Subgroups — Dic₅×#901 #14411471

Order 1920.

1144 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#901	C₂	1	1	yes	maximal, characteristic
2	Dic₅×#235	C₂	1	1	yes	maximal, characteristic
3	C₂×#91286	C₂	1	1	yes	maximal, characteristic
4	#11751202	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×C₈×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
6	#11748324	C₂	1	1	yes	maximal, characteristic, complemented
7	Dic₅×#208	C₂	1	1	yes	maximal, characteristic, complemented
8	#11748052	C₂	1	2	yes	maximal, complemented
9	#11747653	C₂	1	2	yes	maximal, complemented
10	Dic₅×ΓL(1,𝔽₂₅)	C₂	1	2	yes	maximal, complemented
11	D₃×C₈×Dic₅	C₂	1	2	yes	maximal, complemented
12	Dic₅×#131	—	3	1	no	maximal, Hall
13	C₂×C₅×#235	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
15	#91815	C₂²	1	1	yes	characteristic
16	C₂×#6710	C₂²	1	1	yes	characteristic
17	C₂×C₅×#208	C₂²	1	1	yes	characteristic
18	C₅×#901	C₄	1	8	yes	complemented
19	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	—
20	C₂×C₅×D₃×C₈	C₂²	1	2	yes	—
21	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
22	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
23	Dic₅×#67	C₄	1	4	yes	—
24	Dic₅×D₁₂	C₄	1	2	yes	—
25	C₄×D₃×Dic₅	C₂²	1	2	yes	—
26	#91371	C₂²	1	2	yes	—
27	Dic₅×Dic₆	C₄	1	2	yes	—
28	C₂×#6650	C₂²	1	2	yes	—
29	#91286	C₄	1	8	yes	complemented
30	C₂×D₃×#168	C₂²	1	2	yes	—
31	#91099	C₂²	1	2	yes	—
32	C₈×Dic₁₅	C₂²	1	2	yes	—
33	C₃×C₈×Dic₅	C₂²	1	1	yes	characteristic
34	C₃×C₈×Dic₅	C₂²	1	1	yes	characteristic
35	C₃×C₈×Dic₅	C₂²	1	1	yes	characteristic
36	C₃×C₈×Dic₅	C₂²	1	1	yes	characteristic
37	#90954	C₂²	1	2	yes	—
38	#90952	C₂²	1	2	yes	—
39	#90951	C₂²	1	2	yes	—
40	Dic₅×C₃⋊C₈	C₂²	1	2	yes	—
41	C₄×#901	—	5	1	no	maximal, Hall
42	C₂×C₅×#131	—	3	1	no	—
43	#41×Dic₅	—	3	1	no	—
44	C₂×#4094	—	3	1	no	—
45	#65411	—	3	1	no	—
46	#65411	—	3	2	no	—
47	M₁₆×Dic₅	—	3	1	no	—
48	M₁₆×Dic₅	—	3	2	no	—
49	#65390	—	3	2	no	—
50	#65390	—	3	1	no	—
51	C₂×C₈×Dic₅	—	3	2	no	—
52	C₂×C₈×Dic₅	D₃	1	1	yes	characteristic, complemented
53	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
54	C₂×C₅×#67	C₂×C₄	1	2	yes	—
55	C₅×#235	C₂×C₄	1	4	yes	—
56	C₅×#235	C₂×C₄	1	4	yes	—
57	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
59	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
60	C₂²×C₃×Dic₅	C₂×C₄	1	2	yes	—
61	C₂×D₃×Dic₅	C₂×C₄	1	4	yes	—
62	C₂×C₃×C₅×C₈	C₂×C₄	1	4	yes	complemented
63	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
64	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
65	#6719	C₂×C₄	1	2	yes	—
66	C₄⋊Dic₁₅	C₂×C₄	1	2	yes	—
67	C₄×Dic₁₅	C₂³	1	2	yes	—
68	#6710	C₂×C₄	1	4	yes	complemented
