Subgroups — D₅×#4878 #14439798

Order 1920.

720 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×#890	C₂	1	2	yes	maximal
2	#11750979	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#4878	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×D₅×#107	C₂	1	1	yes	maximal, characteristic
5	#11747992	C₂	1	1	yes	maximal, characteristic, complemented
6	#11747989	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×#808	C₂	1	2	yes	maximal
10	#11747151	C₂	1	2	yes	maximal, complemented
11	#11747148	C₂	1	2	yes	maximal, complemented
12	D₅×#499	—	3	1	no	maximal, Hall
13	#91779	C₂²	1	2	yes	—
14	C₅×#890	C₂²	1	2	yes	—
15	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
16	C₃×D₅×C₄⋊C₄	C₂²	1	2	yes	—
17	D₅×C₄⋊Dic₃	—	2	2	no	—
18	D₅×C₄⋊Dic₃	C₂²	1	2	yes	—
19	D₅×Dic₃⋊C₄	—	2	2	no	—
20	C₄×D₅×Dic₃	C₂²	1	1	yes	characteristic
21	#91384	C₂²	1	2	yes	—
22	#91381	C₂²	1	2	yes	—
23	#91335	—	2	2	no	—
24	#91334	—	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	#91092	C₂²	1	2	yes	—
30	C₅×#818	C₂²	1	1	yes	characteristic
31	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic
32	C₅×#808	C₂²	1	2	yes	—
33	C₃×#3950	C₂²	1	1	yes	characteristic
34	C₃×#3939	C₂²	1	2	yes	—
35	#90988	C₂²	1	2	yes	—
36	#90987	C₂²	1	2	yes	—
37	#90986	C₂²	1	2	yes	—
38	#90951	C₂²	1	1	yes	characteristic
39	Dic₃×#168	C₂²	1	1	yes	characteristic
40	C₂×#4878	—	5	1	no	maximal, Hall
41	D₅×#125	—	3	2	no	—
42	C₅×#499	—	3	1	no	—
43	#65353	—	3	2	no	—
44	D₅×#107	—	3	1	no	—
45	D₅×#107	D₃	1	1	yes	characteristic
46	#65167	—	3	1	no	—
47	#65167	—	3	1	no	—
48	D₅×#106	—	3	2	no	—
49	#65147	—	3	2	no	—
50	C₄×C₈×D₅	—	3	1	no	—
51	#64972	—	3	1	no	—
52	C₂×C₃×C₄×D₅	—	2	2	no	—
53	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
54	C₂×D₅×Dic₃	—	2	2	no	—
55	C₂×D₅×Dic₃	D₄	1	1	yes	characteristic
56	C₂×D₅×Dic₃	D₄	1	1	yes	characteristic
57	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
58	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
59	C₄⋊Dic₁₅	—	2	2	no	—
60	C₄⋊Dic₁₅	C₂³	1	2	yes	—
61	#6712	—	2	2	no	—
62	C₄×Dic₁₅	C₂³	1	1	yes	characteristic
63	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
64	C₅×C₄⋊Dic₃	—	2	2	no	—
65	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
66	C₅×Dic₃⋊C₄	—	2	2	no	—
67	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
