440	C₂²×C₅	—	6	2	no	—
441	C₂²×C₅	—	6	1	no	—
442	C₂²×C₅	—	12	4	no	—
443	C₂²×C₅	—	12	2	no	—
444	C₂²×C₅	—	12	2	no	—
445	C₂²×C₅	—	12	2	no	—
446	C₂²×C₅	—	24	8	no	—
447	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
448	C₄×C₅	—	2	1	no	—
449	C₄×C₅	—	3	2	no	—
450	C₄×C₅	—	4	2	no	—
451	C₄×C₅	—	6	1	no	—
452	C₄×C₅	—	12	2	no	—
453	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
454	C₄×C₅	D₃×#41	1	1	yes	characteristic
455	C₂⁴	—	3	1	no	—
456	C₂⁴	—	6	2	no	—
457	C₂×D₄	—	2	2	no	—
458	C₂×D₄	—	3	2	no	—
459	C₂×D₄	—	6	2	no	—
460	C₂×D₄	—	6	4	no	—
461	C₂×D₄	—	6	4	no	—
462	C₂×D₄	—	6	2	no	—
463	C₂×D₄	—	6	2	no	—
464	C₂×D₄	—	6	2	no	—
465	C₂×D₄	—	12	8	no	—
466	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
467	C₂²×C₄	—	3	1	no	—
468	C₂²×C₄	—	3	1	no	—
469	C₂²×C₄	—	3	1	no	—
470	C₂²×C₄	—	3	1	no	—
471	C₂²×C₄	—	3	1	no	—
472	C₂²×C₄	—	6	2	no	—
473	C₂²×C₄	—	6	2	no	—
474	C₂²×C₄	—	6	2	no	—
475	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
476	D₈	—	2	2	no	—
477	D₈	—	6	4	no	—
478	D₈	—	6	2	no	—
479	M₁₆	—	2	2	no	—
480	M₁₆	—	6	2	no	—
481	M₁₆	—	6	2	no	—
482	M₁₆	—	6	2	no	—
483	C₂×C₈	—	3	1	no	—
484	C₂×C₈	—	3	4	no	—
485	C₂×C₈	—	3	1	no	—
486	C₂×C₈	—	6	2	no	—
487	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
488	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
489	C₄⋊C₄	—	3	2	no	—
490	C₄⋊C₄	—	6	2	no	—
491	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
492	C₂²⋊C₄	—	2	2	no	—
493	C₂²⋊C₄	—	6	2	no	—
494	C₂²⋊C₄	—	6	2	no	—
495	C₂²⋊C₄	—	6	2	no	—
496	C₃×C₅	C₂×#469	1	1	yes	characteristic, complemented, Hall
497	C₂²×C₃	—	2	1	no	—
498	C₂²×C₃	—	2	2	no	—
499	C₂²×C₃	—	4	2	no	—
500	C₂²×C₃	—	4	2	no	—
501	C₂²×C₃	—	4	2	no	—
502	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
503	C₂×D₃	—	2	1	no	—
504	C₂×D₃	—	2	2	no	—
505	C₂×D₃	—	4	4	no	—
506	C₂×D₃	—	4	2	no	—
507	C₂×D₃	—	4	2	no	—
508	C₂×D₃	—	4	2	no	—
509	C₂×D₃	—	8	8	no	—
510	C₂×D₃	C₅×#121	1	2	yes	—
511	C₂×D₃	C₅×AGL(1,ℤ/8)	1	4	yes	—
512	C₃×C₄	—	2	1	no	—
513	C₃×C₄	—	4	2	no	—
514	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
515	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
516	Dic₃	—	2	1	no	—
517	Dic₃	—	4	2	no	—
518	Dic₃	C₅×#121	1	2	yes	—
519	C₂×C₅	—	3	4	no	—
520	C₂×C₅	—	4	1	no	—
521	C₂×C₅	—	8	2	no	—
522	C₂×C₅	—	12	1	no	—
523	C₂×C₅	—	24	2	no	—
524	C₂×C₅	D₃×#121	1	1	yes	characteristic
525	C₂×C₅	D₃×AGL(1,ℤ/8)	1	2	yes	—
526	C₂³	—	2	2	no	—
527	C₂³	—	3	1	no	—
528	C₂³	—	3	1	no	—
529	C₂³	—	6	2	no	—
530	C₂³	—	6	4	no	—
531	C₂³	—	6	2	no	—
532	C₂³	—	12	4	no	—
533	C₂³	—	12	4	no	—
534	C₂³	—	12	4	no	—
