Subgroups — C₅×#82036 #14478494

Order 1920.

740 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5769	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5757	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#509	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5194	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#826	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4916	C₂	1	2	yes	maximal, complemented
7	C₅×#4914	C₂	1	2	yes	maximal, complemented
8	C₅×#4911	C₂	1	2	yes	maximal, complemented
9	C₅×D₃×D₁₆	C₂	1	2	yes	maximal, complemented
10	C₅×#4908	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4907	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3415	—	3	1	no	maximal, Hall
13	C₅×#1009	—	2	1	no	—
14	C₅×#1004	—	2	1	no	—
15	C₃×C₅×#135	C₂²	1	1	yes	characteristic, complemented
16	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic, complemented
17	C₅×#949	—	2	1	no	—
18	C₅×#932	—	2	1	no	—
19	C₅×#919	C₂²	1	2	yes	complemented
20	C₅×#914	—	2	2	no	—
21	C₅×#912	C₂²	1	2	yes	complemented
22	C₅×#911	—	2	2	no	—
23	C₅×D₃×D₈	C₂²	1	2	yes	complemented
24	C₅×D₃×D₈	C₂²	1	2	yes	complemented
25	C₅×#904	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₅×D₂₄	C₂²	1	1	yes	characteristic, complemented
27	C₅×#901	C₂²	1	1	yes	characteristic
28	C₃×C₅×SD₃₂	C₂²	1	2	yes	complemented
29	C₃×C₅×D₁₆	C₂²	1	2	yes	complemented
30	C₃×C₅×M₃₂	C₂²	1	1	yes	characteristic, complemented
31	C₅×#829	C₂²	1	1	yes	characteristic, complemented
32	C₅×#828	C₂²	1	1	yes	characteristic, complemented
33	C₅×#827	C₂²	1	1	yes	characteristic, complemented
34	C₅×#826	C₂²	1	1	yes	characteristic, complemented
35	C₅×#826	C₂²	1	2	yes	complemented
36	C₅×#826	C₂²	1	2	yes	complemented
37	C₂×C₅×C₃⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
38	C₅×#800	C₂²	1	2	yes	complemented
39	C₅×D₄₈	C₂²	1	2	yes	complemented
40	C₅×#798	C₂²	1	2	yes	complemented
41	C₅×D₃×C₁₆	C₂²	1	2	yes	complemented
42	#82036	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
43	C₅×#576	—	3	1	no	—
44	C₅×#576	—	3	1	no	—
45	C₅×#509	—	3	2	no	—
46	C₅×#509	—	3	2	no	—
47	C₅×#509	—	3	1	no	—
48	C₅×#509	D₃	1	1	yes	characteristic, complemented
49	C₅×#508	—	3	2	no	—
50	C₅×#508	—	3	1	no	—
51	C₂×C₅×D₁₆	—	3	2	no	—
52	C₂×C₅×D₁₆	—	3	1	no	—
53	C₅×#504	—	3	1	no	—
54	C₃×C₅×#41	—	2	1	no	—
