Subgroups — C₅×#81824 #14439636

Order 1920.

1064 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#915	C₂	1	2	yes	maximal, complemented
3	C₂×C₅×#912	C₂	1	1	yes	maximal, characteristic
4	C₅×#5675	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#495	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5183	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5167	C₂	1	2	yes	maximal, complemented
8	C₅×#5155	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#5060	C₂	1	2	yes	maximal, complemented
10	C₅×#4699	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4689	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3156	—	3	1	no	maximal, Hall
13	C₂×C₅×D₃×Q₈	C₂²	1	2	yes	—
14	C₂×C₅×#237	C₂²	1	2	yes	—
15	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
17	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
18	C₃×C₅×#124	C₂²	1	2	yes	—
19	C₅×#944	C₂²	1	2	yes	—
20	C₂×C₅×#216	C₂²	1	2	yes	—
21	C₂×C₅×#216	C₂²	1	2	yes	—
22	C₅×#936	C₂²	1	2	yes	—
23	C₂×C₅×#214	C₂²	1	2	yes	—
24	C₂×C₅×#214	C₂²	1	2	yes	—
25	C₅×D₃×Q₁₆	—	2	4	no	—
26	C₅×#915	—	2	8	no	—
27	C₅×#912	—	2	4	no	—
28	C₂×C₅×Dic₁₂	C₂²	1	2	yes	—
29	C₂×C₅×Dic₁₂	C₂²	1	1	yes	characteristic
30	C₂×C₅×Dic₁₂	C₂²	1	1	yes	characteristic
31	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
32	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
33	C₅×#883	—	2	4	no	—
34	C₅×#878	—	2	4	no	—
35	C₅×#872	C₂²	1	1	yes	characteristic
36	C₅×#869	C₂²	1	2	yes	—
37	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
38	C₅×#815	C₂²	1	1	yes	characteristic
39	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic
40	C₅×#803	C₂²	1	1	yes	characteristic
41	#81824	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
42	C₂×C₅×#137	—	3	2	no	—
43	C₂×C₅×#135	—	3	1	no	—
44	C₂²×C₅×Q₁₆	—	3	1	no	—
45	C₅×#536	—	3	2	no	—
46	C₅×#497	—	3	2	no	—
47	C₅×#497	—	3	2	no	—
48	C₅×#495	—	3	1	no	—
49	C₅×#495	D₃	1	1	yes	characteristic, complemented
50	C₅×#494	—	3	1	no	—
51	C₅×#494	—	3	1	no	—
52	C₅×#405	—	3	1	no	—
53	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
54	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
55	C₂×C₅×#67	—	2	2	no	—
56	C₂²×C₅×Dic₃	—	2	2	no	—
57	C₅×D₃×Q₈	—	2	4	no	—
58	C₅×D₃×Q₈	—	2	4	no	—
59	C₅×#237	—	2	4	no	—
60	C₅×#237	—	2	4	no	—
61	C₂×C₄×C₅×D₃	—	2	2	no	—
62	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
63	C₂×C₅×Dic₆	—	2	2	no	—
64	C₂×C₅×Dic₆	C₂³	1	2	yes	—
65	C₂×C₅×Dic₆	C₂³	1	2	yes	—
66	C₃×C₅×Q₁₆	—	2	2	no	—
67	C₃×C₅×SD₁₆	—	2	4	no	—
68	C₃×C₅×D₈	—	2	2	no	—
69	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
70	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
71	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
72	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
73	C₅×#217	—	2	4	no	—
74	C₅×#216	—	2	4	no	—