535	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
536	D₄	—	2	2	no	—
537	D₄	—	2	2	no	—
538	D₄	—	4	4	no	—
539	D₄	—	6	2	no	—
540	D₄	—	6	2	no	—
541	D₄	—	12	4	no	—
542	D₄	—	12	4	no	—
543	D₄	—	12	4	no	—
544	D₄	—	12	4	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	3	1	no	—
549	C₂×C₄	—	3	2	no	—
550	C₂×C₄	—	3	2	no	—
551	C₂×C₄	—	3	1	no	—
552	C₂×C₄	—	6	2	no	—
553	C₂×C₄	—	6	2	no	—
554	C₂×C₄	—	6	2	no	—
555	C₂×C₄	—	6	1	no	—
556	C₂×C₄	—	6	1	no	—
557	C₂×C₄	—	6	2	no	—
558	C₂×C₄	—	12	4	no	—
559	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
560	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
561	C₈	—	2	1	no	—
562	C₈	—	3	2	no	—
563	C₈	—	6	1	no	—
564	C₈	C₅×D₃×D₄	1	2	yes	complemented
565	C₂×C₃	—	4	1	no	—
566	C₂×C₃	—	8	2	no	—
567	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
568	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	2	yes	—
569	D₃	—	4	1	no	—
570	D₃	—	8	2	no	—
571	D₃	C₅×#469	1	4	yes	direct product factor
572	C₅	D₃×#469	1	1	yes	characteristic, direct product factor, Sylow
573	C₂²	—	2	2	no	—
574	C₂²	—	2	1	no	—
575	C₂²	—	3	4	no	—
576	C₂²	—	3	2	no	—
577	C₂²	—	4	2	no	—
578	C₂²	—	4	2	no	—
579	C₂²	—	4	2	no	—
580	C₂²	—	6	2	no	—
581	C₂²	—	6	1	no	—
582	C₂²	—	12	4	no	—
583	C₂²	—	12	2	no	—
584	C₂²	—	12	2	no	—
585	C₂²	—	12	2	no	—
586	C₂²	—	24	8	no	—
587	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
588	C₄	—	2	1	no	—
589	C₄	—	3	2	no	—
590	C₄	—	4	2	no	—
591	C₄	—	6	1	no	—
592	C₄	—	12	2	no	—
593	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
594	C₄	C₅×D₃×#41	1	1	yes	characteristic
595	C₃	C₂×C₅×#469	1	1	yes	characteristic, complemented, Sylow
596	C₂	—	3	4	no	—
597	C₂	—	4	1	no	—
598	C₂	—	8	2	no	—
599	C₂	—	12	1	no	—
600	C₂	—	24	2	no	—
601	C₂	C₅×D₃×#121	1	1	yes	characteristic
602	C₂	C₅×D₃×AGL(1,ℤ/8)	1	2	yes	—

	subgroup	G/H
center	C₂²×C₅	C₂×D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#469	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₅×#469	D₃
hypocenter	C₃	C₂×C₅×#469
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#469

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×D₃×D₈	C₂	semidirect
2. C₂×C₅×D₃×M₁₆	C₂	semidirect
3. C₅×D₃×#121	C₂	semidirect
4. C₃×C₅×#469	C₂	semidirect
5. C₅×#5159	C₂	semidirect
6. C₅×#5135	C₂	semidirect
7. C₅×#5039	C₂	semidirect
8. C₅×#4865	C₂	semidirect
9. C₅×D₃×#106	C₂	semidirect
10. C₅×#4782	C₂	semidirect
11. C₅×D₃×#102	C₂	semidirect
16. C₂×C₃×C₅×D₈	C₂²	semidirect
17. C₂×C₃×C₅×M₁₆	C₂²	semidirect
18. C₃×C₅×#121	C₂²	semidirect
20. C₅×#938	C₂²	semidirect
21. C₂×C₅×#213	C₂²	semidirect