55	C₂×C₃×C₅×D₄	—	2	1	no	—
56	C₂×C₅×#67	—	4	2	no	—
57	C₅×#239	—	2	2	no	—
58	C₅×#237	—	2	2	no	—
59	C₅×#237	—	4	1	no	—
60	C₅×D₃×D₄	—	2	2	no	—
61	C₅×D₃×D₄	—	2	2	no	—
62	C₅×D₃×D₄	—	4	2	no	—
63	C₅×D₃×D₄	—	4	1	no	—
64	C₅×#235	—	2	1	no	—
65	C₅×#235	—	4	1	no	—
66	C₅×#235	D₄	1	1	yes	characteristic
67	C₂×C₅×D₁₂	—	2	1	no	—
68	C₂×C₅×D₁₂	—	4	1	no	—
69	C₃×C₅×Q₁₆	C₂³	1	1	yes	characteristic
70	C₃×C₅×SD₁₆	—	2	1	no	—
71	C₃×C₅×D₈	—	2	1	no	—
72	C₃×C₅×D₈	C₂³	1	1	yes	characteristic
73	C₃×C₅×D₈	C₂³	1	2	yes	—
74	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
75	C₅×#215	—	2	2	no	—
76	C₅×#214	—	2	2	no	—
77	C₅×#213	—	2	2	no	—
78	C₅×#213	—	2	2	no	—
79	C₅×#208	D₄	1	1	yes	characteristic
80	C₅×Dic₁₂	C₂³	1	1	yes	characteristic
81	C₅×D₂₄	—	2	1	no	—
82	C₅×D₂₄	C₂³	1	2	yes	—
83	C₅×D₂₄	C₂³	1	1	yes	characteristic
84	C₅×#204	—	2	1	no	—
85	C₅×ΓL(1,𝔽₂₅)	D₄	1	2	yes	—
86	C₅×D₃×C₈	C₂³	1	2	yes	—
87	C₃×C₅×C₁₆	C₂³	1	2	yes	—
88	C₅×C₃⋊C₁₆	C₂³	1	1	yes	characteristic
89	C₅×C₃⋊C₁₆	C₂³	1	1	yes	characteristic
90	#5769	C₂×C₅	1	1	yes	characteristic, complemented
91	#5757	C₂×C₅	1	1	yes	characteristic, complemented
92	C₃×#509	C₂×C₅	1	1	yes	characteristic, complemented
93	#5194	C₂×C₅	1	1	yes	characteristic, complemented
94	C₂×#826	C₂×C₅	1	1	yes	characteristic, complemented
95	#4916	C₂×C₅	1	2	yes	complemented
96	#4914	C₂×C₅	1	2	yes	complemented
97	#4911	C₂×C₅	1	2	yes	complemented
98	D₃×D₁₆	C₂×C₅	1	2	yes	complemented
99	#4908	C₂×C₅	1	1	yes	characteristic, complemented
100	#4907	C₂×C₅	1	1	yes	characteristic, complemented
101	C₅×H(5,𝔽₂)	—	6	1	no	—
102	C₅×H(5,𝔽₂)	—	6	1	no	—
103	C₅×AGL(1,ℤ/8)	—	6	2	no	—
104	C₅×AGL(1,ℤ/8)	—	6	2	no	—
105	C₅×AGL(1,ℤ/8)	—	6	1	no	—
106	C₅×AGL(1,ℤ/8)	—	6	1	no	—
107	C₅×#135	—	3	2	no	—
108	C₅×#135	—	3	2	no	—
109	C₅×#135	—	3	1	no	—
110	C₅×#135	C₂×D₃	1	1	yes	characteristic, complemented
111	C₂×C₅×D₈	—	3	2	no	—
112	C₂×C₅×D₈	—	3	2	no	—
113	C₂×C₅×D₈	—	3	1	no	—
114	C₂×C₅×D₈	C₂×D₃	1	1	yes	characteristic, complemented
115	C₅×#131	—	3	1	no	—
116	C₅×Q₃₂	—	3	1	no	—
117	C₅×SD₃₂	—	3	1	no	—
118	C₅×SD₃₂	—	3	1	no	—
119	C₅×SD₃₂	—	3	2	no	—
120	C₅×SD₃₂	C₂×D₃	1	2	yes	complemented
121	C₅×D₁₆	—	3	1	no	—
122	C₅×D₁₆	—	3	2	no	—
123	C₅×D₁₆	—	3	2	no	—
124	C₅×D₁₆	—	3	2	no	—
125	C₅×D₁₆	C₂×D₃	1	2	yes	complemented
126	C₅×M₃₂	—	3	2	no	—
