Subgroups — D₅×#4874 #14439816

Order 1920.

848 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×#888	C₂	1	2	yes	maximal
2	#11750975	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#4874	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×D₅×#107	C₂	1	1	yes	maximal, characteristic
5	#11748037	C₂	1	1	yes	maximal, characteristic, complemented
6	#11748029	C₂	1	1	yes	maximal, characteristic, complemented
7	D₅×#818	C₂	1	1	yes	maximal, characteristic
8	C₈×D₅×Dic₃	C₂	1	1	yes	maximal, characteristic
9	D₅×#807	C₂	1	2	yes	maximal
10	#11747150	C₂	1	2	yes	maximal, complemented
11	#11747146	C₂	1	2	yes	maximal, complemented
12	D₅×#500	—	3	1	no	maximal, Hall
13	C₂×D₅×Dic₆	—	2	2	no	—
14	#91777	C₂²	1	2	yes	—
15	C₅×#888	C₂²	1	2	yes	—
16	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
17	C₃×D₅×C₄⋊C₄	C₂²	1	2	yes	—
18	#91470	C₂²	1	2	yes	—
19	#91469	C₂²	1	2	yes	—
20	D₅×C₄⋊Dic₃	C₂²	1	2	yes	—
21	D₅×Dic₃⋊C₄	—	2	2	no	—
22	C₄×D₅×Dic₃	C₂²	1	1	yes	characteristic
23	#91329	—	2	2	no	—
24	#91328	—	2	2	no	—
25	C₂×D₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
26	C₃×C₅×#107	C₂²	1	1	yes	characteristic
27	#91102	C₂²	1	1	yes	characteristic
28	C₈×Dic₁₅	C₂²	1	1	yes	characteristic
29	#91091	C₂²	1	2	yes	—
30	C₅×#818	C₂²	1	1	yes	characteristic
31	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic
32	C₅×#807	C₂²	1	2	yes	—
33	C₃×#3950	C₂²	1	1	yes	characteristic
34	C₃×#3939	C₂²	1	2	yes	—
35	#90990	C₂²	1	2	yes	—
36	#90989	C₂²	1	2	yes	—
37	#90988	C₂²	1	2	yes	—
38	#90951	C₂²	1	1	yes	characteristic
39	Dic₃×#168	C₂²	1	1	yes	characteristic
40	C₂×#4874	—	5	1	no	maximal, Hall
41	D₅×C₄⋊Q₈	—	3	2	no	—
42	C₅×#500	—	3	1	no	—
43	#65367	—	3	2	no	—
44	D₅×#107	—	3	1	no	—
45	D₅×#107	—	3	2	no	—
46	D₅×#107	D₃	1	1	yes	characteristic
47	#65163	—	3	1	no	—
48	#65163	—	3	1	no	—
49	#65163	—	3	2	no	—
50	C₄×C₈×D₅	—	3	1	no	—
51	#64971	—	3	1	no	—
52	C₂×Dic₃₀	—	2	2	no	—
53	C₂×C₅×Dic₆	—	2	2	no	—
54	C₂×C₃×C₄×D₅	—	2	2	no	—
55	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
56	C₂×#1204	—	2	2	no	—
57	C₂×#1204	—	2	2	no	—
58	C₂×D₅×Dic₃	—	2	2	no	—
59	C₂×D₅×Dic₃	D₄	1	1	yes	characteristic
60	C₂×D₅×Dic₃	D₄	1	1	yes	characteristic
61	D₅×Dic₆	—	4	8	no	—
62	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
63	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
64	C₄⋊Dic₁₅	C₂³	1	2	yes	—
65	#6712	—	2	2	no	—
66	C₄×Dic₁₅	C₂³	1	1	yes	characteristic
67	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
