Subgroups — D₅×#5000 #14413847

Order 1920.

824 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₅×#117	C₂	1	1	yes	maximal, characteristic
2	#11751101	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5000	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅×#830	C₂	1	2	yes	maximal
5	#11748319	C₂	1	2	yes	maximal, complemented
6	D₅×C₄⋊(C₃⋊C₈)	C₂	1	2	yes	maximal, complemented
7	D₅×#803	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×D₅×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	#11746874	C₂	1	1	yes	maximal, characteristic, complemented
10	#11746873	C₂	1	2	yes	maximal, complemented
11	#11746872	C₂	1	1	yes	maximal, characteristic, complemented
12	D₅×#433	—	3	1	no	maximal, Hall
13	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
14	C₃×C₅×#117	C₂²	1	1	yes	characteristic
15	C₃×#4072	C₂²	1	1	yes	characteristic
16	C₃×#4038	C₄	1	2	yes	—
17	C₃×D₅×C₄⋊C₄	C₄	1	2	yes	—
18	C₃×D₅×C₂²⋊C₄	C₄	1	2	yes	—
19	C₃×#4023	C₄	1	2	yes	—
20	C₃×#4018	C₂²	1	1	yes	characteristic
21	C₃×#4018	C₂²	1	1	yes	characteristic
22	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
23	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
24	C₂×D₅×C₃⋊C₈	C₂²	1	2	yes	—
25	C₂×D₅×C₃⋊C₈	C₂²	1	2	yes	—
26	#91114	C₂²	1	2	yes	—
27	C₄⋊(C₃⋊#168)	C₂²	1	2	yes	complemented
28	#91087	C₂²	1	1	yes	characteristic, complemented
29	C₄×C₃⋊#168	C₂²	1	1	yes	characteristic, complemented
30	C₅×#830	C₂²	1	2	yes	—
31	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	2	yes	complemented
32	C₅×#803	C₂²	1	1	yes	characteristic, complemented
33	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
34	#90982	C₂²	1	2	yes	complemented
35	#90982	C₂²	1	2	yes	complemented
36	#90955	C₂²	1	2	yes	—
37	#90955	C₂²	1	2	yes	—
38	#90952	C₂²	1	2	yes	complemented
39	Dic₅×C₃⋊C₈	C₂²	1	2	yes	complemented
40	C₂×#5000	—	5	1	no	maximal, Hall
41	D₅×#117	D₃	1	1	yes	characteristic
42	C₅×#433	—	3	1	no	—
43	#65289	—	3	1	no	—
44	#65129	—	3	2	no	—
45	D₅×C₄⋊C₈	—	3	2	no	—
46	D₅×C₂²⋊C₈	—	3	2	no	—
47	#65009	—	3	2	no	—
48	#64998	—	3	1	no	—
49	D₅×#97	—	3	1	no	—
50	#64979	—	3	1	no	—
51	C₄×C₈×D₅	—	3	1	no	—
52	C₂³×C₃×D₅	C₂×C₄	1	1	yes	characteristic
53	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
54	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
55	C₂×C₃×C₄×D₅	—	2	4	no	—
56	C₂×C₃×C₄×D₅	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	2	yes	—
59	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
60	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
61	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
62	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
63	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