127	C₅×M₃₂	C₂×D₃	1	1	yes	characteristic, complemented
128	C₂×C₅×C₁₆	—	3	1	no	—
129	C₂×C₅×C₁₆	—	3	2	no	—
130	#3415	—	3	1	no	Sylow
131	C₂³×C₃×C₅	—	4	1	no	—
132	C₂²×C₅×D₃	—	4	1	no	—
133	C₂²×C₅×D₃	—	4	2	no	—
134	C₂²×C₅×D₃	—	4	2	no	—
135	C₃×C₅×Q₈	—	2	1	no	—
136	C₃×C₅×D₄	—	2	1	no	—
137	C₃×C₅×D₄	—	2	2	no	—
138	C₃×C₅×D₄	—	4	1	no	—
139	C₃×C₅×D₄	—	4	1	no	—
140	C₂×C₃×C₄×C₅	—	4	1	no	—
141	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
142	C₅×#67	—	4	1	no	—
143	C₅×#67	—	4	2	no	—
144	C₅×#67	—	4	2	no	—
145	C₅×#67	—	4	2	no	—
146	C₅×#67	D₈	1	2	yes	—
147	C₂×C₅×Dic₃	—	4	2	no	—
148	C₅×D₁₂	—	2	1	no	—
149	C₅×D₁₂	—	2	2	no	—
150	C₅×D₁₂	—	4	2	no	—
151	C₅×D₁₂	—	4	1	no	—
152	C₅×D₁₂	D₈	1	1	yes	characteristic
153	C₄×C₅×D₃	—	4	1	no	—
154	C₄×C₅×D₃	—	4	2	no	—
155	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
156	C₅×Dic₆	—	2	1	no	—
157	C₅×Dic₆	D₈	1	1	yes	characteristic
158	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
159	C₃×C₅×C₈	C₂⁴	1	1	yes	characteristic
160	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	—
161	#1009	—	2	1	no	—
162	#1004	—	2	1	no	—
163	C₃×#135	C₂²×C₅	1	1	yes	characteristic, complemented
164	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic, complemented
165	#949	—	2	1	no	—
166	#932	—	2	1	no	—
167	#919	C₂²×C₅	1	2	yes	complemented
168	#914	—	2	2	no	—
169	#912	C₂²×C₅	1	2	yes	complemented
170	#911	—	2	2	no	—
171	D₃×D₈	C₂²×C₅	1	2	yes	complemented
172	D₃×D₈	C₂²×C₅	1	2	yes	complemented
173	#904	C₂²×C₅	1	1	yes	characteristic, complemented
174	C₂×D₂₄	C₂²×C₅	1	1	yes	characteristic, complemented
175	#901	C₂²×C₅	1	1	yes	characteristic
176	C₃×SD₃₂	C₂²×C₅	1	2	yes	complemented
177	C₃×D₁₆	C₂²×C₅	1	2	yes	complemented
178	C₃×M₃₂	C₂²×C₅	1	1	yes	characteristic, complemented
179	#829	C₂²×C₅	1	1	yes	characteristic, complemented
180	#828	C₂²×C₅	1	1	yes	characteristic, complemented
181	#827	C₂²×C₅	1	1	yes	characteristic, complemented
182	#826	C₂²×C₅	1	2	yes	complemented
183	#826	C₂²×C₅	1	2	yes	complemented
184	#826	C₂²×C₅	1	1	yes	characteristic, complemented
185	C₂×C₃⋊C₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
186	#800	C₂²×C₅	1	2	yes	complemented
187	D₄₈	C₂²×C₅	1	2	yes	complemented
188	#798	C₂²×C₅	1	2	yes	complemented
189	D₃×C₁₆	C₂²×C₅	1	2	yes	complemented
190	C₅×#41	—	2	1	no	—
191	C₅×#41	—	3	1	no	—
192	C₅×#41	—	6	2	no	—