69	C₂×C₃⋊#168	C₂³	1	2	yes	—
70	C₅×#208	C₂×C₄	1	4	yes	complemented
71	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
72	C₅×ΓL(1,𝔽₂₅)	C₂×C₄	1	8	yes	complemented
73	C₅×D₃×C₈	C₂×C₄	1	8	yes	complemented
74	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
75	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
76	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
77	C₂×C₃×#168	C₂×C₄	1	4	yes	complemented
78	C₂×C₃×#168	C₂³	1	1	yes	characteristic
79	C₂×C₃×#168	C₂³	1	1	yes	characteristic
80	Dic₃⋊Dic₅	C₂×C₄	1	4	yes	—
81	(C₂×D₃)⋊Dic₅	C₂×C₄	1	4	yes	—
82	Dic₃×Dic₅	C₂×C₄	1	4	yes	—
83	#6650	C₂×C₄	1	8	yes	complemented
84	D₃×#168	C₂×C₄	1	8	yes	complemented
85	C₂×#901	—	5	1	no	—
86	C₂×#901	D₅	1	1	yes	characteristic
87	C₄×#235	—	5	1	no	—
88	C₂×C₃×C₄×C₈	—	5	1	no	—
89	#5101	—	5	1	no	—
90	#5101	—	5	1	no	—
91	C₄×#208	—	5	1	no	—
92	#4689	—	5	2	no	—
93	#4689	—	5	2	no	—
94	C₄×ΓL(1,𝔽₂₅)	—	5	2	no	—
95	C₄×D₃×C₈	—	5	2	no	—
96	C₂×C₅×#41	—	3	1	no	—
97	C₅×#131	—	3	8	no	—
98	C₂×C₅×M₁₆	—	3	1	no	—
99	C₂×C₅×M₁₆	—	3	2	no	—
100	C₂²×C₅×C₈	—	3	2	no	—
101	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
102	#4094	—	3	8	no	—
103	Q₈×Dic₅	—	3	2	no	—
104	D₄×Dic₅	—	3	4	no	—
105	D₄×Dic₅	—	3	2	no	—
106	#4072	—	3	1	no	—
107	#4072	—	3	2	no	—
108	C₂×C₄×Dic₅	—	3	2	no	—
109	C₂×C₄×Dic₅	C₂×D₃	1	1	yes	characteristic
110	C₂×#681	—	3	1	no	—
111	C₂×#681	—	3	2	no	—
112	C₂²×#168	—	3	2	no	—
113	C₂²×#168	C₂×D₃	1	1	yes	characteristic
114	#3947	—	3	2	no	—
115	#3947	—	3	2	no	—
116	#3947	—	3	2	no	—
117	C₈×Dic₅	—	3	2	no	—
118	C₈×Dic₅	—	3	2	no	—
119	C₈×Dic₅	—	3	2	no	—
120	C₈×Dic₅	C₂×D₃	1	1	yes	characteristic
121	C₈×Dic₅	C₂×D₃	1	1	yes	characteristic
122	C₈×Dic₅	C₂×D₃	1	1	yes	characteristic
123	C₈×Dic₅	C₂×D₃	1	1	yes	characteristic
124	C₄×#131	—	15	1	no	Sylow
125	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
127	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
129	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
130	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
131	C₂×Dic₁₅	C₂²×C₄	1	4	yes	—
132	C₅×#67	C₄²	1	8	yes	—
133	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
134	C₅×D₁₂	C₄²	1	4	yes	—
135	C₄×C₅×D₃	C₂²×C₄	1	4	yes	—
136	C₄×C₅×D₃	C₂²×C₄	1	4	yes	—
137	C₅×Dic₆	C₄²	1	4	yes	—
138	C₂×C₃×Dic₅	—	2	4	no	—
139	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
140	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
141	D₃×Dic₅	—	2	8	no	—
142	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
143	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
144	C₃⋊#168	C₂²×C₄	1	4	yes	—
145	C₃×#168	C₂²×C₄	1	2	yes	—
