Subgroups — D₅×#5122 #14411331

Order 1920.

1184 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₅×M₁₆	C₂	1	1	yes	maximal, characteristic
2	D₅×#926	C₂	1	1	yes	maximal, characteristic
3	C₂²×D₅×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic
4	#11751223	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5122	C₂	1	1	yes	maximal, characteristic, complemented
6	#11748327	C₂	1	1	yes	maximal, characteristic, complemented
7	#11748326	C₂	1	1	yes	maximal, characteristic, complemented
8	#11748051	C₂	1	2	yes	maximal, complemented
9	#11748050	C₂	1	2	yes	maximal, complemented
10	D₅×#815	C₂	1	2	yes	maximal, complemented
11	C₈×D₅×Dic₃	C₂	1	2	yes	maximal, complemented
12	D₅×#405	—	3	1	no	maximal, Hall
13	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
15	#91815	C₂²	1	1	yes	characteristic
16	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
17	C₅×#926	C₂²	1	1	yes	characteristic
18	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₃×#681	C₂²	1	1	yes	characteristic
20	C₃×D₅×M₁₆	C₄	1	8	yes	complemented
21	C₂×C₃×#676	C₂²	1	2	yes	—
22	C₂×C₃×C₈×D₅	C₂²	1	2	yes	—
23	D₅×#217	C₄	1	2	yes	—
24	#91528	C₄	1	2	yes	—
25	D₅×C₄⋊Dic₃	C₄	1	2	yes	—
26	C₄×D₅×Dic₃	C₂²	1	2	yes	—
27	#91358	C₄	1	2	yes	—
28	#91357	C₂²	1	2	yes	—
29	C₂×D₅×C₃⋊C₈	C₄	1	8	yes	complemented
30	C₂×D₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×D₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×D₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×D₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
34	#91099	C₂²	1	2	yes	complemented
35	C₈×Dic₁₅	C₂²	1	2	yes	complemented
36	C₅×#815	C₂²	1	2	yes	complemented
37	C₅×C₈×Dic₃	C₂²	1	2	yes	complemented
38	#90954	C₂²	1	2	yes	complemented
39	#90953	C₂²	1	2	yes	complemented
40	#90951	C₂²	1	2	yes	complemented
41	Dic₃×#168	C₂²	1	2	yes	complemented
42	C₂×#5122	—	5	1	no	maximal, Hall
43	C₂×D₅×M₁₆	D₃	1	1	yes	characteristic
44	C₂²×C₈×D₅	—	3	1	no	—
45	D₅×#117	—	3	1	no	—
46	C₅×#405	—	3	1	no	—
47	#65411	—	3	1	no	—
48	#65390	—	3	1	no	—
49	#65286	—	3	1	no	—
50	#64997	—	3	2	no	—
51	D₅×#97	—	3	2	no	—
52	#64978	—	3	2	no	—
53	C₄×C₈×D₅	—	3	2	no	—
54	C₂³×C₃×D₅	C₂×C₄	1	1	yes	characteristic
55	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
56	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
57	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
58	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
59	C₂×C₃×C₄×D₅	C₂×C₄	1	4	yes	—