193	C₅×#41	—	6	2	no	—
194	C₅×#41	—	6	1	no	—
195	C₅×#41	—	12	1	no	—
196	C₅×#41	—	12	1	no	—
197	C₂×C₅×D₄	—	2	1	no	—
198	C₂×C₅×D₄	—	6	2	no	—
199	C₂×C₅×D₄	—	6	2	no	—
200	C₂×C₅×D₄	—	6	1	no	—
201	C₂×C₅×D₄	—	12	1	no	—
202	C₂×C₅×D₄	—	12	2	no	—
203	C₂×C₅×D₄	—	12	1	no	—
204	C₂×C₅×D₄	—	12	2	no	—
205	C₅×Q₁₆	—	3	1	no	—
206	C₅×Q₁₆	C₂²×D₃	1	1	yes	characteristic
207	C₅×SD₁₆	—	2	1	no	—
208	C₅×SD₁₆	—	6	2	no	—
209	C₅×SD₁₆	—	6	2	no	—
210	C₅×SD₁₆	—	6	1	no	—
211	C₅×D₈	—	2	1	no	—
212	C₅×D₈	—	3	1	no	—
213	C₅×D₈	—	3	2	no	—
214	C₅×D₈	—	6	2	no	—
215	C₅×D₈	—	6	2	no	—
216	C₅×D₈	—	6	1	no	—
217	C₅×D₈	C₂²×D₃	1	1	yes	characteristic
218	C₅×D₈	C₂²×D₃	1	2	yes	—
219	C₅×M₁₆	—	3	1	no	—
220	C₅×M₁₆	—	3	2	no	—
221	C₂×C₅×C₈	—	3	2	no	—
222	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
223	C₅×C₁₆	—	3	1	no	—
224	C₅×C₁₆	—	3	1	no	—
225	C₅×C₁₆	C₂²×D₃	1	2	yes	—
226	#576	—	3	1	no	—
227	#576	—	3	1	no	—
228	#509	—	3	2	no	—
229	#509	—	3	2	no	—
230	#509	—	3	1	no	—
231	#509	C₅×D₃	1	1	yes	characteristic, complemented
232	#508	—	3	1	no	—
233	#508	—	3	2	no	—
234	C₂×D₁₆	—	3	1	no	—
235	C₂×D₁₆	—	3	2	no	—
236	#504	—	3	1	no	—
237	C₂²×C₃×C₅	—	4	2	no	—
238	C₂²×C₃×C₅	—	4	1	no	—
239	C₂²×C₃×C₅	—	16	1	no	—
240	C₂²×C₃×C₅	C₂×D₈	1	1	yes	characteristic
241	C₂×C₅×D₃	—	4	2	no	—
242	C₂×C₅×D₃	—	4	1	no	—
243	C₂×C₅×D₃	—	16	2	no	—
244	C₂×C₅×D₃	—	16	2	no	—
245	C₂×C₅×D₃	—	16	1	no	—
246	C₂×C₅×D₃	C₂×D₈	1	2	yes	—
247	C₃×C₄×C₅	—	4	1	no	—
248	C₃×C₄×C₅	C₂×D₈	1	1	yes	characteristic
249	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
250	C₅×Dic₃	—	4	1	no	—
251	C₅×Dic₃	C₂×D₈	1	2	yes	—
252	C₃×#41	—	2	1	no	—
253	C₂×C₃×D₄	—	2	1	no	—
254	C₂×#67	—	4	2	no	—
255	#239	—	2	2	no	—
256	#237	—	2	2	no	—
257	#237	—	4	1	no	—
258	D₃×D₄	—	2	2	no	—
259	D₃×D₄	—	2	2	no	—
260	D₃×D₄	—	4	2	no	—
261	D₃×D₄	—	4	1	no	—
262	#235	—	2	1	no	—
263	#235	—	4	1	no	—
264	#235	C₅×D₄	1	1	yes	characteristic
265	C₂×D₁₂	—	2	1	no	—
266	C₂×D₁₂	—	4	1	no	—
267	C₃×Q₁₆	C₂³×C₅	1	1	yes	characteristic
268	C₃×SD₁₆	—	2	1	no	—
269	C₃×D₈	—	2	1	no	—
270	C₃×D₈	C₂³×C₅	1	2	yes	—
271	C₃×D₈	C₂³×C₅	1	1	yes	characteristic
272	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
273	#215	—	2	2	no	—
274	#214	—	2	2	no	—
275	#213	—	2	2	no	—
276	#213	—	2	2	no	—
277	#208	C₅×D₄	1	1	yes	characteristic
278	Dic₁₂	C₂³×C₅	1	1	yes	characteristic