68	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
69	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
70	C₃×#683	—	2	2	no	—
71	C₂×C₃×#168	C₂³	1	1	yes	characteristic
72	C₃×C₈×D₅	Q₈	1	4	yes	—
73	Dic₃⋊Dic₅	—	2	2	no	—
74	#6669	—	2	2	no	—
75	#6668	—	2	2	no	—
76	#6668	—	2	2	no	—
77	#6668	—	2	2	no	—
78	Dic₃×Dic₅	D₄	1	1	yes	characteristic
79	Dic₃×Dic₅	D₄	1	1	yes	characteristic
80	D₅×C₃⋊C₈	Q₈	1	4	yes	—
81	C₂×#890	—	5	2	no	—
82	C₂×C₃×#107	—	5	1	no	—
83	C₂×#818	—	5	1	no	—
84	C₂×C₈×Dic₃	—	5	1	no	—
85	C₂×#808	—	5	2	no	—
86	#4878	—	5	2	no	—
87	#4878	—	5	1	no	—
88	#4878	—	5	1	no	—
89	#4878	—	5	1	no	—
90	#4878	—	5	2	no	—
91	#4878	D₅	1	1	yes	characteristic, direct product factor
92	C₅×#125	—	3	2	no	—
93	C₂×C₈×D₅	—	3	1	no	—
94	C₂×C₈×D₅	C₂×D₃	1	1	yes	characteristic
95	D₅×C₄⋊C₄	—	3	2	no	—
96	D₅×C₄⋊C₄	—	6	2	no	—
97	D₅×C₄⋊C₄	—	6	2	no	—
98	D₅×C₄⋊C₄	C₂×D₃	1	2	yes	—
99	#4036	—	3	2	no	—
100	#4036	—	3	2	no	—
101	#4035	—	6	2	no	—
102	#4035	—	6	2	no	—
103	C₄²×D₅	—	3	1	no	—
104	#4016	—	3	2	no	—
105	C₅×#107	—	3	1	no	—
106	C₅×#107	C₂×D₃	1	1	yes	characteristic
107	C₅×#106	—	3	2	no	—
108	C₄×C₅×C₈	—	3	1	no	—
109	#3950	—	3	1	no	—
110	#3950	C₂×D₃	1	1	yes	characteristic
111	#3949	—	3	2	no	—
112	C₈×Dic₅	—	3	1	no	—
113	C₈×Dic₅	—	3	1	no	—
114	#3940	—	3	2	no	—
115	#3940	—	3	2	no	—
116	#3939	—	3	2	no	—
117	#3939	C₂×D₃	1	2	yes	—
118	C₄×#168	—	3	1	no	—
119	C₂×#499	—	15	1	no	Sylow
120	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
121	C₂×C₃×C₄×C₅	—	2	2	no	—
122	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
123	C₂×Dic₁₅	—	2	2	no	—
124	C₂×Dic₁₅	C₂×D₄	1	1	yes	characteristic
125	C₂×Dic₁₅	C₂×D₄	1	1	yes	characteristic
126	C₂×C₅×Dic₃	—	2	2	no	—
127	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
128	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
129	C₂×C₃×Dic₅	—	2	2	no	—
130	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
131	C₃×C₄×D₅	—	4	4	no	—
132	C₃×C₄×D₅	C₂×Q₈	1	2	yes	—
133	C₃×C₄×D₅	C₂×Q₈	1	2	yes	—
134	D₅×Dic₃	—	2	2	no	—
135	D₅×Dic₃	—	2	2	no	—
136	D₅×Dic₃	—	4	4	no	—
137	C₃×C₅×C₈	C₂×Q₈	1	2	yes	—
138	C₃⋊#168	C₂×Q₈	1	2	yes	—
139	C₃×#168	C₂×Q₈	1	2	yes	—
140	C₅×C₃⋊C₈	C₂×Q₈	1	2	yes	—
141	C₂²×C₃×C₈	—	5	1	no	—
142	C₂×C₃×C₄⋊C₄	—	5	2	no	—
143	C₂×C₄⋊Dic₃	—	5	2	no	—
144	C₂×C₄⋊Dic₃	—	10	2	no	—
145	C₂×Dic₃⋊C₄	—	10	2	no	—
146	C₂×C₄×Dic₃	—	5	1	no	—