60	C₂×C₃×C₄×D₅	C₂×C₄	1	4	yes	—
61	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
62	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
63	C₂×D₅×Dic₃	C₂×C₄	1	4	yes	—
64	C₃×C₅×M₁₆	C₂×C₄	1	4	yes	complemented
65	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
66	#6719	C₂×C₄	1	2	yes	—
67	C₄⋊Dic₁₅	C₂×C₄	1	2	yes	—
68	C₄×Dic₁₅	C₂³	1	2	yes	—
69	C₂×C₃⋊#168	C₂×C₄	1	4	yes	complemented
70	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
71	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
72	C₅×#217	C₂×C₄	1	2	yes	—
73	C₅×C₄⋊Dic₃	C₂×C₄	1	2	yes	—
74	C₄×C₅×Dic₃	C₂³	1	2	yes	—
75	C₂×C₅×C₃⋊C₈	C₂×C₄	1	4	yes	complemented
76	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
77	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
78	C₃×#681	C₂×C₄	1	4	yes	complemented
79	C₂×C₃×#168	C₂³	1	2	yes	—
80	C₃×#676	C₂×C₄	1	8	yes	complemented
81	C₃×C₈×D₅	C₂×C₄	1	8	yes	—
82	#6668	C₂×C₄	1	4	yes	—
83	#6665	C₂×C₄	1	4	yes	—
84	Dic₃×Dic₅	C₂×C₄	1	4	yes	—
85	D₅×C₃⋊C₈	C₂×C₄	1	4	yes	—
86	D₅×C₃⋊C₈	C₂×C₄	1	4	yes	—
87	D₅×C₃⋊C₈	C₂×C₄	1	4	yes	complemented
88	D₅×C₃⋊C₈	C₂×C₄	1	4	yes	complemented
89	C₂²×C₃×M₁₆	—	5	1	no	—
90	C₂×#926	—	5	1	no	—
91	C₂³×C₃⋊C₈	—	5	1	no	—
92	#5122	—	5	1	no	—
93	#5122	—	5	1	no	—
94	#5122	—	5	1	no	—
95	#5122	—	5	2	no	—
96	#5122	—	5	2	no	—
97	#5122	D₅	1	1	yes	characteristic, direct product factor
98	C₂×#815	—	5	2	no	—
99	C₂×C₈×Dic₃	—	5	2	no	—
100	C₂²×C₄×D₅	C₂×D₃	1	1	yes	characteristic
101	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
102	C₂²×C₅×C₈	—	3	1	no	—
103	C₅×#117	—	3	1	no	—
104	#4072	—	3	1	no	—
105	C₂×#681	C₂×D₃	1	1	yes	characteristic
106	C₂²×#168	—	3	1	no	—
107	D₅×M₁₆	Dic₃	1	8	yes	complemented
108	C₂×#676	C₂×D₃	1	2	yes	—
109	C₂×C₈×D₅	—	3	8	no	—
110	C₂×C₈×D₅	—	3	1	no	—
111	C₂×C₈×D₅	—	3	1	no	—
112	C₂×C₈×D₅	—	3	1	no	—
113	C₂×C₈×D₅	—	3	1	no	—
114	C₂×C₈×D₅	C₂×D₃	1	2	yes	—
115	#4038	—	3	2	no	—
116	D₅×C₄⋊C₄	—	3	2	no	—
117	D₅×C₂²⋊C₄	—	3	2	no	—
118	#4023	—	3	2	no	—
119	#4018	—	3	2	no	—
120	C₄²×D₅	—	3	2	no	—
121	C₅×#97	—	3	2	no	—
122	C₄×C₅×C₈	—	3	2	no	—
123	#3947	—	3	2	no	—
124	#3947	—	3	2	no	—
125	C₈×Dic₅	—	3	2	no	—
126	C₈×Dic₅	—	3	2	no	—
127	#3935	—	3	2	no	—
128	C₄×#168	—	3	2	no	—
129	C₂×#405	—	15	1	no	Sylow
130	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₃×D₅	—	2	4	no	—
132	C₂²×C₃×D₅	C₄²	1	4	yes	—
133	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
137	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