68	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
69	C₅×Dic₃⋊C₄	—	2	2	no	—
70	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
71	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
72	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
73	C₃×#683	—	2	2	no	—
74	C₂×C₃×#168	C₂³	1	1	yes	characteristic
75	C₃×C₈×D₅	Q₈	1	4	yes	complemented
76	Dic₃⋊Dic₅	—	2	2	no	—
77	#6669	—	2	2	no	—
78	#6668	—	2	2	no	—
79	Dic₃×Dic₅	D₄	1	1	yes	characteristic
80	Dic₃×Dic₅	D₄	1	1	yes	characteristic
81	D₅×C₃⋊C₈	Q₈	1	4	yes	complemented
82	C₂×#888	—	5	2	no	—
83	C₂×C₃×#107	—	5	1	no	—
84	C₂×#818	—	5	1	no	—
85	C₂×C₈×Dic₃	—	5	1	no	—
86	C₂×#807	—	5	2	no	—
87	#4874	—	5	2	no	—
88	#4874	—	5	1	no	—
89	#4874	—	5	1	no	—
90	#4874	—	5	1	no	—
91	#4874	—	5	2	no	—
92	#4874	D₅	1	1	yes	characteristic, direct product factor
93	C₂×Q₈×D₅	—	6	2	no	—
94	C₅×C₄⋊Q₈	—	3	2	no	—
95	#4090	—	6	2	no	—
96	C₂×C₈×D₅	—	3	1	no	—
97	C₂×C₈×D₅	C₂×D₃	1	1	yes	characteristic
98	D₅×C₄⋊C₄	—	3	2	no	—
99	D₅×C₄⋊C₄	—	6	2	no	—
100	D₅×C₄⋊C₄	C₂×D₃	1	2	yes	—
101	#4034	—	3	2	no	—
102	#4034	—	3	2	no	—
103	#4034	—	6	2	no	—
104	C₄²×D₅	—	3	1	no	—
105	#4015	—	3	2	no	—
106	C₅×#107	—	3	1	no	—
107	C₅×#107	—	3	2	no	—
108	C₅×#107	C₂×D₃	1	1	yes	characteristic
109	C₄×C₅×C₈	—	3	1	no	—
110	#3950	—	3	1	no	—
111	#3950	—	3	2	no	—
112	#3950	C₂×D₃	1	1	yes	characteristic
113	C₈×Dic₅	—	3	1	no	—
114	C₈×Dic₅	—	3	1	no	—
115	#3939	—	3	2	no	—
116	#3939	—	3	2	no	—
117	#3939	—	3	2	no	—
118	#3939	C₂×D₃	1	2	yes	—
119	C₄×#168	—	3	1	no	—
120	C₂×#500	—	15	1	no	Sylow
121	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
122	C₂×C₃×C₄×C₅	—	2	2	no	—
123	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
124	C₂×Dic₁₅	—	2	2	no	—
125	C₂×Dic₁₅	C₂×D₄	1	1	yes	characteristic
126	C₂×Dic₁₅	C₂×D₄	1	1	yes	characteristic
127	Dic₃₀	—	4	4	no	—
128	C₂×C₅×Dic₃	—	2	2	no	—
129	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
130	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
131	C₅×Dic₆	—	4	4	no	—
132	C₂×C₃×Dic₅	—	2	2	no	—
133	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
134	C₃×C₄×D₅	—	4	4	no	—
135	C₃×C₄×D₅	C₂×Q₈	1	2	yes	—
136	C₃×C₄×D₅	C₂×Q₈	1	2	yes	—
137	#1204	—	4	4	no	—
138	#1204	—	4	4	no	—
139	D₅×Dic₃	—	4	4	no	—
140	D₅×Dic₃	D₈	1	4	yes	—
141	D₅×Dic₃	Q₁₆	1	4	yes	—
142	C₃×C₅×C₈	C₂×Q₈	1	2	yes	complemented
143	C₃⋊#168	C₂×Q₈	1	2	yes	complemented
144	C₃×#168	C₂×Q₈	1	2	yes	complemented
145	C₅×C₃⋊C₈	C₂×Q₈	1	2	yes	complemented
146	C₂²×Dic₆	—	10	2	no	—
147	C₂²×C₃×C₈	—	5	1	no	—