64	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
65	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
66	C₂×C₃⋊#168	C₂³	1	2	yes	—
67	C₂×C₃⋊#168	C₂³	1	2	yes	—
68	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
69	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
70	C₃×C₂²⋊Dic₅	C₂×C₄	1	2	yes	—
71	C₃×#685	C₂×C₄	1	2	yes	—
72	C₃×#685	C₂×C₄	1	2	yes	—
73	C₃×C₄⋊Dic₅	C₂×C₄	1	2	yes	—
74	C₃×#683	C₂×C₄	1	2	yes	—
75	C₃×#683	C₂×C₄	1	2	yes	—
76	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
77	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
78	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
79	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
80	D₅×C₃⋊C₈	—	2	4	no	—
81	D₅×C₃⋊C₈	—	2	4	no	—
82	C₂×C₃×#117	—	5	1	no	—
83	C₂×#830	—	5	2	no	—
84	#5000	—	5	1	no	—
85	#5000	—	5	2	no	—
86	#5000	—	5	2	no	—
87	#5000	—	5	1	no	—
88	#5000	—	5	1	no	—
89	#5000	D₅	1	1	yes	characteristic, direct product factor
90	C₂×C₄⋊(C₃⋊C₈)	—	5	2	no	—
91	C₂×#803	—	5	1	no	—
92	C₂×C₄×C₃⋊C₈	—	5	1	no	—
93	C₂²×C₄×D₅	C₂×D₃	1	1	yes	characteristic
94	C₅×#117	C₂×D₃	1	1	yes	characteristic
95	#4072	C₂×D₃	1	1	yes	characteristic
96	C₂×C₈×D₅	—	3	2	no	—
97	C₂×C₈×D₅	—	3	2	no	—
98	#4038	Dic₃	1	2	yes	—
99	D₅×C₄⋊C₄	Dic₃	1	2	yes	—
100	D₅×C₂²⋊C₄	Dic₃	1	2	yes	—
101	#4023	Dic₃	1	2	yes	—
102	#4018	C₂×D₃	1	1	yes	characteristic
103	#4018	C₂×D₃	1	1	yes	characteristic
104	C₄²×D₅	C₂×D₃	1	1	yes	characteristic
105	C₄²×D₅	C₂×D₃	1	1	yes	characteristic
106	C₅×C₄⋊C₈	—	3	2	no	—
107	C₅×C₂²⋊C₈	—	3	2	no	—
108	C₅×#97	—	3	1	no	—
109	C₄×C₅×C₈	—	3	1	no	—
110	C₂²⋊#168	—	3	2	no	—
111	#3952	—	3	2	no	—
112	#3952	—	3	2	no	—
113	#3947	—	3	2	no	—
114	#3946	—	3	2	no	—
115	#3946	—	3	2	no	—
116	C₈×Dic₅	—	3	2	no	—
117	C₄⋊#168	—	3	2	no	—
118	#3935	—	3	1	no	—
119	C₄×#168	—	3	1	no	—
120	C₂×#433	—	15	1	no	Sylow
121	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₃×D₅	—	2	2	no	—
123	C₂²×C₃×D₅	—	2	4	no	—
124	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₃×C₄×C₅	—	2	2	no	—
127	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
128	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
129	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
131	C₂×C₃×Dic₅	—	2	2	no	—
132	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
133	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
134	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
136	C₃×C₄×D₅	—	2	2	no	—
137	C₃×C₄×D₅	—	2	4	no	—
138	C₃×C₄×D₅	—	2	4	no	—
139	C₃×C₄×D₅	—	2	2	no	—
140	C₃×C₄×D₅	—	2	2	no	—
141	C₃×C₄×D₅	#41	1	4	yes	—
142	C₃⋊#168	—	2	2	no	—
143	C₃⋊#168	—	2	2	no	—
144	C₅×C₃⋊C₈	—	2	2	no	—