138	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
139	C₂×Dic₁₅	C₂²×C₄	1	4	yes	—
140	C₂×C₅×Dic₃	C₂²×C₄	1	4	yes	—
141	C₂×C₃×Dic₅	C₄²	1	4	yes	—
142	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
143	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
144	C₃×C₄×D₅	C₄²	1	4	yes	—
145	C₃×C₄×D₅	C₄²	1	4	yes	—
146	C₃×C₄×D₅	C₂²×C₄	1	2	yes	—
147	C₃×C₄×D₅	C₂²×C₄	1	2	yes	—
148	C₃×C₄×D₅	C₂²×C₄	1	2	yes	—
149	C₃×C₄×D₅	C₂²×C₄	1	2	yes	—
150	D₅×Dic₃	—	2	8	no	—
151	C₃×C₅×C₈	C₂²×C₄	1	4	yes	—
152	C₃⋊#168	C₂²×C₄	1	2	yes	—
153	C₃⋊#168	C₂²×C₄	1	2	yes	—
154	C₃×#168	C₂²×C₄	1	4	yes	—
155	C₅×C₃⋊C₈	C₂²×C₄	1	2	yes	—
156	C₅×C₃⋊C₈	C₂²×C₄	1	2	yes	—
157	C₂³×C₃×C₄	—	5	1	no	—
158	C₂×C₃×M₁₆	—	5	1	no	—
159	C₂×C₃×M₁₆	—	5	8	no	—
160	C₂×C₃×M₁₆	—	5	2	no	—
161	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
162	C₂²×C₃×C₈	—	5	2	no	—
163	C₂×#217	—	5	2	no	—
164	#926	—	5	1	no	—
165	#926	—	5	2	no	—
166	#926	—	5	2	no	—
167	#926	—	5	2	no	—
168	#926	C₂×D₅	1	1	yes	characteristic
169	C₂×C₄⋊Dic₃	—	5	2	no	—
170	C₂×C₄×Dic₃	—	5	2	no	—
171	C₂²×C₃⋊C₈	—	5	1	no	—
172	C₂²×C₃⋊C₈	—	5	8	no	—
173	C₂²×C₃⋊C₈	—	5	1	no	—
174	C₂²×C₃⋊C₈	—	5	1	no	—
175	C₂²×C₃⋊C₈	—	5	1	no	—
176	C₂²×C₃⋊C₈	—	5	1	no	—
177	C₂²×C₃⋊C₈	C₂×D₅	1	1	yes	characteristic
178	#815	—	5	2	no	—
179	#815	—	5	2	no	—
180	#815	—	5	2	no	—
181	#815	C₂×D₅	1	2	yes	complemented
182	C₈×Dic₃	—	5	2	no	—
183	C₈×Dic₃	—	5	2	no	—
184	C₈×Dic₃	—	5	2	no	—
185	C₈×Dic₃	C₂×D₅	1	2	yes	complemented
186	C₂³×D₅	C₄×D₃	1	1	yes	characteristic
187	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
188	C₂²×Dic₅	C₄×D₃	1	1	yes	characteristic
189	C₂×C₄×D₅	—	3	4	no	—
190	C₂×C₄×D₅	C₄×D₃	1	1	yes	characteristic
191	C₂×C₄×D₅	C₄×D₃	1	1	yes	characteristic
192	C₂×C₄×D₅	C₄×D₃	1	4	yes	—
193	C₂×C₄×D₅	C₂×Dic₃	1	4	yes	—
194	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
195	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
196	C₅×M₁₆	C₂×Dic₃	1	4	yes	complemented
197	C₂×C₅×C₈	—	3	4	no	—
198	C₂×C₅×C₈	—	3	1	no	—
199	C₂×C₅×C₈	—	3	1	no	—
200	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
201	C₅×C₄⋊C₄	—	3	2	no	—
202	C₅×C₂²⋊C₄	—	3	2	no	—
203	C₄²×C₅	—	3	2	no	—
204	C₂²⋊Dic₅	—	3	2	no	—
205	#685	—	3	4	no	—
206	C₄⋊Dic₅	—	3	2	no	—
207	#683	—	3	4	no	—
208	C₄×Dic₅	—	3	2	no	—
209	C₄×Dic₅	—	3	4	no	—
210	#681	C₂×Dic₃	1	4	yes	complemented
211	C₂×#168	—	3	4	no	—
212	C₂×#168	—	3	1	no	—
213	C₂×#168	—	3	1	no	—
214	C₂×#168	C₂²×D₃	1	2	yes	—
215	#676	C₂×Dic₃	1	8	yes	complemented