279	D₂₄	—	2	1	no	—
280	D₂₄	C₂³×C₅	1	1	yes	characteristic
281	D₂₄	C₂³×C₅	1	2	yes	—
282	#204	—	2	1	no	—
283	ΓL(1,𝔽₂₅)	C₅×D₄	1	2	yes	—
284	D₃×C₈	C₂³×C₅	1	2	yes	—
285	C₃×C₁₆	C₂³×C₅	1	2	yes	—
286	C₃⋊C₁₆	C₂³×C₅	1	1	yes	characteristic
287	C₃⋊C₁₆	C₂³×C₅	1	1	yes	characteristic
288	C₂³×C₅	—	4	1	no	—
289	C₂³×C₅	—	12	2	no	—
290	C₂³×C₅	—	12	2	no	—
291	C₂³×C₅	—	12	1	no	—
292	C₅×Q₈	—	2	1	no	—
293	C₅×Q₈	—	3	1	no	—
294	C₅×Q₈	—	6	1	no	—
295	C₅×D₄	—	2	2	no	—
296	C₅×D₄	—	2	1	no	—
297	C₅×D₄	—	3	2	no	—
298	C₅×D₄	—	3	1	no	—
299	C₅×D₄	—	4	1	no	—
300	C₅×D₄	—	4	1	no	—
301	C₅×D₄	—	6	1	no	—
302	C₅×D₄	—	6	2	no	—
303	C₅×D₄	—	12	2	no	—
304	C₅×D₄	—	12	2	no	—
305	C₅×D₄	—	12	2	no	—
306	C₅×D₄	—	12	2	no	—
307	C₅×D₄	—	12	1	no	—
308	C₅×D₄	—	12	1	no	—
309	C₂×C₄×C₅	—	3	2	no	—
310	C₂×C₄×C₅	—	4	1	no	—
311	C₂×C₄×C₅	—	12	2	no	—
312	C₂×C₄×C₅	—	12	2	no	—
313	C₂×C₄×C₅	—	12	1	no	—
314	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
315	C₅×C₈	—	3	2	no	—
316	C₅×C₈	D₃×D₄	1	1	yes	characteristic
317	C₅×C₈	C₂³×D₃	1	1	yes	characteristic
318	H(5,𝔽₂)	—	6	1	no	—
319	H(5,𝔽₂)	—	6	1	no	—
320	AGL(1,ℤ/8)	—	6	2	no	—
321	AGL(1,ℤ/8)	—	6	2	no	—
322	AGL(1,ℤ/8)	—	6	1	no	—
323	AGL(1,ℤ/8)	—	6	1	no	—
324	#135	—	3	2	no	—
325	#135	—	3	2	no	—
326	#135	—	3	1	no	—
327	#135	C₂×C₅×D₃	1	1	yes	characteristic, complemented
328	C₂×D₈	—	3	2	no	—
329	C₂×D₈	—	3	2	no	—
330	C₂×D₈	—	3	1	no	—
331	C₂×D₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
332	#131	—	3	1	no	—
333	Q₃₂	—	3	1	no	—
334	SD₃₂	—	3	1	no	—
335	SD₃₂	—	3	1	no	—
336	SD₃₂	—	3	2	no	—
337	SD₃₂	C₂×C₅×D₃	1	2	yes	complemented
338	D₁₆	—	3	2	no	—
339	D₁₆	—	3	1	no	—
340	D₁₆	—	3	2	no	—
341	D₁₆	—	3	2	no	—
342	D₁₆	C₂×C₅×D₃	1	2	yes	complemented
343	M₃₂	—	3	2	no	—
344	M₃₂	C₂×C₅×D₃	1	1	yes	characteristic, complemented
345	C₂×C₁₆	—	3	1	no	—
346	C₂×C₁₆	—	3	2	no	—
347	C₂×C₃×C₅	—	2	1	no	—
348	C₂×C₃×C₅	—	8	1	no	—
349	C₂×C₃×C₅	—	8	2	no	—
350	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
351	C₅×D₃	—	2	2	no	—
352	C₅×D₃	—	8	2	no	—
353	C₅×D₃	—	8	1	no	—
354	C₂³×C₃	—	4	1	no	—
355	C₂²×D₃	—	4	1	no	—
356	C₂²×D₃	—	4	2	no	—
357	C₂²×D₃	—	4	2	no	—
358	C₃×Q₈	—	2	1	no	—
359	C₃×D₄	—	2	1	no	—
360	C₃×D₄	—	2	2	no	—
361	C₃×D₄	—	4	1	no	—
362	C₃×D₄	—	4	1	no	—
363	C₂×C₃×C₄	—	4	1	no	—
364	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
365	#67	—	4	1	no	—