145	C₅×C₃⋊C₈	—	2	2	no	—
146	C₂³×C₃×C₄	—	5	1	no	—
147	C₃×#117	—	5	1	no	—
148	C₃×#117	—	5	2	no	—
149	C₃×#117	—	5	2	no	—
150	C₃×#117	—	5	1	no	—
151	C₃×#117	—	5	1	no	—
152	C₃×#117	C₂×D₅	1	1	yes	characteristic
153	C₂×C₃×C₄⋊C₄	—	5	2	no	—
154	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
155	C₂×C₃×C₄²	—	5	1	no	—
156	C₂×C₃×C₄²	—	5	1	no	—
157	C₂²×C₃⋊C₈	—	5	2	no	—
158	C₂²×C₃⋊C₈	—	5	2	no	—
159	#830	—	5	2	no	—
160	#830	—	5	2	no	—
161	#830	—	5	2	no	—
162	#830	C₂×D₅	1	2	yes	—
163	C₄⋊(C₃⋊C₈)	—	5	2	no	—
164	C₄⋊(C₃⋊C₈)	—	5	2	no	—
165	C₄⋊(C₃⋊C₈)	—	5	2	no	—
166	C₄⋊(C₃⋊C₈)	C₂×D₅	1	2	yes	complemented
167	#803	—	5	1	no	—
168	#803	—	5	2	no	—
169	#803	C₂×D₅	1	1	yes	characteristic, complemented
170	C₄×C₃⋊C₈	—	5	1	no	—
171	C₄×C₃⋊C₈	—	5	2	no	—
172	C₄×C₃⋊C₈	C₂×D₅	1	1	yes	characteristic, complemented
173	C₂³×D₅	C₂×Dic₃	1	1	yes	characteristic
174	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
175	C₂²×Dic₅	C₂×Dic₃	1	1	yes	characteristic
176	C₂×C₄×D₅	—	2	4	no	—
177	C₂×C₄×D₅	C₂×Dic₃	1	1	yes	characteristic
178	C₂×C₄×D₅	C₂×Dic₃	1	1	yes	characteristic
179	C₂×C₄×D₅	C₂×Dic₃	1	2	yes	—
180	C₂×C₄×D₅	C₂×Dic₃	1	2	yes	—
181	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
182	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
183	C₂×C₅×C₈	—	3	2	no	—
184	C₂×C₅×C₈	—	3	2	no	—
185	C₅×C₄⋊C₄	C₂×Dic₃	1	2	yes	—
186	C₅×C₂²⋊C₄	C₂×Dic₃	1	2	yes	—
187	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
188	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
189	C₂²⋊Dic₅	C₂×Dic₃	1	2	yes	—
190	#685	C₂×Dic₃	1	2	yes	—
191	#685	C₂×Dic₃	1	2	yes	—
192	C₄⋊Dic₅	C₂×Dic₃	1	2	yes	—
193	#683	C₂×Dic₃	1	2	yes	—
194	#683	C₂×Dic₃	1	2	yes	—
195	C₄×Dic₅	C₂×Dic₃	1	2	yes	—
196	C₄×Dic₅	C₂×Dic₃	1	2	yes	—
197	C₄×Dic₅	C₂²×D₃	1	1	yes	characteristic
198	C₄×Dic₅	C₂²×D₃	1	1	yes	characteristic
199	C₂×#168	—	3	2	no	—
200	C₂×#168	—	3	2	no	—
201	C₈×D₅	—	6	4	no	—
202	C₈×D₅	—	6	4	no	—
203	C₂×#117	—	5	1	no	—
204	#433	—	3	1	no	—
205	#433	—	15	1	no	—
206	#433	—	15	1	no	—
207	#433	—	15	2	no	—
208	#433	—	15	2	no	—
209	#433	—	15	1	no	—
210	C₂×C₄⋊C₈	—	15	2	no	—
211	C₂×C₂²⋊C₈	—	15	2	no	—
212	C₂×#97	—	15	1	no	—
213	C₂×C₄×C₈	—	15	1	no	—
214	C₂²×C₃×C₅	—	2	1	no	—
215	C₂²×C₃×C₅	—	2	2	no	—
216	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
217	C₂×C₃×D₅	—	2	1	no	—
218	C₂×C₃×D₅	—	2	2	no	—
219	C₂×C₃×D₅	—	4	4	no	—
220	C₂×C₃×D₅	#117	1	2	yes	—
221	C₂×C₃×D₅	#131	1	4	yes	—
222	C₃×C₄×C₅	—	2	1	no	—
223	C₃×C₄×C₅	—	2	2	no	—
224	C₃×C₄×C₅	—	2	2	no	—
225	C₃×C₄×C₅	C₂×#41	1	2	yes	—
226	C₃×Dic₅	—	2	1	no	—
227	C₃×Dic₅	—	2	2	no	—
228	C₃×Dic₅	—	2	2	no	—
229	C₃×Dic₅	#117	1	2	yes	—
230	C₂⁴×C₃	—	5	1	no	—
231	C₂²×C₃×C₄	—	5	1	no	—