216	C₈×D₅	—	3	4	no	—
217	C₈×D₅	—	3	4	no	—
218	C₈×D₅	—	3	4	no	—
219	C₈×D₅	—	3	4	no	—
220	C₈×D₅	C₂×Dic₃	1	8	yes	—
221	C₂²×M₁₆	—	5	1	no	—
222	C₂³×C₈	—	15	1	no	—
223	C₂×#117	—	15	1	no	—
224	#405	—	3	1	no	—
225	#405	—	15	2	no	—
226	#405	—	15	2	no	—
227	#405	—	15	1	no	—
228	#405	—	15	1	no	—
229	#405	—	15	1	no	—
230	C₂×#97	—	15	2	no	—
231	C₂×C₄×C₈	—	15	2	no	—
232	C₂²×C₃×C₅	—	2	2	no	—
233	C₂²×C₃×C₅	C₂×C₄²	1	2	yes	—
234	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
235	C₂×C₃×D₅	—	2	2	no	—
236	C₂×C₃×D₅	—	2	8	no	—
237	C₂×C₃×D₅	C₂×C₄²	1	2	yes	—
238	C₂×C₃×D₅	C₂×C₄²	1	2	yes	—
239	C₂×C₃×D₅	#131	1	4	yes	—
240	C₃×C₄×C₅	C₂×C₄²	1	2	yes	—
241	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
242	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
243	Dic₁₅	—	2	4	no	—
244	C₃×Dic₅	C₂×C₄²	1	2	yes	—
245	C₃×Dic₅	C₂×C₄²	1	2	yes	—
246	C₅×Dic₃	—	2	4	no	—
247	C₂⁴×C₃	—	5	1	no	—
248	C₂²×C₃×C₄	—	5	1	no	—
249	C₂²×C₃×C₄	—	5	4	no	—
250	C₂²×C₃×C₄	—	5	1	no	—
251	C₂²×C₃×C₄	—	5	1	no	—
252	C₂²×C₃×C₄	—	5	4	no	—
253	C₂²×C₃×C₄	—	5	1	no	—
254	C₂²×C₃×C₄	—	5	1	no	—
255	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
256	C₂²×Dic₃	—	5	4	no	—
257	C₃×M₁₆	—	5	4	no	—
258	C₃×M₁₆	—	5	8	no	—
259	C₃×M₁₆	C₄×D₅	1	4	yes	complemented
260	C₂×C₃×C₈	—	5	2	no	—
261	C₂×C₃×C₈	—	5	8	no	—
262	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
263	#217	—	5	2	no	—
264	#217	—	5	4	no	—
265	#217	C₄×D₅	1	2	yes	—
266	C₄⋊Dic₃	—	5	2	no	—
267	C₄⋊Dic₃	—	5	4	no	—
268	C₄⋊Dic₃	C₄×D₅	1	2	yes	—
269	C₄×Dic₃	—	5	2	no	—
270	C₄×Dic₃	—	5	4	no	—
271	C₄×Dic₃	C₂²×D₅	1	2	yes	—
272	C₂×C₃⋊C₈	—	5	4	no	—
273	C₂×C₃⋊C₈	—	5	1	no	—
274	C₂×C₃⋊C₈	—	5	1	no	—
275	C₂×C₃⋊C₈	—	5	4	no	—
276	C₂×C₃⋊C₈	—	5	4	no	—
277	C₂×C₃⋊C₈	—	5	4	no	—
278	C₂×C₃⋊C₈	—	5	4	no	—
279	C₂×C₃⋊C₈	C₄×D₅	1	4	yes	complemented
280	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
281	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
282	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
283	C₂²×D₅	—	2	4	no	—
284	C₂²×D₅	C₄×Dic₃	1	4	yes	—
285	C₂²×D₅	C₂×C₄×D₃	1	1	yes	characteristic
286	C₂²×D₅	C₂×C₄×D₃	1	1	yes	characteristic
287	C₂×C₄×C₅	—	3	4	no	—
288	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
289	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
290	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
291	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
292	C₂×Dic₅	—	3	4	no	—
293	C₂×Dic₅	C₄×Dic₃	1	4	yes	—