22. C₅×#930	C₂²	semidirect
23. C₂×C₅×#208	C₂²	semidirect
26. C₂×C₅×D₂₄	C₂²	semidirect
27. C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	semidirect
28. C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	semidirect
31. C₅×#895	C₂²	semidirect
35. C₃×C₅×#106	C₂²	semidirect
36. C₃×C₅×#102	C₂²	semidirect
37. C₅×#832	C₂²	semidirect
38. C₅×#821	C₂²	semidirect
39. C₅×#817	C₂²	semidirect
40. C₅×#809	C₂²	semidirect
41. C₅×#808	C₂²	semidirect
42. D₃×#469	C₅	direct (N × H)
51. C₅×#469	D₃	direct (N × H)
94. C₅×D₃×C₈	D₄	semidirect
95. C₂×D₃×D₈	C₂×C₅	semidirect
96. C₂×D₃×M₁₆	C₂×C₅	semidirect
97. D₃×#121	C₂×C₅	semidirect
98. C₃×#469	C₂×C₅	semidirect
99. #5159	C₂×C₅	semidirect
100. #5135	C₂×C₅	semidirect
101. #5039	C₂×C₅	semidirect
102. #4865	C₂×C₅	semidirect
103. D₃×#106	C₂×C₅	semidirect
104. #4782	C₂×C₅	semidirect
105. D₃×#102	C₂×C₅	semidirect
112. C₂×C₅×D₈	C₂×D₃	semidirect
117. C₂×C₅×M₁₆	C₂×D₃	semidirect
125. C₅×#121	C₂×D₃	semidirect
130. C₅×#106	C₂×D₃	semidirect
134. C₅×#102	C₂×D₃	semidirect
172. C₃×C₅×C₈	C₂×D₄	semidirect
174. C₅×C₃⋊C₈	C₂×D₄	semidirect
178. C₂×C₃×D₈	C₂²×C₅	semidirect
179. C₂×C₃×M₁₆	C₂²×C₅	semidirect
180. C₃×#121	C₂²×C₅	semidirect
182. #938	C₂²×C₅	semidirect
183. C₂×#213	C₂²×C₅	semidirect
184. #930	C₂²×C₅	semidirect
185. C₂×#208	C₂²×C₅	semidirect
188. C₂×D₂₄	C₂²×C₅	semidirect
189. C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	semidirect
190. C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	semidirect
193. #895	C₂²×C₅	semidirect
197. C₃×#106	C₂²×C₅	semidirect
198. C₃×#102	C₂²×C₅	semidirect
199. #832	C₂²×C₅	semidirect
200. #821	C₂²×C₅	semidirect
201. #817	C₂²×C₅	semidirect
202. #809	C₂²×C₅	semidirect
203. #808	C₂²×C₅	semidirect
253. #469	C₅×D₃	direct (N × H)
318. D₃×C₈	C₅×D₄	semidirect
357. C₅×C₈	D₃×D₄	semidirect
364. C₂×D₈	C₂×C₅×D₃	semidirect
369. C₂×M₁₆	C₂×C₅×D₃	semidirect
377. #121	C₂×C₅×D₃	semidirect
382. #106	C₂×C₅×D₃	semidirect
386. #102	C₂×C₅×D₃	semidirect
393. C₅×D₃	#469	direct (N × H)
430. C₃×C₈	C₂×C₅×D₄	semidirect
432. C₃⋊C₈	C₂×C₅×D₄	semidirect
496. C₃×C₅	C₂×#469	semidirect
564. C₈	C₅×D₃×D₄	semidirect
571. D₃	C₅×#469	direct (N × H)
572. C₅	D₃×#469	direct (N × H)
595. C₃	C₂×C₅×#469	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×D₃×D₈	2
C₂×C₅×D₃×M₁₆	2
C₅×D₃×#121	2
C₃×C₅×#469	2
C₅×#5159	2
C₅×#5135	2
C₅×#5039	2
C₅×#4865	2
C₅×D₃×#106	2
C₅×#4782	2
C₅×D₃×#102	2
C₂×C₅×#469	3
D₃×#469	5

Subgroups — C5×D3×#469 #14427972

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×#469 #14427972