75	C₅×#216	—	2	4	no	—
76	C₅×#214	—	2	4	no	—
77	C₅×#214	—	2	4	no	—
78	C₅×(C₂×D₃)⋊C₄	D₄	1	2	yes	—
79	C₅×C₄⋊Dic₃	—	2	4	no	—
80	C₅×Dic₃⋊C₄	—	2	4	no	—
81	C₅×Dic₃⋊C₄	D₄	1	2	yes	—
82	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
83	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
84	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
85	C₅×Dic₁₂	—	2	2	no	—
86	C₅×Dic₁₂	—	2	4	no	—
87	C₅×Dic₁₂	—	2	2	no	—
88	C₅×ΓL(1,𝔽₂₅)	D₄	1	4	yes	—
89	C₅×D₃×C₈	D₄	1	4	yes	—
90	C₂×D₃×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
91	C₂×#915	C₂×C₅	1	2	yes	complemented
92	C₂×#912	C₂×C₅	1	1	yes	characteristic
93	#5675	C₂×C₅	1	2	yes	complemented
94	C₃×#495	C₂×C₅	1	1	yes	characteristic, complemented
95	#5183	C₂×C₅	1	1	yes	characteristic, complemented
96	#5167	C₂×C₅	1	2	yes	complemented
97	#5155	C₂×C₅	1	1	yes	characteristic, complemented
98	#5060	C₂×C₅	1	2	yes	complemented
99	#4699	C₂×C₅	1	1	yes	characteristic, complemented
100	#4689	C₂×C₅	1	1	yes	characteristic, complemented
101	C₂×C₅×#41	—	3	2	no	—
102	C₂²×C₅×Q₈	—	3	2	no	—
103	C₅×#137	—	6	8	no	—
104	C₅×#135	—	6	4	no	—
105	C₂×C₅×Q₁₆	—	3	2	no	—
106	C₂×C₅×Q₁₆	—	3	2	no	—
107	C₂×C₅×Q₁₆	—	3	1	no	—
108	C₂×C₅×Q₁₆	—	3	1	no	—
109	C₂×C₅×Q₁₆	—	3	2	no	—
110	C₂×C₅×Q₁₆	—	6	4	no	—
111	C₂×C₅×Q₁₆	C₂×D₃	1	1	yes	characteristic
112	C₂×C₅×SD₁₆	—	3	2	no	—
113	C₂×C₅×SD₁₆	—	3	2	no	—
114	C₂×C₅×SD₁₆	C₂×D₃	1	2	yes	—
115	C₂×C₅×D₈	C₂×D₃	1	1	yes	characteristic
116	C₂×C₅×M₁₆	—	3	1	no	—
117	C₂²×C₅×C₈	—	3	1	no	—
118	C₅×C₄⋊Q₈	—	3	2	no	—
119	C₅×C₄⋊Q₈	—	3	2	no	—
120	C₅×#124	—	3	2	no	—
121	C₅×#124	C₂×D₃	1	2	yes	—
122	C₅×#123	—	6	4	no	—
123	C₅×C₂²⋊Q₈	—	6	4	no	—
124	C₅×#117	—	3	1	no	—
125	C₅×#97	—	3	1	no	—
126	C₅×#97	—	3	1	no	—
127	C₄×C₅×C₈	—	3	1	no	—
128	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
129	#3156	—	3	1	no	Sylow
130	C₂³×C₃×C₅	—	2	2	no	—
131	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
132	C₃×C₅×Q₈	—	2	2	no	—
133	C₃×C₅×Q₈	—	2	2	no	—
134	C₃×C₅×D₄	—	2	2	no	—
135	C₃×C₅×D₄	—	2	2	no	—
136	C₂×C₃×C₄×C₅	—	2	2	no	—
137	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
138	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
139	C₅×#67	—	4	4	no	—
140	C₂×C₅×Dic₃	—	2	2	no	—
141	C₂×C₅×Dic₃	—	2	2	no	—
142	C₂×C₅×Dic₃	—	4	4	no	—
143	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
144	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
145	C₄×C₅×D₃	—	4	4	no	—
146	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
147	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
148	C₅×Dic₆	—	2	2	no	—
149	C₅×Dic₆	—	2	2	no	—
150	C₅×Dic₆	—	2	2	no	—
151	C₅×Dic₆	—	2	2	no	—
152	C₅×Dic₆	—	4	4	no	—
153	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
154	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
155	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	—