294	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
295	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
296	C₄×D₅	—	6	8	no	—
297	C₄×D₅	C₄×Dic₃	1	4	yes	—
298	C₄×D₅	C₄×Dic₃	1	4	yes	—
299	C₄×D₅	C₂×C₄×D₃	1	2	yes	—
300	C₄×D₅	C₂×C₄×D₃	1	2	yes	—
301	C₄×D₅	C₂²×Dic₃	1	2	yes	—
302	C₄×D₅	C₂²×Dic₃	1	2	yes	—
303	C₅×C₈	—	3	2	no	—
304	C₅×C₈	—	3	2	no	—
305	C₅×C₈	C₂²×Dic₃	1	4	yes	—
306	#168	—	3	2	no	—
307	#168	—	3	2	no	—
308	#168	C₂²×Dic₃	1	4	yes	—
309	C₂³×C₄	—	5	1	no	—
310	C₂×M₁₆	—	5	1	no	—
311	C₂×M₁₆	—	5	8	no	—
312	C₂×M₁₆	—	5	2	no	—
313	C₂×M₁₆	D₃×D₅	1	1	yes	characteristic
314	C₂²×C₈	—	3	1	no	—
315	C₂²×C₈	—	5	2	no	—
316	C₂²×C₈	—	15	1	no	—
317	C₂²×C₈	—	15	1	no	—
318	C₂²×C₈	—	15	1	no	—
319	C₂²×C₈	—	15	1	no	—
320	C₂²×C₈	—	15	8	no	—
321	C₂²×C₈	—	15	1	no	—
322	#117	—	3	1	no	—
323	#117	—	15	2	no	—
324	#117	—	15	2	no	—
325	#117	—	15	2	no	—
326	#117	—	15	1	no	—
327	C₂×C₄⋊C₄	—	15	2	no	—
328	C₂×C₂²⋊C₄	—	15	2	no	—
329	C₂×C₄²	—	15	2	no	—
330	#97	—	3	2	no	—
331	#97	—	15	2	no	—
332	#97	—	15	2	no	—
333	#97	—	15	2	no	—
334	C₄×C₈	—	3	2	no	—
335	C₄×C₈	—	15	2	no	—
336	C₄×C₈	—	15	2	no	—
337	C₄×C₈	—	15	2	no	—
338	C₂×C₃×C₅	—	2	2	no	—
339	C₂×C₃×C₅	C₂²×C₄²	1	1	yes	characteristic
340	C₂×C₃×C₅	C₂×#131	1	2	yes	—
341	C₃×D₅	—	2	2	no	—
342	C₃×D₅	#405	1	4	yes	complemented
343	C₂³×C₃	—	5	1	no	—
344	C₂³×C₃	—	5	1	no	—
345	C₂³×C₃	—	5	4	no	—
346	C₂³×C₃	—	10	4	no	—
347	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
348	C₂×C₃×C₄	—	5	1	no	—
349	C₂×C₃×C₄	—	5	1	no	—
350	C₂×C₃×C₄	—	5	4	no	—
351	C₂×C₃×C₄	—	5	2	no	—
352	C₂×C₃×C₄	—	5	2	no	—
353	C₂×C₃×C₄	—	5	2	no	—
354	C₂×C₃×C₄	—	5	2	no	—
355	C₂×C₃×C₄	—	5	4	no	—
356	C₂×C₃×C₄	—	5	4	no	—
357	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
358	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
359	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
360	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
361	C₂×Dic₃	—	5	4	no	—
362	C₂×Dic₃	—	10	8	no	—
363	C₂×Dic₃	C₂×C₄×D₅	1	4	yes	—
364	C₃×C₈	—	5	4	no	—
365	C₃×C₈	C₂×C₄×D₅	1	4	yes	—
366	C₃⋊C₈	—	5	2	no	—
367	C₃⋊C₈	—	5	2	no	—
368	C₃⋊C₈	C₂×C₄×D₅	1	2	yes	—
369	C₃⋊C₈	C₂×C₄×D₅	1	2	yes	—
370	C₂²×C₅	—	2	2	no	—
371	C₂²×C₅	C₂×C₄×Dic₃	1	2	yes	—
372	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
373	C₂×D₅	—	2	2	no	—
374	C₂×D₅	—	2	8	no	—
375	C₂×D₅	#907	1	4	yes	—
376	C₂×D₅	C₂×C₄×Dic₃	1	2	yes	—
377	C₂×D₅	C₂×C₄×Dic₃	1	2	yes	—
378	C₄×C₅	—	6	4	no	—
379	C₄×C₅	C₂×C₄×Dic₃	1	2	yes	—
380	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