366	#67	—	4	2	no	—
367	#67	—	4	2	no	—
368	#67	—	4	2	no	—
369	#67	C₅×D₈	1	2	yes	—
370	C₂×Dic₃	—	4	2	no	—
371	D₁₂	—	2	1	no	—
372	D₁₂	—	2	2	no	—
373	D₁₂	—	4	2	no	—
374	D₁₂	—	4	1	no	—
375	D₁₂	C₅×D₈	1	1	yes	characteristic
376	C₄×D₃	—	4	1	no	—
377	C₄×D₃	—	4	2	no	—
378	C₄×D₃	C₂×C₅×D₄	1	2	yes	—
379	Dic₆	—	2	1	no	—
380	Dic₆	C₅×D₈	1	1	yes	characteristic
381	C₃×C₈	C₂×C₅×D₄	1	1	yes	characteristic
382	C₃×C₈	C₂⁴×C₅	1	1	yes	characteristic
383	C₃⋊C₈	C₂×C₅×D₄	1	2	yes	—
384	C₂²×C₅	—	3	2	no	—
385	C₂²×C₅	—	4	1	no	—
386	C₂²×C₅	—	4	2	no	—
387	C₂²×C₅	—	12	2	no	—
388	C₂²×C₅	—	12	1	no	—
389	C₂²×C₅	—	16	1	no	—
390	C₂²×C₅	—	48	1	no	—
391	C₂²×C₅	—	48	2	no	—
392	C₂²×C₅	—	48	2	no	—
393	C₂²×C₅	D₃×D₈	1	1	yes	characteristic
394	C₄×C₅	—	3	2	no	—
395	C₄×C₅	—	4	1	no	—
396	C₄×C₅	—	12	1	no	—
397	C₄×C₅	D₃×D₈	1	1	yes	characteristic
398	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
399	#41	—	2	1	no	—
400	#41	—	3	1	no	—
401	#41	—	6	2	no	—
402	#41	—	6	2	no	—
403	#41	—	6	1	no	—
404	#41	—	12	1	no	—
405	#41	—	12	1	no	—
406	C₂×D₄	—	2	1	no	—
407	C₂×D₄	—	6	2	no	—
408	C₂×D₄	—	6	2	no	—
409	C₂×D₄	—	6	1	no	—
410	C₂×D₄	—	12	1	no	—
411	C₂×D₄	—	12	2	no	—
412	C₂×D₄	—	12	1	no	—
413	C₂×D₄	—	12	2	no	—
414	Q₁₆	—	3	1	no	—
415	Q₁₆	C₂²×C₅×D₃	1	1	yes	characteristic
416	SD₁₆	—	2	1	no	—
417	SD₁₆	—	6	2	no	—
418	SD₁₆	—	6	2	no	—
419	SD₁₆	—	6	1	no	—
420	D₈	—	2	1	no	—
421	D₈	—	3	2	no	—
422	D₈	—	3	1	no	—
423	D₈	—	6	2	no	—
424	D₈	—	6	2	no	—
425	D₈	—	6	1	no	—
426	D₈	C₂²×C₅×D₃	1	2	yes	—
427	D₈	C₂²×C₅×D₃	1	1	yes	characteristic
428	M₁₆	—	3	1	no	—
429	M₁₆	—	3	2	no	—
430	C₂×C₈	—	3	2	no	—
431	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
432	C₁₆	—	3	1	no	—
433	C₁₆	—	3	1	no	—
434	C₁₆	C₂²×C₅×D₃	1	2	yes	—
435	C₃×C₅	#3415	1	1	yes	characteristic, complemented, Hall
436	C₂²×C₃	—	4	2	no	—
437	C₂²×C₃	—	4	1	no	—
438	C₂²×C₃	—	16	1	no	—
439	C₂²×C₃	C₂×C₅×D₈	1	1	yes	characteristic
440	C₂×D₃	—	4	2	no	—
441	C₂×D₃	—	4	1	no	—
442	C₂×D₃	—	16	2	no	—
443	C₂×D₃	—	16	2	no	—
444	C₂×D₃	—	16	1	no	—
445	C₂×D₃	C₂×C₅×D₈	1	2	yes	—
446	C₃×C₄	—	4	1	no	—
447	C₃×C₄	C₂×C₅×D₈	1	1	yes	characteristic
448	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
449	Dic₃	—	4	1	no	—
450	Dic₃	C₂×C₅×D₈	1	2	yes	—
451	C₂×C₅	—	2	1	no	—
452	C₂×C₅	—	6	2	no	—
453	C₂×C₅	—	8	2	no	—
454	C₂×C₅	—	8	1	no	—
455	C₂×C₅	—	24	2	no	—