146	C₃×#168	C₂²×C₄	1	2	yes	—
147	C₅×C₃⋊C₈	C₂²×C₄	1	4	yes	—
148	C₂×#235	C₂×D₅	1	1	yes	characteristic
149	C₂²×C₃×C₈	—	5	1	no	—
150	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
151	C₂×C₃×C₄²	—	5	1	no	—
152	C₄×#67	—	5	4	no	—
153	#926	—	5	1	no	—
154	C₂×#208	—	5	1	no	—
155	C₂×#208	C₂×D₅	1	1	yes	characteristic
156	#901	—	5	8	no	—
157	#901	Dic₅	1	8	yes	direct product factor
158	C₂×ΓL(1,𝔽₂₅)	—	5	2	no	—
159	C₂×ΓL(1,𝔽₂₅)	C₂×D₅	1	2	yes	—
160	C₂×D₃×C₈	—	5	2	no	—
161	C₂×D₃×C₈	C₂×D₅	1	2	yes	—
162	C₄×D₁₂	—	5	2	no	—
163	#872	—	5	2	no	—
164	C₄²×D₃	—	5	2	no	—
165	C₄×Dic₆	—	5	2	no	—
166	C₃×C₄×C₈	—	5	1	no	—
167	C₃×C₄×C₈	—	5	1	no	—
168	C₃×C₄×C₈	—	5	1	no	—
169	C₃×C₄×C₈	—	5	1	no	—
170	#815	—	5	2	no	—
171	#815	—	5	2	no	—
172	C₈×Dic₃	—	5	2	no	—
173	C₈×Dic₃	—	5	2	no	—
174	#803	—	5	2	no	—
175	C₄×C₃⋊C₈	—	5	2	no	—
176	C₅×#41	—	3	4	no	—
177	C₅×#41	—	3	4	no	—
178	C₂×C₅×Q₈	—	3	1	no	—
179	C₂×C₅×D₄	—	3	2	no	—
180	C₂×C₅×D₄	—	3	1	no	—
181	C₂²×C₄×C₅	—	3	2	no	—
182	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
183	C₂²×Dic₅	—	3	4	no	—
184	C₂²×Dic₅	C₄×D₃	1	2	yes	—
185	C₅×M₁₆	—	3	4	no	—
186	C₅×M₁₆	—	3	8	no	—
187	C₂×C₅×C₈	—	3	2	no	—
188	C₂×C₅×C₈	—	3	8	no	—
189	C₂×C₅×C₈	C₄×D₃	1	4	yes	complemented
190	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
191	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
192	C₂²⋊Dic₅	—	3	2	no	—
193	C₂²⋊Dic₅	—	3	4	no	—
194	C₄⋊Dic₅	—	3	2	no	—
195	C₄⋊Dic₅	—	3	4	no	—
196	C₄×Dic₅	—	3	2	no	—
197	C₄×Dic₅	—	3	4	no	—
198	C₄×Dic₅	C₄×D₃	1	2	yes	—
199	C₄×Dic₅	C₂²×D₃	1	1	yes	characteristic
200	C₄×Dic₅	C₂²×D₃	1	1	yes	characteristic
201	#681	—	3	4	no	—
202	#681	—	3	8	no	—
203	C₂×#168	—	3	2	no	—
204	C₂×#168	—	3	8	no	—
205	C₂×#168	C₄×D₃	1	4	yes	complemented
206	C₂×#168	C₂²×D₃	1	1	yes	characteristic
207	C₂×#168	C₂²×D₃	1	1	yes	characteristic
208	C₂×#131	—	3	1	no	—
209	C₂×#131	—	15	1	no	—
210	C₄×#41	—	15	1	no	—
211	#405	—	15	2	no	—
212	#405	—	15	2	no	—
213	#405	—	15	1	no	—
214	#405	—	15	1	no	—
215	C₄×M₁₆	—	15	2	no	—
216	C₄×M₁₆	—	15	1	no	—
217	C₂×C₄×C₈	—	5	1	no	—
218	C₂×C₄×C₈	—	15	2	no	—
219	C₂²×C₃×C₅	—	2	2	no	—
220	C₂²×C₃×C₅	C₂×C₄²	1	2	yes	—
221	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
222	C₂×C₅×D₃	—	2	4	no	—
223	C₂×C₅×D₃	C₂×C₄²	1	4	yes	—
224	C₃×C₄×C₅	C₂×C₄²	1	2	yes	—
225	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
226	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
227	Dic₁₅	—	2	4	no	—
228	C₃×Dic₅	—	2	2	no	—
229	C₃×Dic₅	#131	1	4	yes	complemented
230	C₅×Dic₃	C₂×C₄²	1	4	yes	—
231	C₂²×C₃×C₄	—	5	2	no	—
232	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
233	C₂×#67	C₄×D₅	1	2	yes	—