381	C₄×C₅	C₂³×Dic₃	1	1	yes	characteristic
382	Dic₅	—	6	4	no	—
383	Dic₅	C₂×C₄×Dic₃	1	2	yes	—
384	Dic₅	C₂×C₄×Dic₃	1	2	yes	—
385	C₂⁴	—	5	1	no	—
386	C₂²×C₄	—	5	1	no	—
387	C₂²×C₄	—	5	1	no	—
388	C₂²×C₄	—	5	1	no	—
389	C₂²×C₄	—	5	4	no	—
390	C₂²×C₄	—	5	4	no	—
391	C₂²×C₄	—	5	1	no	—
392	C₂²×C₄	—	5	1	no	—
393	C₂²×C₄	—	15	4	no	—
394	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
395	M₁₆	—	5	4	no	—
396	M₁₆	—	5	8	no	—
397	M₁₆	D₅×Dic₃	1	4	yes	complemented
398	C₂×C₈	—	3	4	no	—
399	C₂×C₈	—	3	1	no	—
400	C₂×C₈	—	3	1	no	—
401	C₂×C₈	—	5	2	no	—
402	C₂×C₈	—	5	8	no	—
403	C₂×C₈	—	15	4	no	—
404	C₂×C₈	—	15	4	no	—
405	C₂×C₈	—	15	4	no	—
406	C₂×C₈	—	15	4	no	—
407	C₂×C₈	—	15	4	no	—
408	C₂×C₈	—	15	1	no	—
409	C₂×C₈	—	15	1	no	—
410	C₂×C₈	C₂×D₃×D₅	1	2	yes	—
411	C₄⋊C₄	—	3	2	no	—
412	C₄⋊C₄	—	15	4	no	—
413	C₄⋊C₄	—	15	2	no	—
414	C₂²⋊C₄	—	3	2	no	—
415	C₂²⋊C₄	—	15	4	no	—
416	C₂²⋊C₄	—	15	2	no	—
417	C₄²	—	3	2	no	—
418	C₄²	—	15	4	no	—
419	C₄²	—	15	2	no	—
420	C₃×C₅	C₂×#405	1	1	yes	characteristic, complemented, Hall
421	C₂²×C₃	—	2	2	no	—
422	C₂²×C₃	—	5	2	no	—
423	C₂²×C₃	—	5	4	no	—
424	C₂²×C₃	—	5	2	no	—
425	C₂²×C₃	—	10	8	no	—
426	C₂²×C₃	—	10	2	no	—
427	C₂²×C₃	C₄²×D₅	1	2	yes	—
428	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
429	C₃×C₄	—	5	2	no	—
430	C₃×C₄	—	5	2	no	—
431	C₃×C₄	C₄²×D₅	1	2	yes	—
432	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
433	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
434	Dic₃	—	2	4	no	—
435	Dic₃	—	10	4	no	—
436	C₂×C₅	—	2	2	no	—
437	C₂×C₅	C₂×#907	1	2	yes	—
438	C₂×C₅	C₂²×C₄×Dic₃	1	1	yes	characteristic
439	D₅	—	2	2	no	—
440	D₅	#5122	1	4	yes	direct product factor
441	C₂³	—	5	1	no	—
442	C₂³	—	5	1	no	—
443	C₂³	—	5	4	no	—
444	C₂³	—	10	4	no	—
445	C₂³	C₄×D₃×D₅	1	1	yes	characteristic
446	C₂×C₄	—	3	4	no	—
447	C₂×C₄	—	5	1	no	—
448	C₂×C₄	—	5	1	no	—
449	C₂×C₄	—	5	4	no	—
450	C₂×C₄	—	5	2	no	—
451	C₂×C₄	—	5	2	no	—
452	C₂×C₄	—	5	2	no	—
453	C₂×C₄	—	5	2	no	—
454	C₂×C₄	—	5	4	no	—
455	C₂×C₄	—	5	4	no	—
456	C₂×C₄	—	15	4	no	—
457	C₂×C₄	—	30	8	no	—
458	C₂×C₄	C₄×D₃×D₅	1	2	yes	—
459	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
460	C₂×C₄	C₂×D₅×Dic₃	1	2	yes	—
461	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
462	C₈	—	3	2	no	—
463	C₈	—	3	2	no	—
464	C₈	—	5	4	no	—
465	C₈	—	15	2	no	—
466	C₈	—	15	2	no	—
467	C₈	C₂×D₅×Dic₃	1	4	yes	—
468	C₂×C₃	—	2	2	no	—
469	C₂×C₃	—	5	4	no	—
470	C₂×C₃	—	10	2	no	—
471	C₂×C₃	C₂×C₄²×D₅	1	1	yes	characteristic