147	C₂²×C₃⋊C₈	—	5	1	no	—
148	#890	—	5	2	no	—
149	#890	—	5	2	no	—
150	#890	—	5	2	no	—
151	#890	—	10	2	no	—
152	#890	—	10	2	no	—
153	#890	C₂×D₅	1	2	yes	—
154	C₃×#107	—	5	1	no	—
155	C₃×#107	—	5	2	no	—
156	C₃×#107	C₂×D₅	1	1	yes	characteristic
157	#818	—	5	1	no	—
158	#818	—	5	2	no	—
159	#818	C₂×D₅	1	1	yes	characteristic
160	C₈×Dic₃	—	5	1	no	—
161	C₈×Dic₃	—	5	1	no	—
162	C₈×Dic₃	—	5	1	no	—
163	C₈×Dic₃	C₂×D₅	1	1	yes	characteristic
164	#808	—	5	2	no	—
165	#808	—	5	2	no	—
166	#808	—	5	2	no	—
167	#808	C₂×D₅	1	2	yes	—
168	C₂×C₄×D₅	—	2	2	no	—
169	C₂×C₄×D₅	—	3	1	no	—
170	C₂×C₄×D₅	—	3	1	no	—
171	C₂×C₄×D₅	—	6	2	no	—
172	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
173	C₂×C₅×C₈	—	3	1	no	—
174	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
175	C₅×C₄⋊C₄	—	3	2	no	—
176	C₅×C₄⋊C₄	—	6	2	no	—
177	C₅×C₄⋊C₄	—	6	2	no	—
178	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
179	C₄²×C₅	—	3	1	no	—
180	C₄⋊Dic₅	—	3	2	no	—
181	C₄⋊Dic₅	—	6	2	no	—
182	C₄⋊Dic₅	—	6	2	no	—
183	C₄⋊Dic₅	C₂²×D₃	1	2	yes	—
184	#683	—	2	2	no	—
185	#683	—	6	2	no	—
186	#683	—	6	2	no	—
187	#683	—	6	2	no	—
188	#683	—	6	2	no	—
189	#683	—	6	2	no	—
190	C₄×Dic₅	—	3	1	no	—
191	C₄×Dic₅	—	3	1	no	—
192	C₄×Dic₅	—	3	1	no	—
193	C₂×#168	—	3	1	no	—
194	C₂×#168	C₂²×D₃	1	1	yes	characteristic
195	C₈×D₅	—	3	4	no	—
196	C₈×D₅	Dic₆	1	4	yes	—
197	C₂×#125	—	15	2	no	—
198	#499	—	3	1	no	—
199	#499	—	15	1	no	—
200	#499	—	15	2	no	—
201	#499	—	15	1	no	—
202	#499	—	15	2	no	—
203	#499	—	15	1	no	—
204	C₂×#107	—	5	1	no	—
205	C₂×#107	—	15	1	no	—
206	C₂×#106	—	15	2	no	—
207	C₂×C₄×C₈	—	15	1	no	—
208	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
209	C₂×C₃×D₅	C₄⋊Q₈	1	2	yes	—
210	C₂×C₃×D₅	#135	1	2	yes	—
211	C₂×C₃×D₅	#135	1	2	yes	—
212	C₃×C₄×C₅	—	4	2	no	—
213	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
214	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
215	Dic₁₅	—	2	1	no	—
216	Dic₁₅	—	2	1	no	—
217	Dic₁₅	—	4	2	no	—
218	C₃×Dic₅	—	4	2	no	—
219	C₃×Dic₅	C₄⋊Q₈	1	2	yes	—
220	C₅×Dic₃	—	2	1	no	—
221	C₅×Dic₃	—	2	1	no	—
222	C₅×Dic₃	—	4	2	no	—
223	C₂²×C₃×C₄	—	5	1	no	—
224	C₂²×C₃×C₄	—	10	2	no	—
225	C₂²×Dic₃	—	5	1	no	—
226	C₂²×Dic₃	—	5	1	no	—
227	C₂²×Dic₃	—	10	2	no	—
228	C₂×C₃×C₈	—	5	1	no	—
229	C₂×C₃×C₈	—	5	4	no	—
230	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