232	C₂²×C₃×C₄	—	5	1	no	—
233	C₂²×C₃×C₄	—	5	2	no	—
234	C₂²×C₃×C₄	—	5	2	no	—
235	C₂²×C₃×C₄	—	5	1	no	—
236	C₂²×C₃×C₄	—	5	1	no	—
237	C₂²×C₃×C₄	—	5	1	no	—
238	C₂²×C₃×C₄	—	10	4	no	—
239	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
240	C₃×C₄⋊C₄	—	5	2	no	—
241	C₃×C₄⋊C₄	—	5	2	no	—
242	C₃×C₄⋊C₄	—	5	2	no	—
243	C₃×C₄⋊C₄	C₄×D₅	1	2	yes	—
244	C₃×C₂²⋊C₄	—	5	2	no	—
245	C₃×C₂²⋊C₄	—	5	2	no	—
246	C₃×C₂²⋊C₄	—	5	2	no	—
247	C₃×C₂²⋊C₄	C₄×D₅	1	2	yes	—
248	C₃×C₄²	—	5	2	no	—
249	C₃×C₄²	—	5	2	no	—
250	C₃×C₄²	—	5	1	no	—
251	C₃×C₄²	—	5	1	no	—
252	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
253	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
254	C₂×C₃⋊C₈	—	5	2	no	—
255	C₂×C₃⋊C₈	—	5	2	no	—
256	C₂×C₃⋊C₈	—	10	4	no	—
257	C₂×C₃⋊C₈	—	10	4	no	—
258	C₂×C₃⋊C₈	C₂²×D₅	1	2	yes	—
259	C₂×C₃⋊C₈	C₂²×D₅	1	2	yes	—
260	C₂³×C₅	C₂²×Dic₃	1	1	yes	characteristic
261	C₂²×D₅	—	2	2	no	—
262	C₂²×D₅	—	2	4	no	—
263	C₂²×D₅	C₂²×Dic₃	1	1	yes	characteristic
264	C₂²×D₅	C₂²×Dic₃	1	1	yes	characteristic
265	C₂×C₄×C₅	—	2	2	no	—
266	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
267	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
268	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
269	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
270	C₂×Dic₅	—	2	2	no	—
271	C₂×Dic₅	C₂²×Dic₃	1	2	yes	—
272	C₂×Dic₅	C₂²×Dic₃	1	2	yes	—
273	C₂×Dic₅	C₂²×Dic₃	1	1	yes	characteristic
274	C₂×Dic₅	C₂²×Dic₃	1	1	yes	characteristic
275	C₄×D₅	—	2	2	no	—
276	C₄×D₅	—	2	4	no	—
277	C₄×D₅	—	2	4	no	—
278	C₄×D₅	—	2	2	no	—
279	C₄×D₅	—	2	2	no	—
280	C₄×D₅	#235	1	4	yes	—
281	C₅×C₈	—	6	2	no	—
282	C₅×C₈	—	6	2	no	—
283	#168	—	6	2	no	—
284	#168	—	6	2	no	—
285	C₂³×C₄	—	5	1	no	—
286	C₂²×C₈	—	15	2	no	—
287	C₂²×C₈	—	15	2	no	—
288	#117	—	5	1	no	—
289	#117	—	5	2	no	—
290	#117	—	5	2	no	—
291	#117	—	5	1	no	—
292	#117	—	5	1	no	—
293	#117	D₃×D₅	1	1	yes	characteristic
294	C₂×C₄⋊C₄	—	5	2	no	—
295	C₂×C₂²⋊C₄	—	5	2	no	—
296	C₂×C₄²	—	5	1	no	—
297	C₂×C₄²	—	5	1	no	—
298	C₄⋊C₈	—	3	2	no	—
299	C₄⋊C₈	—	15	2	no	—
300	C₄⋊C₈	—	15	2	no	—
301	C₄⋊C₈	—	15	2	no	—
302	C₂²⋊C₈	—	3	2	no	—
303	C₂²⋊C₈	—	15	2	no	—
304	C₂²⋊C₈	—	15	2	no	—
305	C₂²⋊C₈	—	15	2	no	—
306	#97	—	3	1	no	—
307	#97	—	15	2	no	—
308	#97	—	15	1	no	—
309	C₄×C₈	—	3	1	no	—
310	C₄×C₈	—	15	2	no	—
311	C₄×C₈	—	15	1	no	—
312	C₂×C₃×C₅	—	4	1	no	—
313	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
314	C₂×C₃×C₅	C₂×#131	1	2	yes	—
315	C₃×D₅	—	4	1	no	—
316	C₃×D₅	#433	1	4	yes	complemented
317	C₂³×C₃	—	5	1	no	—
318	C₂³×C₃	—	5	1	no	—
319	C₂³×C₃	—	10	2	no	—
320	C₂³×C₃	—	10	4	no	—
321	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
322	C₂×C₃×C₄	—	2	2	no	—
323	C₂×C₃×C₄	—	5	1	no	—