472	C₂×C₃	D₅×#131	1	2	yes	—
473	C₅	C₂×#5122	1	1	yes	characteristic, complemented, Sylow
474	C₂²	—	2	2	no	—
475	C₂²	—	5	4	no	—
476	C₂²	—	5	2	no	—
477	C₂²	—	5	2	no	—
478	C₂²	—	10	8	no	—
479	C₂²	—	10	2	no	—
480	C₂²	C₄×D₅×Dic₃	1	2	yes	—
481	C₂²	C₂×C₄×D₃×D₅	1	1	yes	characteristic
482	C₄	—	5	2	no	—
483	C₄	—	5	2	no	—
484	C₄	—	6	4	no	—
485	C₄	—	30	4	no	—
486	C₄	C₄×D₅×Dic₃	1	2	yes	—
487	C₄	C₂×C₄×D₃×D₅	1	1	yes	characteristic
488	C₄	C₂²×D₅×Dic₃	1	1	yes	characteristic
489	C₃	D₅×#405	1	1	yes	characteristic, complemented, Sylow
490	C₂	—	2	2	no	—
491	C₂	—	5	4	no	—
492	C₂	—	10	2	no	—
493	C₂	D₅×#907	1	2	yes	—
494	C₂	C₂×C₄×D₅×Dic₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₃×D₅
commutator	C₂×C₃×C₅	C₂²×C₄²
Fitting	C₂×C₃×C₅×M₁₆	C₂²
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂³×C₃×D₅	C₂×C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₂×M₁₆	D₃×D₅
hypocenter	C₃×C₅	C₂×#405
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
4. #11751223	C₂	semidirect
5. C₅×#5122	C₂	semidirect
6. #11748327	C₂	semidirect
7. #11748326	C₂	semidirect
8. #11748051	C₂	semidirect
9. #11748050	C₂	semidirect
10. D₅×#815	C₂	semidirect
11. C₈×D₅×Dic₃	C₂	semidirect
20. C₃×D₅×M₁₆	C₄	semidirect
29. C₂×D₅×C₃⋊C₈	C₄	semidirect
34. #91099	C₂²	semidirect
35. C₈×Dic₁₅	C₂²	semidirect
36. C₅×#815	C₂²	semidirect
37. C₅×C₈×Dic₃	C₂²	semidirect
38. #90954	C₂²	semidirect
39. #90953	C₂²	semidirect
40. #90951	C₂²	semidirect
41. Dic₃×#168	C₂²	semidirect
64. C₃×C₅×M₁₆	C₂×C₄	semidirect
69. C₂×C₃⋊#168	C₂×C₄	semidirect
75. C₂×C₅×C₃⋊C₈	C₂×C₄	semidirect
78. C₃×#681	C₂×C₄	semidirect
80. C₃×#676	C₂×C₄	semidirect
87. D₅×C₃⋊C₈	C₂×C₄	semidirect
88. D₅×C₃⋊C₈	C₂×C₄	semidirect
97. #5122	D₅	direct (N × H)
107. D₅×M₁₆	Dic₃	semidirect
181. #815	C₂×D₅	semidirect
185. C₈×Dic₃	C₂×D₅	semidirect
196. C₅×M₁₆	C₂×Dic₃	semidirect
210. #681	C₂×Dic₃	semidirect
215. #676	C₂×Dic₃	semidirect
259. C₃×M₁₆	C₄×D₅	semidirect
279. C₂×C₃⋊C₈	C₄×D₅	semidirect
342. C₃×D₅	#405	semidirect
397. M₁₆	D₅×Dic₃	semidirect
420. C₃×C₅	C₂×#405	semidirect
440. D₅	#5122	direct (N × H)
473. C₅	C₂×#5122	semidirect
489. C₃	D₅×#405	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×D₅×M₁₆	2
D₅×#926	2
C₂²×D₅×C₃⋊C₈	2
#11751223	2
C₅×#5122	2
#11748327	2
#11748326	2
#11748051	2
#11748050	2
D₅×#815	2
C₈×D₅×Dic₃	2
D₅×#405	3
C₂×#5122	5

Subgroups — D5×#5122 #14411331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×#5122 #14411331