156	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	—
157	C₂×D₃×Q₈	C₂²×C₅	1	2	yes	—
158	C₂×#237	C₂²×C₅	1	2	yes	—
159	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic
160	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
161	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
162	C₃×#124	C₂²×C₅	1	2	yes	—
163	#944	C₂²×C₅	1	2	yes	—
164	C₂×#216	C₂²×C₅	1	2	yes	—
165	C₂×#216	C₂²×C₅	1	2	yes	—
166	#936	C₂²×C₅	1	2	yes	—
167	C₂×#214	C₂²×C₅	1	2	yes	—
168	C₂×#214	C₂²×C₅	1	2	yes	—
169	D₃×Q₁₆	—	2	4	no	—
170	#915	—	2	8	no	—
171	#912	—	2	4	no	—
172	C₂×Dic₁₂	C₂²×C₅	1	1	yes	characteristic
173	C₂×Dic₁₂	C₂²×C₅	1	2	yes	—
174	C₂×Dic₁₂	C₂²×C₅	1	1	yes	characteristic
175	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	1	yes	characteristic
176	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
177	#883	—	2	4	no	—
178	#878	—	2	4	no	—
179	#872	C₂²×C₅	1	1	yes	characteristic
180	#869	C₂²×C₅	1	2	yes	—
181	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
182	#815	C₂²×C₅	1	1	yes	characteristic
183	C₈×Dic₃	C₂²×C₅	1	1	yes	characteristic
184	#803	C₂²×C₅	1	1	yes	characteristic
185	C₅×#41	—	6	4	no	—
186	C₅×#41	—	6	4	no	—
187	C₂×C₅×Q₈	—	3	2	no	—
188	C₂×C₅×Q₈	—	3	2	no	—
189	C₂×C₅×Q₈	—	6	2	no	—
190	C₂×C₅×Q₈	—	6	4	no	—
191	C₂×C₅×Q₈	—	6	4	no	—
192	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
193	C₂×C₅×D₄	—	6	2	no	—
194	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
195	C₂²×C₄×C₅	—	3	1	no	—
196	C₂²×C₄×C₅	—	6	2	no	—
197	C₂²×C₄×C₅	—	6	2	no	—
198	C₅×Q₁₆	—	2	2	no	—
199	C₅×Q₁₆	—	6	4	no	—
200	C₅×Q₁₆	—	6	4	no	—
201	C₅×Q₁₆	—	6	2	no	—
202	C₅×Q₁₆	—	6	2	no	—
203	C₅×Q₁₆	—	6	4	no	—
204	C₅×SD₁₆	—	2	4	no	—
205	C₅×SD₁₆	—	6	4	no	—
206	C₅×SD₁₆	—	6	4	no	—
207	C₅×D₈	—	2	2	no	—
208	C₅×M₁₆	—	3	4	no	—
209	C₂×C₅×C₈	—	3	1	no	—
210	C₂×C₅×C₈	—	3	1	no	—
211	C₂×C₅×C₈	—	3	4	no	—
212	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
213	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
214	C₅×C₄⋊C₄	—	3	2	no	—
215	C₅×C₄⋊C₄	—	6	4	no	—
216	C₅×C₄⋊C₄	—	6	4	no	—
217	C₅×C₂²⋊C₄	—	2	4	no	—
218	C₅×C₂²⋊C₄	—	3	2	no	—
219	C₅×C₂²⋊C₄	—	6	4	no	—
220	C₄²×C₅	—	3	1	no	—
221	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
222	C₂×#137	—	3	2	no	—
223	C₂×#135	—	3	1	no	—
224	C₂²×Q₁₆	—	3	1	no	—
225	#536	—	3	2	no	—
226	#497	—	3	2	no	—
227	#497	—	3	2	no	—
228	#495	—	3	1	no	—
229	#495	C₅×D₃	1	1	yes	characteristic, complemented
230	#494	—	3	1	no	—
231	#494	—	3	1	no	—
232	#405	—	3	1	no	—
233	C₂²×C₃×C₅	—	4	2	no	—
234	C₂²×C₃×C₅	—	4	4	no	—
235	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
236	C₂×C₅×D₃	—	2	2	no	—
237	C₂×C₅×D₃	#127	1	2	yes	—
238	C₃×C₄×C₅	—	2	2	no	—
239	C₃×C₄×C₅	—	4	2	no	—
240	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
241	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