456	C₂×C₅	—	24	1	no	—
457	C₂×C₅	C₂×D₃×D₈	1	1	yes	characteristic
458	C₂³	—	4	1	no	—
459	C₂³	—	12	2	no	—
460	C₂³	—	12	2	no	—
461	C₂³	—	12	1	no	—
462	Q₈	—	2	1	no	—
463	Q₈	—	3	1	no	—
464	Q₈	—	6	1	no	—
465	D₄	—	2	2	no	—
466	D₄	—	2	1	no	—
467	D₄	—	3	2	no	—
468	D₄	—	3	1	no	—
469	D₄	—	4	1	no	—
470	D₄	—	4	1	no	—
471	D₄	—	6	1	no	—
472	D₄	—	6	2	no	—
473	D₄	—	12	2	no	—
474	D₄	—	12	2	no	—
475	D₄	—	12	2	no	—
476	D₄	—	12	2	no	—
477	D₄	—	12	1	no	—
478	D₄	—	12	1	no	—
479	C₂×C₄	—	3	2	no	—
480	C₂×C₄	—	4	1	no	—
481	C₂×C₄	—	12	2	no	—
482	C₂×C₄	—	12	2	no	—
483	C₂×C₄	—	12	1	no	—
484	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
485	C₈	—	3	2	no	—
486	C₈	C₅×D₃×D₄	1	1	yes	characteristic
487	C₈	C₂³×C₅×D₃	1	1	yes	characteristic
488	C₂×C₃	—	2	1	no	—
489	C₂×C₃	—	8	1	no	—
490	C₂×C₃	—	8	2	no	—
491	C₂×C₃	C₂²×C₅×D₈	1	1	yes	characteristic
492	D₃	—	2	2	no	—
493	D₃	—	8	2	no	—
494	D₃	—	8	1	no	—
495	C₅	#82036	1	1	yes	characteristic, direct product factor, Sylow
496	C₂²	—	3	2	no	—
497	C₂²	—	4	1	no	—
498	C₂²	—	4	2	no	—
499	C₂²	—	12	2	no	—
500	C₂²	—	12	1	no	—
501	C₂²	—	16	1	no	—
502	C₂²	—	48	1	no	—
503	C₂²	—	48	2	no	—
504	C₂²	—	48	2	no	—
505	C₂²	C₅×D₃×D₈	1	1	yes	characteristic
506	C₄	—	3	2	no	—
507	C₄	—	4	1	no	—
508	C₄	—	12	1	no	—
509	C₄	C₅×D₃×D₈	1	1	yes	characteristic
510	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
511	C₃	C₅×#3415	1	1	yes	characteristic, complemented, Sylow
512	C₂	—	2	1	no	—
513	C₂	—	6	2	no	—
514	C₂	—	8	2	no	—
515	C₂	—	8	1	no	—
516	C₂	—	24	2	no	—
517	C₂	—	24	1	no	—
518	C₂	C₂×C₅×D₃×D₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅	C₂×D₃×D₈
commutator, cosocle	C₃×C₈	C₂⁴×C₅
Frattini	C₈	C₂³×C₅×D₃
Fitting	C₃×C₅×#509	C₂
socle	C₂×C₃×C₅	C₂²×D₈
hypercenter	C₅×#509	D₃
hypocenter	C₃	C₅×#3415
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₅ ◁ C₂×C₄×C₅ ◁ C₂×C₅×C₈ ◁ C₅×#509

Complements

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

N	H ≅ G/N	type
1. C₅×#5769	C₂	semidirect
2. C₅×#5757	C₂	semidirect
3. C₃×C₅×#509	C₂	semidirect
4. C₅×#5194	C₂	semidirect
5. C₂×C₅×#826	C₂	semidirect
6. C₅×#4916	C₂	semidirect
7. C₅×#4914	C₂	semidirect
8. C₅×#4911	C₂	semidirect
9. C₅×D₃×D₁₆	C₂	semidirect
10. C₅×#4908	C₂	semidirect
11. C₅×#4907	C₂	semidirect
15. C₃×C₅×#135	C₂²	semidirect
16. C₂×C₃×C₅×D₈	C₂²	semidirect