324	C₂×C₃×C₄	—	5	4	no	—
325	C₂×C₃×C₄	—	5	2	no	—
326	C₂×C₃×C₄	—	5	2	no	—
327	C₂×C₃×C₄	—	5	1	no	—
328	C₂×C₃×C₄	—	10	2	no	—
329	C₂×C₃×C₄	—	10	4	no	—
330	C₂×C₃×C₄	—	10	4	no	—
331	C₂×C₃×C₄	—	10	2	no	—
332	C₂×C₃×C₄	—	10	2	no	—
333	C₂×C₃×C₄	—	10	2	no	—
334	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
335	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
336	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
337	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
338	C₃⋊C₈	—	2	2	no	—
339	C₃⋊C₈	—	2	2	no	—
340	C₃⋊C₈	—	10	2	no	—
341	C₃⋊C₈	—	10	2	no	—
342	C₂²×C₅	—	2	1	no	—
343	C₂²×C₅	—	2	2	no	—
344	C₂²×C₅	C₂³×Dic₃	1	1	yes	characteristic
345	C₂×D₅	—	2	1	no	—
346	C₂×D₅	—	2	2	no	—
347	C₂×D₅	—	4	4	no	—
348	C₂×D₅	#926	1	2	yes	—
349	C₂×D₅	#948	1	4	yes	—
350	C₄×C₅	—	2	1	no	—
351	C₄×C₅	—	2	2	no	—
352	C₄×C₅	—	2	2	no	—
353	C₄×C₅	C₂×#235	1	2	yes	—
354	Dic₅	—	2	1	no	—
355	Dic₅	—	2	2	no	—
356	Dic₅	—	2	2	no	—
357	Dic₅	#926	1	2	yes	—
358	C₂⁴	—	5	1	no	—
359	C₂²×C₄	—	5	1	no	—
360	C₂²×C₄	—	5	1	no	—
361	C₂²×C₄	—	5	2	no	—
362	C₂²×C₄	—	5	2	no	—
363	C₂²×C₄	—	5	1	no	—
364	C₂²×C₄	—	5	1	no	—
365	C₂²×C₄	—	5	1	no	—
366	C₂²×C₄	—	10	4	no	—
367	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
368	C₂×C₈	—	3	2	no	—
369	C₂×C₈	—	3	2	no	—
370	C₂×C₈	—	15	2	no	—
371	C₂×C₈	—	15	2	no	—
372	C₂×C₈	—	30	4	no	—
373	C₂×C₈	—	30	4	no	—
374	C₄⋊C₄	—	5	2	no	—
375	C₄⋊C₄	—	5	2	no	—
376	C₄⋊C₄	—	5	2	no	—
377	C₄⋊C₄	D₅×Dic₃	1	2	yes	—
378	C₂²⋊C₄	—	5	2	no	—
379	C₂²⋊C₄	—	5	2	no	—
380	C₂²⋊C₄	—	5	2	no	—
381	C₂²⋊C₄	D₅×Dic₃	1	2	yes	—
382	C₄²	—	5	2	no	—
383	C₄²	—	5	2	no	—
384	C₄²	—	5	1	no	—
385	C₄²	—	5	1	no	—
386	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
387	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
388	C₃×C₅	C₂×#433	1	1	yes	characteristic, complemented, Hall
389	C₂²×C₃	—	2	2	no	—
390	C₂²×C₃	—	2	1	no	—
391	C₂²×C₃	—	5	4	no	—
392	C₂²×C₃	—	5	2	no	—
393	C₂²×C₃	—	10	2	no	—
394	C₂²×C₃	—	10	1	no	—
395	C₂²×C₃	—	20	4	no	—
396	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
397	C₃×C₄	—	2	2	no	—
398	C₃×C₄	—	2	2	no	—
399	C₃×C₄	—	2	1	no	—
400	C₃×C₄	—	5	2	no	—
401	C₃×C₄	—	10	2	no	—
402	C₃×C₄	—	10	2	no	—
403	C₃×C₄	—	10	1	no	—
404	C₃×C₄	D₅×#41	1	2	yes	—
405	C₂×C₅	—	4	1	no	—
406	C₂×C₅	C₂×#926	1	1	yes	characteristic
407	C₂×C₅	C₂×#948	1	2	yes	—
408	D₅	—	4	1	no	—
409	D₅	#5000	1	4	yes	direct product factor
410	C₂³	—	5	1	no	—
411	C₂³	—	5	1	no	—
412	C₂³	—	10	2	no	—
413	C₂³	—	10	4	no	—
414	C₂³	C₂×D₅×Dic₃	1	1	yes	characteristic
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	5	1	no	—
417	C₂×C₄	—	5	4	no	—
418	C₂×C₄	—	5	2	no	—
419	C₂×C₄	—	5	2	no	—
420	C₂×C₄	—	5	1	no	—
421	C₂×C₄	—	10	2	no	—