242	C₅×Dic₃	—	2	2	no	—
243	C₅×Dic₃	—	4	2	no	—
244	C₅×Dic₃	—	4	2	no	—
245	C₅×Dic₃	#127	1	2	yes	—
246	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
247	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
248	C₂×#67	—	2	2	no	—
249	C₂²×Dic₃	—	2	2	no	—
250	D₃×Q₈	—	2	4	no	—
251	D₃×Q₈	—	2	4	no	—
252	#237	—	2	4	no	—
253	#237	—	2	4	no	—
254	C₂×C₄×D₃	—	2	2	no	—
255	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
256	C₂×Dic₆	—	2	2	no	—
257	C₂×Dic₆	C₂³×C₅	1	2	yes	—
258	C₂×Dic₆	C₂³×C₅	1	2	yes	—
259	C₃×Q₁₆	—	2	2	no	—
260	C₃×SD₁₆	—	2	4	no	—
261	C₃×D₈	—	2	2	no	—
262	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
263	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
264	C₃×C₂²⋊C₄	—	2	4	no	—
265	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
266	#217	—	2	4	no	—
267	#216	—	2	4	no	—
268	#216	—	2	4	no	—
269	#214	—	2	4	no	—
270	#214	—	2	4	no	—
271	(C₂×D₃)⋊C₄	C₅×D₄	1	2	yes	—
272	C₄⋊Dic₃	—	2	4	no	—
273	Dic₃⋊C₄	—	2	4	no	—
274	Dic₃⋊C₄	C₅×D₄	1	2	yes	—
275	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
276	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
277	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
278	Dic₁₂	—	2	2	no	—
279	Dic₁₂	—	2	4	no	—
280	Dic₁₂	—	2	2	no	—
281	ΓL(1,𝔽₂₅)	C₅×D₄	1	4	yes	—
282	D₃×C₈	C₅×D₄	1	4	yes	—
283	C₂³×C₅	—	2	2	no	—
284	C₂³×C₅	—	3	1	no	—
285	C₅×Q₈	—	2	2	no	—
286	C₅×Q₈	—	2	2	no	—
287	C₅×Q₈	—	6	2	no	—
288	C₅×Q₈	—	6	2	no	—
289	C₅×Q₈	—	6	2	no	—
290	C₅×Q₈	—	6	2	no	—
291	C₅×Q₈	—	12	4	no	—
292	C₅×D₄	—	2	2	no	—
293	C₅×D₄	—	2	2	no	—
294	C₅×D₄	—	12	4	no	—
295	C₂×C₄×C₅	—	2	2	no	—
296	C₂×C₄×C₅	—	3	1	no	—
297	C₂×C₄×C₅	—	3	2	no	—
298	C₂×C₄×C₅	—	3	2	no	—
299	C₂×C₄×C₅	—	3	2	no	—
300	C₂×C₄×C₅	—	6	2	no	—
301	C₂×C₄×C₅	—	6	2	no	—
302	C₂×C₄×C₅	—	12	4	no	—
303	C₂×C₄×C₅	—	12	4	no	—
304	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
305	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
306	C₅×C₈	—	3	2	no	—
307	C₅×C₈	—	3	2	no	—
308	C₅×C₈	D₃×D₄	1	2	yes	—
309	C₅×C₈	D₃×D₄	1	2	yes	—
310	C₂×#41	—	3	2	no	—
311	C₂²×Q₈	—	3	2	no	—
312	#137	—	6	8	no	—
313	#135	—	6	4	no	—
314	C₂×Q₁₆	—	3	2	no	—
315	C₂×Q₁₆	—	3	2	no	—
316	C₂×Q₁₆	—	3	1	no	—
317	C₂×Q₁₆	—	3	1	no	—
318	C₂×Q₁₆	—	3	2	no	—
319	C₂×Q₁₆	—	6	4	no	—
320	C₂×Q₁₆	C₂×C₅×D₃	1	1	yes	characteristic
321	C₂×SD₁₆	—	3	2	no	—
322	C₂×SD₁₆	—	3	2	no	—
323	C₂×SD₁₆	C₂×C₅×D₃	1	2	yes	—
324	C₂×D₈	C₂×C₅×D₃	1	1	yes	characteristic
325	C₂×M₁₆	—	3	1	no	—
326	C₂²×C₈	—	3	1	no	—
327	C₄⋊Q₈	—	3	2	no	—
328	C₄⋊Q₈	—	3	2	no	—
329	#124	—	3	2	no	—
330	#124	C₂×C₅×D₃	1	2	yes	—
331	#123	—	6	4	no	—
332	C₂²⋊Q₈	—	6	4	no	—
333	#117	—	3	1	no	—
334	#97	—	3	1	no	—
335	#97	—	3	1	no	—
336	C₄×C₈	—	3	1	no	—
337	C₄×C₈	C₂×C₅×D₃	1	1	yes	characteristic
338	C₂×C₃×C₅	—	8	2	no	—
339	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