148	C₂×C₃×C₄⋊C₄	—	5	2	no	—
149	C₂×C₄⋊Dic₃	—	5	2	no	—
150	C₂×Dic₃⋊C₄	—	10	2	no	—
151	C₂×C₄×Dic₃	—	5	1	no	—
152	C₂²×C₃⋊C₈	—	5	1	no	—
153	#888	—	5	2	no	—
154	#888	—	5	2	no	—
155	#888	—	5	2	no	—
156	#888	—	10	2	no	—
157	#888	—	10	2	no	—
158	#888	C₂×D₅	1	2	yes	—
159	C₃×#107	—	5	1	no	—
160	C₃×#107	—	5	2	no	—
161	C₃×#107	C₂×D₅	1	1	yes	characteristic
162	#818	—	5	1	no	—
163	#818	—	5	2	no	—
164	#818	C₂×D₅	1	1	yes	characteristic
165	C₈×Dic₃	—	5	1	no	—
166	C₈×Dic₃	—	5	1	no	—
167	C₈×Dic₃	—	5	1	no	—
168	C₈×Dic₃	C₂×D₅	1	1	yes	characteristic
169	#807	—	5	2	no	—
170	#807	—	5	2	no	—
171	#807	—	5	2	no	—
172	#807	C₂×D₅	1	2	yes	—
173	C₂×C₅×Q₈	—	6	2	no	—
174	Q₈×D₅	—	12	8	no	—
175	C₂×C₄×D₅	—	2	2	no	—
176	C₂×C₄×D₅	—	3	1	no	—
177	C₂×C₄×D₅	—	3	1	no	—
178	C₂×C₄×D₅	—	6	2	no	—
179	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
180	C₂×Dic₁₀	—	6	2	no	—
181	C₂×Dic₁₀	—	6	2	no	—
182	C₂×Dic₁₀	—	6	2	no	—
183	C₂×C₅×C₈	—	3	1	no	—
184	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
185	C₅×C₄⋊C₄	—	3	2	no	—
186	C₅×C₄⋊C₄	—	6	2	no	—
187	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
188	C₄²×C₅	—	3	1	no	—
189	C₄⋊Dic₅	—	3	2	no	—
190	C₄⋊Dic₅	—	6	2	no	—
191	C₄⋊Dic₅	C₂²×D₃	1	2	yes	—
192	#683	—	2	2	no	—
193	#683	—	6	2	no	—
194	#683	—	6	2	no	—
195	#683	—	6	2	no	—
196	C₄×Dic₅	—	3	1	no	—
197	C₄×Dic₅	—	3	1	no	—
198	C₄×Dic₅	—	3	1	no	—
199	C₂×#168	—	3	1	no	—
200	C₂×#168	C₂²×D₃	1	1	yes	characteristic
201	C₈×D₅	—	3	4	no	—
202	C₈×D₅	Dic₆	1	4	yes	complemented
203	C₂×C₄⋊Q₈	—	15	2	no	—
204	#500	—	3	1	no	—
205	#500	—	15	1	no	—
206	#500	—	15	2	no	—
207	#500	—	15	1	no	—
208	#500	—	15	2	no	—
209	#500	—	15	1	no	—
210	C₂×#107	—	5	1	no	—
211	C₂×#107	—	15	2	no	—
212	C₂×#107	—	15	1	no	—
213	C₂×C₄×C₈	—	15	1	no	—
214	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
215	C₂×C₃×D₅	C₄⋊Q₈	1	2	yes	—
216	C₂×C₃×D₅	C₂×D₈	1	2	yes	—
217	C₂×C₃×D₅	C₂×Q₁₆	1	2	yes	—
218	C₃×C₄×C₅	—	4	2	no	—
219	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
220	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
221	Dic₁₅	—	4	2	no	—
222	Dic₁₅	C₂×D₈	1	2	yes	—
223	Dic₁₅	C₂×Q₁₆	1	2	yes	—
224	C₃×Dic₅	—	4	2	no	—
225	C₃×Dic₅	C₄⋊Q₈	1	2	yes	—
226	C₅×Dic₃	—	4	2	no	—
227	C₅×Dic₃	C₂×D₈	1	2	yes	—
228	C₅×Dic₃	C₂×Q₁₆	1	2	yes	—
229	C₂²×C₃×C₄	—	5	1	no	—
230	C₂²×C₃×C₄	—	10	2	no	—
231	C₂²×Dic₃	—	5	1	no	—
232	C₂²×Dic₃	—	5	1	no	—
233	C₂²×Dic₃	—	10	2	no	—
234	C₂×Dic₆	—	2	2	no	—
235	C₂×Dic₆	—	10	2	no	—
236	C₂×Dic₆	—	10	2	no	—
237	C₂×Dic₆	—	10	2	no	—