422	C₂×C₄	—	10	2	no	—
423	C₂×C₄	—	10	4	no	—
424	C₂×C₄	—	10	4	no	—
425	C₂×C₄	—	10	2	no	—
426	C₂×C₄	—	10	2	no	—
427	C₂×C₄	C₂×D₅×Dic₃	1	2	yes	—
428	C₂×C₄	C₂×D₅×Dic₃	1	2	yes	—
429	C₂×C₄	C₂×D₅×Dic₃	1	1	yes	characteristic
430	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
431	C₈	—	6	2	no	—
432	C₈	—	6	2	no	—
433	C₈	—	30	2	no	—
434	C₈	—	30	2	no	—
435	C₂×C₃	—	4	1	no	—
436	C₂×C₃	—	5	4	no	—
437	C₂×C₃	—	20	1	no	—
438	C₂×C₃	D₅×#117	1	1	yes	characteristic
439	C₂×C₃	D₅×#131	1	2	yes	—
440	C₅	C₂×#5000	1	1	yes	characteristic, complemented, Sylow
441	C₂²	—	2	2	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	5	4	no	—
444	C₂²	—	5	2	no	—
445	C₂²	—	10	2	no	—
446	C₂²	—	10	1	no	—
447	C₂²	—	20	4	no	—
448	C₂²	C₂²×D₅×Dic₃	1	1	yes	characteristic
449	C₄	—	2	2	no	—
450	C₄	—	2	2	no	—
451	C₄	—	2	1	no	—
452	C₄	—	5	2	no	—
453	C₄	—	10	2	no	—
454	C₄	—	10	2	no	—
455	C₄	—	10	1	no	—
456	C₄	D₅×#235	1	2	yes	—
457	C₃	D₅×#433	1	1	yes	characteristic, complemented, Sylow
458	C₂	—	4	1	no	—
459	C₂	—	5	4	no	—
460	C₂	—	20	1	no	—
461	C₂	D₅×#926	1	1	yes	characteristic
462	C₂	D₅×#948	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₃×D₅
commutator, socle	C₂²×C₃×C₅	C₂³×C₄
Fitting	C₃×C₅×#117	C₂²
prime radical	C₂³×C₃×D₅	C₂×C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	#117	D₃×D₅
hypocenter	C₃×C₅	C₂×#433
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ #117

Complements

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

N	H ≅ G/N	type
2. #11751101	C₂	semidirect
3. C₅×#5000	C₂	semidirect
5. #11748319	C₂	semidirect
6. D₅×C₄⋊(C₃⋊C₈)	C₂	semidirect
7. D₅×#803	C₂	semidirect
8. C₄×D₅×C₃⋊C₈	C₂	semidirect
9. #11746874	C₂	semidirect
10. #11746873	C₂	semidirect
11. #11746872	C₂	semidirect
27. C₄⋊(C₃⋊#168)	C₂²	semidirect
28. #91087	C₂²	semidirect
29. C₄×C₃⋊#168	C₂²	semidirect
31. C₅×C₄⋊(C₃⋊C₈)	C₂²	semidirect
32. C₅×#803	C₂²	semidirect
33. C₄×C₅×C₃⋊C₈	C₂²	semidirect
34. #90982	C₂²	semidirect
35. #90982	C₂²	semidirect
38. #90952	C₂²	semidirect
39. Dic₅×C₃⋊C₈	C₂²	semidirect
89. #5000	D₅	direct (N × H)
166. C₄⋊(C₃⋊C₈)	C₂×D₅	semidirect
169. #803	C₂×D₅	semidirect
172. C₄×C₃⋊C₈	C₂×D₅	semidirect
316. C₃×D₅	#433	semidirect
388. C₃×C₅	C₂×#433	semidirect
409. D₅	#5000	direct (N × H)
440. C₅	C₂×#5000	semidirect
457. C₃	D₅×#433	semidirect

Maximal subgroups

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

subgroup	index
C₃×D₅×#117	2
#11751101	2
C₅×#5000	2
D₅×#830	2
#11748319	2
D₅×C₄⋊(C₃⋊C₈)	2
D₅×#803	2
C₄×D₅×C₃⋊C₈	2
#11746874	2
#11746873	2
#11746872	2
D₅×#433	3
C₂×#5000	5

Subgroups — D5×#5000 #14413847

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×#5000 #14413847