340	C₂×C₃×C₅	#578	1	2	yes	—
341	C₅×D₃	—	2	2	no	—
342	C₂³×C₃	—	2	2	no	—
343	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
344	C₃×Q₈	—	2	2	no	—
345	C₃×Q₈	—	2	2	no	—
346	C₃×D₄	—	2	2	no	—
347	C₃×D₄	—	2	2	no	—
348	C₂×C₃×C₄	—	2	2	no	—
349	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
350	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
351	#67	—	4	4	no	—
352	C₂×Dic₃	—	2	2	no	—
353	C₂×Dic₃	—	2	2	no	—
354	C₂×Dic₃	—	4	4	no	—
355	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
356	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
357	C₄×D₃	—	4	4	no	—
358	C₄×D₃	C₂×C₅×D₄	1	2	yes	—
359	C₄×D₃	C₂×C₅×D₄	1	2	yes	—
360	Dic₆	—	2	2	no	—
361	Dic₆	—	2	2	no	—
362	Dic₆	—	2	2	no	—
363	Dic₆	—	2	2	no	—
364	Dic₆	—	4	4	no	—
365	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
366	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
367	C₃⋊C₈	C₂×C₅×D₄	1	2	yes	—
368	C₃⋊C₈	C₂×C₅×D₄	1	2	yes	—
369	C₂²×C₅	—	3	2	no	—
370	C₂²×C₅	—	4	2	no	—
371	C₂²×C₅	—	4	4	no	—
372	C₂²×C₅	—	6	2	no	—
373	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
374	C₄×C₅	—	2	2	no	—
375	C₄×C₅	—	3	2	no	—
376	C₄×C₅	—	4	2	no	—
377	C₄×C₅	—	6	2	no	—
378	C₄×C₅	—	12	2	no	—
379	C₄×C₅	—	12	2	no	—
380	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
381	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
382	#41	—	6	4	no	—
383	#41	—	6	4	no	—
384	C₂×Q₈	—	3	2	no	—
385	C₂×Q₈	—	3	2	no	—
386	C₂×Q₈	—	6	2	no	—
387	C₂×Q₈	—	6	4	no	—
388	C₂×Q₈	—	6	4	no	—
389	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
390	C₂×D₄	—	6	2	no	—
391	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
392	C₂²×C₄	—	3	1	no	—
393	C₂²×C₄	—	6	2	no	—
394	C₂²×C₄	—	6	2	no	—
395	Q₁₆	—	2	2	no	—
396	Q₁₆	—	6	4	no	—
397	Q₁₆	—	6	4	no	—
398	Q₁₆	—	6	2	no	—
399	Q₁₆	—	6	2	no	—
400	Q₁₆	—	6	4	no	—
401	SD₁₆	—	2	4	no	—
402	SD₁₆	—	6	4	no	—
403	SD₁₆	—	6	4	no	—
404	D₈	—	2	2	no	—
405	M₁₆	—	3	4	no	—
406	C₂×C₈	—	3	1	no	—
407	C₂×C₈	—	3	1	no	—
408	C₂×C₈	—	3	4	no	—
409	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
410	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
411	C₄⋊C₄	—	3	2	no	—
412	C₄⋊C₄	—	6	4	no	—
413	C₄⋊C₄	—	6	4	no	—
414	C₂²⋊C₄	—	2	4	no	—
415	C₂²⋊C₄	—	3	2	no	—
416	C₂²⋊C₄	—	6	4	no	—
417	C₄²	—	3	1	no	—
418	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
419	C₃×C₅	#3156	1	1	yes	characteristic, complemented, Hall
420	C₂²×C₃	—	4	2	no	—
421	C₂²×C₃	—	4	4	no	—
422	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
423	C₂×D₃	—	2	2	no	—
424	C₂×D₃	C₅×#127	1	2	yes	—
425	C₃×C₄	—	2	2	no	—
426	C₃×C₄	—	4	2	no	—
427	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
428	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
429	Dic₃	—	2	2	no	—
430	Dic₃	—	4	2	no	—
431	Dic₃	—	4	2	no	—
432	Dic₃	C₅×#127	1	2	yes	—