238	C₂×Dic₆	—	20	8	no	—
239	C₂×C₃×C₈	—	5	1	no	—
240	C₂×C₃×C₈	—	5	4	no	—
241	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
242	C₃×C₄⋊C₄	—	5	2	no	—
243	C₃×C₄⋊C₄	—	10	2	no	—
244	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
245	C₄⋊Dic₃	—	5	2	no	—
246	C₄⋊Dic₃	—	10	2	no	—
247	C₄⋊Dic₃	C₂²×D₅	1	2	yes	—
248	Dic₃⋊C₄	—	2	2	no	—
249	Dic₃⋊C₄	—	10	2	no	—
250	Dic₃⋊C₄	—	10	2	no	—
251	Dic₃⋊C₄	—	10	2	no	—
252	C₄×Dic₃	—	5	1	no	—
253	C₄×Dic₃	—	5	1	no	—
254	C₄×Dic₃	—	5	1	no	—
255	C₄×Dic₃	C₂²×D₅	1	1	yes	characteristic
256	C₂×C₃⋊C₈	—	5	1	no	—
257	C₂×C₃⋊C₈	—	5	4	no	—
258	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
259	C₂²×D₅	D₃×D₄	1	1	yes	characteristic
260	C₅×Q₈	—	12	4	no	—
261	C₂×C₄×C₅	—	2	2	no	—
262	C₂×C₄×C₅	—	3	1	no	—
263	C₂×C₄×C₅	—	3	1	no	—
264	C₂×C₄×C₅	—	6	2	no	—
265	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
266	C₂×Dic₅	—	2	2	no	—
267	C₂×Dic₅	—	3	1	no	—
268	C₂×Dic₅	—	3	1	no	—
269	C₂×Dic₅	—	6	2	no	—
270	C₂×Dic₅	D₃×D₄	1	1	yes	characteristic
271	C₄×D₅	—	3	4	no	—
272	C₄×D₅	—	3	4	no	—
273	C₄×D₅	—	4	4	no	—
274	C₄×D₅	—	12	4	no	—
275	C₄×D₅	C₂×Dic₆	1	2	yes	—
276	C₄×D₅	D₃×Q₈	1	2	yes	—
277	Dic₁₀	—	12	4	no	—
278	Dic₁₀	—	12	4	no	—
279	Dic₁₀	—	12	4	no	—
280	C₅×C₈	—	3	2	no	—
281	C₅×C₈	C₂×Dic₆	1	2	yes	complemented
282	#168	—	3	2	no	—
283	#168	C₂×Dic₆	1	2	yes	complemented
284	C₂²×Q₈	—	30	2	no	—
285	C₂²×C₈	—	5	1	no	—
286	C₂²×C₈	—	15	1	no	—
287	C₄⋊Q₈	—	3	2	no	—
288	C₄⋊Q₈	—	15	2	no	—
289	C₄⋊Q₈	—	15	2	no	—
290	C₄⋊Q₈	—	15	2	no	—
291	C₄⋊Q₈	—	30	2	no	—
292	C₄⋊Q₈	—	30	2	no	—
293	C₂×C₄⋊C₄	—	5	2	no	—
294	C₂×C₄⋊C₄	—	15	2	no	—
295	C₂×C₄⋊C₄	—	30	2	no	—
296	C₂×C₄²	—	15	1	no	—
297	#107	—	3	1	no	—
298	#107	—	3	2	no	—
299	#107	—	5	1	no	—
300	#107	—	5	2	no	—
301	#107	—	15	2	no	—
302	#107	—	15	2	no	—
303	#107	—	15	2	no	—
304	#107	—	15	1	no	—
305	#107	—	15	2	no	—
306	#107	D₃×D₅	1	1	yes	characteristic
307	C₄×C₈	—	3	1	no	—
308	C₄×C₈	—	15	1	no	—
309	C₄×C₈	—	15	1	no	—
310	C₄×C₈	—	15	1	no	—
311	C₂×C₃×C₅	C₂×C₄⋊Q₈	1	1	yes	characteristic
312	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
313	C₂×C₃×C₅	C₂²×Q₁₆	1	1	yes	characteristic
314	C₃×D₅	#500	1	4	yes	complemented
315	C₂³×C₃	—	5	1	no	—
316	C₂×C₃×C₄	—	2	2	no	—
317	C₂×C₃×C₄	—	5	1	no	—
318	C₂×C₃×C₄	—	5	2	no	—
319	C₂×C₃×C₄	—	5	2	no	—
320	C₂×C₃×C₄	—	10	2	no	—
321	C₂×C₃×C₄	—	20	4	no	—
322	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
323	C₂×Dic₃	—	2	2	no	—
324	C₂×Dic₃	—	5	1	no	—
325	C₂×Dic₃	—	5	1	no	—
326	C₂×Dic₃	—	5	4	no	—