234	#235	C₄×D₅	1	4	yes	—
235	#235	C₂×Dic₅	1	4	yes	—
236	C₂×D₁₂	C₄×D₅	1	1	yes	characteristic
237	C₂×C₄×D₃	—	5	4	no	—
238	C₂×C₄×D₃	C₂²×D₅	1	2	yes	—
239	C₂×Dic₆	C₄×D₅	1	1	yes	characteristic
240	C₂×C₃×C₈	—	5	4	no	—
241	C₂×C₃×C₈	—	5	1	no	—
242	C₂×C₃×C₈	—	5	1	no	—
243	C₂×C₃×C₈	C₂×Dic₅	1	4	yes	complemented
244	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
245	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
246	C₃×C₄²	—	5	2	no	—
247	C₃×C₄²	—	5	1	no	—
248	C₃×C₄²	—	5	1	no	—
249	#217	—	5	2	no	—
250	(C₂×D₃)⋊C₄	—	5	4	no	—
251	C₄⋊Dic₃	—	5	2	no	—
252	Dic₃⋊C₄	—	5	4	no	—
253	C₄×Dic₃	—	5	2	no	—
254	C₄×Dic₃	—	5	4	no	—
255	#208	—	5	4	no	—
256	#208	C₂×Dic₅	1	4	yes	complemented
257	C₂×C₃⋊C₈	—	5	2	no	—
258	C₂×C₃⋊C₈	C₂²×D₅	1	2	yes	—
259	ΓL(1,𝔽₂₅)	—	5	8	no	—
260	ΓL(1,𝔽₂₅)	C₂×Dic₅	1	8	yes	complemented
261	D₃×C₈	—	5	8	no	—
262	D₃×C₈	C₂×Dic₅	1	8	yes	complemented
263	C₂³×C₅	—	3	2	no	—
264	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
265	C₅×Q₈	—	3	4	no	—
266	C₅×D₄	—	3	8	no	—
267	C₅×D₄	—	3	4	no	—
268	C₂×C₄×C₅	—	3	2	no	—
269	C₂×C₄×C₅	—	3	4	no	—
270	C₂×C₄×C₅	—	3	4	no	—
271	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
272	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
273	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
274	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
275	C₂×Dic₅	—	2	4	no	—
276	C₂×Dic₅	—	3	4	no	—
277	C₂×Dic₅	—	6	8	no	—
278	C₂×Dic₅	C₂×C₄×D₃	1	2	yes	—
279	C₂×Dic₅	C₂×C₄×D₃	1	2	yes	—
280	C₅×C₈	—	3	4	no	—
281	C₅×C₈	C₂×C₄×D₃	1	2	yes	—
282	C₅×C₈	C₂×C₄×D₃	1	2	yes	—
283	#168	—	3	4	no	—
284	#168	C₂×C₄×D₃	1	2	yes	—
285	#168	C₂×C₄×D₃	1	2	yes	—
286	C₂×#41	—	3	1	no	—
287	#131	—	3	8	no	—
288	#131	—	15	8	no	—
289	C₂×M₁₆	—	3	1	no	—
290	C₂×M₁₆	—	3	2	no	—
291	C₂×M₁₆	—	15	2	no	—
292	C₂×M₁₆	—	15	1	no	—
293	C₂²×C₈	—	3	2	no	—
294	C₂²×C₈	—	5	1	no	—
295	C₂²×C₈	—	15	2	no	—
296	C₂²×C₈	D₃×D₅	1	1	yes	characteristic
297	C₄×Q₈	—	15	2	no	—
298	C₄×D₄	—	15	2	no	—
299	C₄×D₄	—	15	4	no	—
300	#117	—	15	2	no	—
301	#117	—	15	1	no	—
302	C₂×C₄²	—	5	1	no	—
303	C₂×C₄²	—	15	2	no	—
304	#97	—	15	2	no	—
305	#97	—	15	2	no	—
306	#97	—	15	2	no	—
307	C₄×C₈	—	5	1	no	—
308	C₄×C₈	—	5	1	no	—
309	C₄×C₈	—	5	1	no	—
310	C₄×C₈	—	5	1	no	—
311	C₄×C₈	—	15	2	no	—
312	C₄×C₈	—	15	2	no	—
313	C₄×C₈	—	15	2	no	—
314	C₂×C₃×C₅	—	2	2	no	—
315	C₂×C₃×C₅	C₂²×C₄²	1	1	yes	characteristic
316	C₂×C₃×C₅	C₂×#131	1	2	yes	—
317	C₅×D₃	—	2	4	no	—
318	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
319	C₂²×D₃	C₂×C₄×D₅	1	2	yes	—
320	C₂×C₃×C₄	—	5	2	no	—
321	C₂×C₃×C₄	—	5	2	no	—
322	C₂×C₃×C₄	—	10	4	no	—
323	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