19. C₅×#919	C₂²	semidirect
21. C₅×#912	C₂²	semidirect
23. C₅×D₃×D₈	C₂²	semidirect
24. C₅×D₃×D₈	C₂²	semidirect
25. C₅×#904	C₂²	semidirect
26. C₂×C₅×D₂₄	C₂²	semidirect
28. C₃×C₅×SD₃₂	C₂²	semidirect
29. C₃×C₅×D₁₆	C₂²	semidirect
30. C₃×C₅×M₃₂	C₂²	semidirect
31. C₅×#829	C₂²	semidirect
32. C₅×#828	C₂²	semidirect
33. C₅×#827	C₂²	semidirect
34. C₅×#826	C₂²	semidirect
35. C₅×#826	C₂²	semidirect
36. C₅×#826	C₂²	semidirect
37. C₂×C₅×C₃⋊C₁₆	C₂²	semidirect
38. C₅×#800	C₂²	semidirect
39. C₅×D₄₈	C₂²	semidirect
40. C₅×#798	C₂²	semidirect
41. C₅×D₃×C₁₆	C₂²	semidirect
42. #82036	C₅	direct (N × H)
48. C₅×#509	D₃	semidirect
90. #5769	C₂×C₅	semidirect
91. #5757	C₂×C₅	semidirect
92. C₃×#509	C₂×C₅	semidirect
93. #5194	C₂×C₅	semidirect
94. C₂×#826	C₂×C₅	semidirect
95. #4916	C₂×C₅	semidirect
96. #4914	C₂×C₅	semidirect
97. #4911	C₂×C₅	semidirect
98. D₃×D₁₆	C₂×C₅	semidirect
99. #4908	C₂×C₅	semidirect
100. #4907	C₂×C₅	semidirect
110. C₅×#135	C₂×D₃	semidirect
114. C₂×C₅×D₈	C₂×D₃	semidirect
120. C₅×SD₃₂	C₂×D₃	semidirect
125. C₅×D₁₆	C₂×D₃	semidirect
127. C₅×M₃₂	C₂×D₃	semidirect
163. C₃×#135	C₂²×C₅	semidirect
164. C₂×C₃×D₈	C₂²×C₅	semidirect
167. #919	C₂²×C₅	semidirect
169. #912	C₂²×C₅	semidirect
171. D₃×D₈	C₂²×C₅	semidirect
172. D₃×D₈	C₂²×C₅	semidirect
173. #904	C₂²×C₅	semidirect
174. C₂×D₂₄	C₂²×C₅	semidirect
176. C₃×SD₃₂	C₂²×C₅	semidirect
177. C₃×D₁₆	C₂²×C₅	semidirect
178. C₃×M₃₂	C₂²×C₅	semidirect
179. #829	C₂²×C₅	semidirect
180. #828	C₂²×C₅	semidirect
181. #827	C₂²×C₅	semidirect
182. #826	C₂²×C₅	semidirect
183. #826	C₂²×C₅	semidirect
184. #826	C₂²×C₅	semidirect
185. C₂×C₃⋊C₁₆	C₂²×C₅	semidirect
186. #800	C₂²×C₅	semidirect
187. D₄₈	C₂²×C₅	semidirect
188. #798	C₂²×C₅	semidirect
189. D₃×C₁₆	C₂²×C₅	semidirect
231. #509	C₅×D₃	semidirect
327. #135	C₂×C₅×D₃	semidirect
331. C₂×D₈	C₂×C₅×D₃	semidirect
337. SD₃₂	C₂×C₅×D₃	semidirect
342. D₁₆	C₂×C₅×D₃	semidirect
344. M₃₂	C₂×C₅×D₃	semidirect
435. C₃×C₅	#3415	semidirect
495. C₅	#82036	direct (N × H)
511. C₃	C₅×#3415	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5769	2
C₅×#5757	2
C₃×C₅×#509	2
C₅×#5194	2
C₂×C₅×#826	2
C₅×#4916	2
C₅×#4914	2
C₅×#4911	2
C₅×D₃×D₁₆	2
C₅×#4908	2
C₅×#4907	2
C₅×#3415	3
#82036	5

Subgroups — C5×#82036 #14478494

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#82036 #14478494