327	C₂×Dic₃	—	5	4	no	—
328	C₂×Dic₃	—	10	2	no	—
329	C₂×Dic₃	—	20	4	no	—
330	C₂×Dic₃	D₄×D₅	1	1	yes	characteristic
331	C₂×Dic₃	D₄×D₅	1	1	yes	characteristic
332	Dic₆	—	4	4	no	—
333	Dic₆	—	20	4	no	—
334	Dic₆	—	20	4	no	—
335	Dic₆	—	20	4	no	—
336	C₃×C₈	—	5	2	no	—
337	C₃×C₈	Q₈×D₅	1	2	yes	complemented
338	C₃⋊C₈	—	5	2	no	—
339	C₃⋊C₈	Q₈×D₅	1	2	yes	complemented
340	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
341	C₂×D₅	#888	1	2	yes	—
342	C₂×D₅	D₃×D₈	1	2	yes	—
343	C₂×D₅	D₃×Q₁₆	1	2	yes	—
344	C₄×C₅	—	3	2	no	—
345	C₄×C₅	—	3	2	no	—
346	C₄×C₅	—	4	2	no	—
347	C₄×C₅	—	12	2	no	—
348	C₄×C₅	C₂²×Dic₆	1	1	yes	characteristic
349	C₄×C₅	C₂×D₃×Q₈	1	1	yes	characteristic
350	Dic₅	—	3	2	no	—
351	Dic₅	—	3	2	no	—
352	Dic₅	—	4	2	no	—
353	Dic₅	—	12	2	no	—
354	Dic₅	#888	1	2	yes	—
355	C₂×Q₈	—	6	2	no	—
356	C₂×Q₈	—	30	2	no	—
357	C₂×Q₈	—	30	2	no	—
358	C₂×Q₈	—	30	2	no	—
359	C₂×Q₈	—	60	8	no	—
360	C₂²×C₄	—	5	1	no	—
361	C₂²×C₄	—	10	2	no	—
362	C₂²×C₄	—	15	1	no	—
363	C₂²×C₄	—	15	1	no	—
364	C₂²×C₄	—	30	2	no	—
365	C₂×C₈	—	3	1	no	—
366	C₂×C₈	—	5	1	no	—
367	C₂×C₈	—	5	4	no	—
368	C₂×C₈	—	15	4	no	—
369	C₂×C₈	—	15	1	no	—
370	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
371	C₄⋊C₄	—	3	2	no	—
372	C₄⋊C₄	—	5	2	no	—
373	C₄⋊C₄	—	6	2	no	—
374	C₄⋊C₄	—	10	2	no	—
375	C₄⋊C₄	—	15	2	no	—
376	C₄⋊C₄	—	30	2	no	—
377	C₄⋊C₄	—	30	2	no	—
378	C₄⋊C₄	—	30	2	no	—
379	C₄⋊C₄	—	30	2	no	—
380	C₄⋊C₄	C₂×D₃×D₅	1	2	yes	—
381	C₄²	—	3	1	no	—
382	C₄²	—	15	1	no	—
383	C₄²	—	15	1	no	—
384	C₄²	—	15	1	no	—
385	C₃×C₅	C₂×#500	1	1	yes	characteristic, complemented, Hall
386	C₂²×C₃	—	5	2	no	—
387	C₂²×C₃	—	5	2	no	—
388	C₂²×C₃	—	5	2	no	—
389	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
390	C₃×C₄	—	4	2	no	—
391	C₃×C₄	—	5	2	no	—
392	C₃×C₄	—	20	2	no	—
393	C₃×C₄	C₂×Q₈×D₅	1	1	yes	characteristic
394	C₃×C₄	C₂×Q₈×D₅	1	1	yes	characteristic
395	Dic₃	—	4	2	no	—
396	Dic₃	—	5	2	no	—
397	Dic₃	—	5	2	no	—
398	Dic₃	—	20	2	no	—
399	Dic₃	D₅×D₈	1	2	yes	—
400	Dic₃	D₅×Q₁₆	1	2	yes	—
401	C₂×C₅	C₂×#888	1	1	yes	characteristic
402	C₂×C₅	C₂×D₃×D₈	1	1	yes	characteristic
403	C₂×C₅	C₂×D₃×Q₁₆	1	1	yes	characteristic
404	D₅	#4874	1	4	yes	direct product factor
405	C₂³	—	5	1	no	—
406	Q₈	—	12	4	no	—
407	Q₈	—	60	4	no	—
408	Q₈	—	60	4	no	—
409	Q₈	—	60	4	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	3	1	no	—
412	C₂×C₄	—	3	1	no	—
413	C₂×C₄	—	5	1	no	—
414	C₂×C₄	—	5	2	no	—
415	C₂×C₄	—	5	2	no	—
416	C₂×C₄	—	6	2	no	—
417	C₂×C₄	—	10	2	no	—
418	C₂×C₄	—	15	4	no	—
419	C₂×C₄	—	15	4	no	—