324	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
325	C₂×C₃×C₄	C₂²×Dic₅	1	2	yes	—
326	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
327	#67	C₄×Dic₅	1	8	yes	—
328	C₂×Dic₃	—	5	4	no	—
329	C₂×Dic₃	C₂×C₄×D₅	1	2	yes	—
330	D₁₂	C₄×Dic₅	1	4	yes	—
331	C₄×D₃	—	10	8	no	—
332	C₄×D₃	C₂×C₄×D₅	1	4	yes	—
333	C₄×D₃	C₂²×Dic₅	1	4	yes	—
334	Dic₆	C₄×Dic₅	1	4	yes	—
335	C₃×C₈	—	5	2	no	—
336	C₃×C₈	—	5	2	no	—
337	C₃×C₈	C₂²×Dic₅	1	2	yes	—
338	C₃×C₈	C₂²×Dic₅	1	2	yes	—
339	C₃⋊C₈	—	5	4	no	—
340	C₃⋊C₈	C₂²×Dic₅	1	4	yes	—
341	C₂²×C₅	—	2	2	no	—
342	C₂²×C₅	—	3	4	no	—
343	C₂²×C₅	—	6	4	no	—
344	C₂²×C₅	C₄²×D₃	1	2	yes	—
345	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
346	C₄×C₅	—	3	4	no	—
347	C₄×C₅	C₄²×D₃	1	2	yes	—
348	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
349	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
350	Dic₅	—	2	2	no	—
351	Dic₅	—	6	4	no	—
352	Dic₅	#901	1	4	yes	direct product factor
353	#41	—	3	4	no	—
354	#41	—	3	4	no	—
355	C₂×Q₈	—	3	1	no	—
356	C₂×D₄	—	3	2	no	—
357	C₂×D₄	—	3	1	no	—
358	C₂²×C₄	—	3	2	no	—
359	C₂²×C₄	—	5	2	no	—
360	C₂²×C₄	—	15	4	no	—
361	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
362	M₁₆	—	3	4	no	—
363	M₁₆	—	3	8	no	—
364	M₁₆	—	15	8	no	—
365	M₁₆	—	15	4	no	—
366	C₂×C₈	—	3	2	no	—
367	C₂×C₈	—	3	8	no	—
368	C₂×C₈	—	5	4	no	—
369	C₂×C₈	—	5	1	no	—
370	C₂×C₈	—	5	1	no	—
371	C₂×C₈	—	15	8	no	—
372	C₂×C₈	—	15	2	no	—
373	C₂×C₈	D₃×Dic₅	1	4	yes	complemented
374	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
375	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
376	C₄⋊C₄	—	15	4	no	—
377	C₄⋊C₄	—	15	2	no	—
378	C₂²⋊C₄	—	15	4	no	—
379	C₂²⋊C₄	—	15	2	no	—
380	C₄²	—	5	2	no	—
381	C₄²	—	5	1	no	—
382	C₄²	—	5	1	no	—
383	C₄²	—	15	4	no	—
384	C₄²	—	15	2	no	—
385	C₃×C₅	C₄×#131	1	1	yes	characteristic, complemented, Hall
386	C₂²×C₃	—	2	2	no	—
387	C₂²×C₃	C₂×C₄×Dic₅	1	2	yes	—
388	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
389	C₂×D₃	—	2	4	no	—
390	C₂×D₃	C₂×C₄×Dic₅	1	4	yes	—
391	C₃×C₄	—	5	4	no	—
392	C₃×C₄	—	10	2	no	—
393	C₃×C₄	C₂×C₄×Dic₅	1	2	yes	—
394	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
395	C₃×C₄	C₂³×Dic₅	1	1	yes	characteristic
396	Dic₃	—	10	4	no	—
397	Dic₃	C₂×C₄×Dic₅	1	4	yes	—
398	C₂×C₅	—	2	2	no	—
399	C₂×C₅	—	6	4	no	—
400	C₂×C₅	C₂×C₄²×D₃	1	1	yes	characteristic
401	C₂×C₅	C₂×#901	1	2	yes	—
402	C₂³	—	3	2	no	—
403	C₂³	C₄×D₃×D₅	1	1	yes	characteristic
404	Q₈	—	3	4	no	—
405	D₄	—	3	8	no	—
406	D₄	—	3	4	no	—
407	C₂×C₄	—	3	2	no	—
408	C₂×C₄	—	3	4	no	—
409	C₂×C₄	—	3	4	no	—
410	C₂×C₄	—	5	2	no	—
411	C₂×C₄	—	5	2	no	—
412	C₂×C₄	—	10	4	no	—
413	C₂×C₄	—	15	4	no	—