433	C₂×C₅	—	6	2	no	—
434	C₂×C₅	—	8	2	no	—
435	C₂×C₅	D₃×#127	1	1	yes	characteristic
436	C₂×C₅	#5771	1	2	yes	—
437	C₂³	—	2	2	no	—
438	C₂³	—	3	1	no	—
439	Q₈	—	2	2	no	—
440	Q₈	—	2	2	no	—
441	Q₈	—	6	2	no	—
442	Q₈	—	6	2	no	—
443	Q₈	—	6	2	no	—
444	Q₈	—	6	2	no	—
445	Q₈	—	12	4	no	—
446	D₄	—	2	2	no	—
447	D₄	—	2	2	no	—
448	D₄	—	12	4	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	3	1	no	—
451	C₂×C₄	—	3	2	no	—
452	C₂×C₄	—	3	2	no	—
453	C₂×C₄	—	3	2	no	—
454	C₂×C₄	—	6	2	no	—
455	C₂×C₄	—	6	2	no	—
456	C₂×C₄	—	12	4	no	—
457	C₂×C₄	—	12	4	no	—
458	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
459	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
460	C₈	—	3	2	no	—
461	C₈	—	3	2	no	—
462	C₈	C₅×D₃×D₄	1	2	yes	—
463	C₈	C₅×D₃×D₄	1	2	yes	—
464	C₂×C₃	—	8	2	no	—
465	C₂×C₃	C₂×C₅×#127	1	1	yes	characteristic
466	C₂×C₃	C₅×#578	1	2	yes	—
467	D₃	—	2	2	no	—
468	C₅	#81824	1	1	yes	characteristic, direct product factor, Sylow
469	C₂²	—	3	2	no	—
470	C₂²	—	4	2	no	—
471	C₂²	—	4	4	no	—
472	C₂²	—	6	2	no	—
473	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
474	C₄	—	2	2	no	—
475	C₄	—	3	2	no	—
476	C₄	—	4	2	no	—
477	C₄	—	6	2	no	—
478	C₄	—	12	2	no	—
479	C₄	—	12	2	no	—
480	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
481	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
482	C₃	C₅×#3156	1	1	yes	characteristic, complemented, Sylow
483	C₂	—	6	2	no	—
484	C₂	—	8	2	no	—
485	C₂	C₅×D₃×#127	1	1	yes	characteristic
486	C₂	C₅×#5771	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×#495	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₅×#912	C₂
hypercenter	C₅×#495	D₃
hypocenter	C₃	C₅×#3156
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#495

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×D₃×Q₁₆	C₂	semidirect
2. C₂×C₅×#915	C₂	semidirect
4. C₅×#5675	C₂	semidirect
5. C₃×C₅×#495	C₂	semidirect
6. C₅×#5183	C₂	semidirect
7. C₅×#5167	C₂	semidirect
8. C₅×#5155	C₂	semidirect
9. C₅×#5060	C₂	semidirect
10. C₅×#4699	C₂	semidirect
11. C₅×#4689	C₂	semidirect
41. #81824	C₅	direct (N × H)
49. C₅×#495	D₃	semidirect
90. C₂×D₃×Q₁₆	C₂×C₅	semidirect
91. C₂×#915	C₂×C₅	semidirect
93. #5675	C₂×C₅	semidirect
94. C₃×#495	C₂×C₅	semidirect
95. #5183	C₂×C₅	semidirect
96. #5167	C₂×C₅	semidirect
97. #5155	C₂×C₅	semidirect
98. #5060	C₂×C₅	semidirect
99. #4699	C₂×C₅	semidirect
100. #4689	C₂×C₅	semidirect
229. #495	C₅×D₃	semidirect
419. C₃×C₅	#3156	semidirect
468. C₅	#81824	direct (N × H)
482. C₃	C₅×#3156	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×Q₁₆	2
C₂×C₅×#915	2
C₂×C₅×#912	2
C₅×#5675	2
C₃×C₅×#495	2
C₅×#5183	2
C₅×#5167	2
C₅×#5155	2
C₅×#5060	2
C₅×#4699	2
C₅×#4689	2
C₅×#3156	3
#81824	5

Subgroups — C5×#81824 #14439636

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#81824 #14439636