420	C₂×C₄	—	15	1	no	—
421	C₂×C₄	—	15	1	no	—
422	C₂×C₄	—	20	4	no	—
423	C₂×C₄	—	30	2	no	—
424	C₂×C₄	—	60	4	no	—
425	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
426	C₈	—	3	2	no	—
427	C₈	—	5	2	no	—
428	C₈	—	15	2	no	—
429	C₈	D₅×Dic₆	1	2	yes	complemented
430	C₂×C₃	—	5	4	no	—
431	C₂×C₃	D₅×C₄⋊Q₈	1	1	yes	characteristic
432	C₂×C₃	C₂×D₅×D₈	1	1	yes	characteristic
433	C₂×C₃	C₂×D₅×Q₁₆	1	1	yes	characteristic
434	C₅	C₂×#4874	1	1	yes	characteristic, complemented, Sylow
435	C₂²	—	5	2	no	—
436	C₂²	—	5	2	no	—
437	C₂²	—	5	2	no	—
438	C₂²	D₃×D₄×D₅	1	1	yes	characteristic
439	C₄	—	3	2	no	—
440	C₄	—	3	2	no	—
441	C₄	—	4	2	no	—
442	C₄	—	5	2	no	—
443	C₄	—	12	2	no	—
444	C₄	—	15	2	no	—
445	C₄	—	15	2	no	—
446	C₄	—	20	2	no	—
447	C₄	—	60	2	no	—
448	C₄	C₂×D₅×Dic₆	1	1	yes	characteristic
449	C₄	D₃×Q₈×D₅	1	1	yes	characteristic
450	C₃	D₅×#500	1	1	yes	characteristic, complemented, Sylow
451	C₂	—	5	4	no	—
452	C₂	D₅×#888	1	1	yes	characteristic
453	C₂	D₃×D₅×D₈	1	1	yes	characteristic
454	C₂	D₃×D₅×Q₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₃×D₄×D₅
commutator, cosocle	C₂×C₃×C₄×C₅	C₂⁴
Frattini	C₂×C₄	C₂²×D₃×D₅
Fitting	C₃×C₅×#107	C₂²
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂²×C₃×D₅	C₂×D₄
hypercenter	#107	D₃×D₅
hypocenter	C₃×C₅	C₂×#500
LCS	G ▷ C₂×C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

Complements

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

N	H ≅ G/N	type
2. #11750975	C₂	semidirect
3. C₅×#4874	C₂	semidirect
5. #11748037	C₂	semidirect
6. #11748029	C₂	semidirect
10. #11747150	C₂	semidirect
11. #11747146	C₂	semidirect
75. C₃×C₈×D₅	Q₈	semidirect
81. D₅×C₃⋊C₈	Q₈	semidirect
92. #4874	D₅	direct (N × H)
142. C₃×C₅×C₈	C₂×Q₈	semidirect
143. C₃⋊#168	C₂×Q₈	semidirect
144. C₃×#168	C₂×Q₈	semidirect
145. C₅×C₃⋊C₈	C₂×Q₈	semidirect
202. C₈×D₅	Dic₆	semidirect
281. C₅×C₈	C₂×Dic₆	semidirect
283. #168	C₂×Dic₆	semidirect
314. C₃×D₅	#500	semidirect
337. C₃×C₈	Q₈×D₅	semidirect
339. C₃⋊C₈	Q₈×D₅	semidirect
385. C₃×C₅	C₂×#500	semidirect
404. D₅	#4874	direct (N × H)
429. C₈	D₅×Dic₆	semidirect
434. C₅	C₂×#4874	semidirect
450. C₃	D₅×#500	semidirect

Maximal subgroups

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

subgroup	index
D₅×#888	2
#11750975	2
C₅×#4874	2
C₃×D₅×#107	2
#11748037	2
#11748029	2
D₅×#818	2
C₈×D₅×Dic₃	2
D₅×#807	2
#11747150	2
#11747146	2
D₅×#500	3
C₂×#4874	5

Subgroups — D5×#4874 #14439816

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×#4874 #14439816