414	C₂×C₄	—	30	8	no	—
415	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
416	C₂×C₄	C₄×D₃×D₅	1	2	yes	—
417	C₂×C₄	C₂×D₃×Dic₅	1	2	yes	—
418	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
419	C₈	—	3	4	no	—
420	C₈	—	5	2	no	—
421	C₈	—	5	2	no	—
422	C₈	—	15	4	no	—
423	C₈	C₂×D₃×Dic₅	1	2	yes	—
424	C₈	C₂×D₃×Dic₅	1	2	yes	—
425	C₂×C₃	—	2	2	no	—
426	C₂×C₃	D₅×#131	1	2	yes	—
427	C₂×C₃	C₂²×C₄×Dic₅	1	1	yes	characteristic
428	D₃	—	2	4	no	—
429	C₅	C₄×#901	1	1	yes	characteristic, complemented, Sylow
430	C₂²	—	2	2	no	—
431	C₂²	—	3	4	no	—
432	C₂²	—	6	4	no	—
433	C₂²	C₄×D₃×Dic₅	1	2	yes	—
434	C₂²	C₂×C₄×D₃×D₅	1	1	yes	characteristic
435	C₄	—	3	4	no	—
436	C₄	—	5	4	no	—
437	C₄	—	10	2	no	—
438	C₄	—	30	4	no	—
439	C₄	C₄×D₃×Dic₅	1	2	yes	—
440	C₄	C₂×C₄×D₃×D₅	1	1	yes	characteristic
441	C₄	C₂²×D₃×Dic₅	1	1	yes	characteristic
442	C₃	Dic₅×#131	1	1	yes	characteristic, complemented, Sylow
443	C₂	—	2	2	no	—
444	C₂	—	6	4	no	—
445	C₂	D₅×#901	1	2	yes	—
446	C₂	C₂×C₄×D₃×Dic₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×D₃×D₅
commutator	C₂×C₃×C₅	C₂²×C₄²
Frattini	C₂×C₄	C₂²×D₃×D₅
Fitting	C₂²×C₃×C₅×C₈	C₂²
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂×C₅×#235	C₂²
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₂²×C₈	D₃×D₅
hypocenter	C₃×C₅	C₄×#131
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
4. #11751202	C₂	semidirect
5. C₂×C₃×C₈×Dic₅	C₂	semidirect
6. #11748324	C₂	semidirect
7. Dic₅×#208	C₂	semidirect
8. #11748052	C₂	semidirect
9. #11747653	C₂	semidirect
10. Dic₅×ΓL(1,𝔽₂₅)	C₂	semidirect
11. D₃×C₈×Dic₅	C₂	semidirect
18. C₅×#901	C₄	semidirect
29. #91286	C₄	semidirect
52. C₂×C₈×Dic₅	D₃	semidirect
62. C₂×C₃×C₅×C₈	C₂×C₄	semidirect
68. #6710	C₂×C₄	semidirect
70. C₅×#208	C₂×C₄	semidirect
72. C₅×ΓL(1,𝔽₂₅)	C₂×C₄	semidirect
73. C₅×D₃×C₈	C₂×C₄	semidirect
77. C₂×C₃×#168	C₂×C₄	semidirect
83. #6650	C₂×C₄	semidirect
84. D₃×#168	C₂×C₄	semidirect
157. #901	Dic₅	direct (N × H)
189. C₂×C₅×C₈	C₄×D₃	semidirect
205. C₂×#168	C₄×D₃	semidirect
229. C₃×Dic₅	#131	semidirect
243. C₂×C₃×C₈	C₂×Dic₅	semidirect
256. #208	C₂×Dic₅	semidirect
260. ΓL(1,𝔽₂₅)	C₂×Dic₅	semidirect
262. D₃×C₈	C₂×Dic₅	semidirect
352. Dic₅	#901	direct (N × H)
373. C₂×C₈	D₃×Dic₅	semidirect
385. C₃×C₅	C₄×#131	semidirect
429. C₅	C₄×#901	semidirect
442. C₃	Dic₅×#131	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#901	2
Dic₅×#235	2
C₂×#91286	2
#11751202	2
C₂×C₃×C₈×Dic₅	2
#11748324	2
Dic₅×#208	2
#11748052	2
#11747653	2
Dic₅×ΓL(1,𝔽₂₅)	2
D₃×C₈×Dic₅	2
Dic₅×#131	3
C₄×#901	5

Subgroups — Dic5×#901 #14411471

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₅×#901 #14411471