231	C₃×C₄⋊C₄	—	5	2	no	—
232	C₃×C₄⋊C₄	—	10	2	no	—
233	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
234	C₄⋊Dic₃	—	2	2	no	—
235	C₄⋊Dic₃	—	5	2	no	—
236	C₄⋊Dic₃	—	10	2	no	—
237	C₄⋊Dic₃	—	10	2	no	—
238	C₄⋊Dic₃	—	10	2	no	—
239	C₄⋊Dic₃	—	10	2	no	—
240	C₄⋊Dic₃	C₂²×D₅	1	2	yes	—
241	Dic₃⋊C₄	—	2	2	no	—
242	Dic₃⋊C₄	—	10	2	no	—
243	Dic₃⋊C₄	—	10	2	no	—
244	Dic₃⋊C₄	—	10	2	no	—
245	C₄×Dic₃	—	5	1	no	—
246	C₄×Dic₃	—	5	1	no	—
247	C₄×Dic₃	—	5	1	no	—
248	C₄×Dic₃	C₂²×D₅	1	1	yes	characteristic
249	C₂×C₃⋊C₈	—	5	1	no	—
250	C₂×C₃⋊C₈	—	5	4	no	—
251	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
252	C₂²×D₅	D₃×D₄	1	1	yes	characteristic
253	C₂×C₄×C₅	—	2	2	no	—
254	C₂×C₄×C₅	—	3	1	no	—
255	C₂×C₄×C₅	—	3	1	no	—
256	C₂×C₄×C₅	—	6	2	no	—
257	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
258	C₂×Dic₅	—	2	2	no	—
259	C₂×Dic₅	—	3	1	no	—
260	C₂×Dic₅	—	3	1	no	—
261	C₂×Dic₅	—	6	2	no	—
262	C₂×Dic₅	D₃×D₄	1	1	yes	characteristic
263	C₄×D₅	—	4	4	no	—
264	C₄×D₅	—	6	2	no	—
265	C₄×D₅	—	6	2	no	—
266	C₄×D₅	—	12	4	no	—
267	C₄×D₅	C₂×Dic₆	1	2	yes	—
268	C₄×D₅	D₃×Q₈	1	2	yes	—
269	C₅×C₈	—	3	2	no	—
270	C₅×C₈	C₂×Dic₆	1	2	yes	—
271	#168	—	3	2	no	—
272	#168	C₂×Dic₆	1	2	yes	—
273	C₂²×C₈	—	5	1	no	—
274	C₂²×C₈	—	15	1	no	—
275	#125	—	3	2	no	—
276	#125	—	15	2	no	—
277	#125	—	15	2	no	—
278	#125	—	15	2	no	—
279	#125	—	30	2	no	—
280	#125	—	30	2	no	—
281	C₂×C₄⋊C₄	—	5	2	no	—
282	C₂×C₄⋊C₄	—	15	2	no	—
283	C₂×C₄⋊C₄	—	30	2	no	—
284	C₂×C₄⋊C₄	—	30	2	no	—
285	C₂×C₄²	—	15	1	no	—
286	#107	—	3	1	no	—
287	#107	—	5	1	no	—
288	#107	—	5	2	no	—
289	#107	—	15	2	no	—
290	#107	—	15	1	no	—
291	#107	D₃×D₅	1	1	yes	characteristic
292	#106	—	3	2	no	—
293	#106	—	15	2	no	—
294	#106	—	15	2	no	—
295	#106	—	15	2	no	—
296	C₄×C₈	—	3	1	no	—
297	C₄×C₈	—	15	1	no	—
298	C₄×C₈	—	15	1	no	—
299	C₄×C₈	—	15	1	no	—
300	C₂×C₃×C₅	C₂×C₄⋊Q₈	1	1	yes	characteristic
301	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
302	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
303	C₃×D₅	#499	1	4	yes	complemented
304	C₂³×C₃	—	5	1	no	—
305	C₂×C₃×C₄	—	2	2	no	—
306	C₂×C₃×C₄	—	5	1	no	—
307	C₂×C₃×C₄	—	5	2	no	—
308	C₂×C₃×C₄	—	5	2	no	—
309	C₂×C₃×C₄	—	10	2	no	—
310	C₂×C₃×C₄	—	20	4	no	—
311	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
312	C₂×Dic₃	—	2	2	no	—
313	C₂×Dic₃	—	5	1	no	—
314	C₂×Dic₃	—	5	1	no	—
315	C₂×Dic₃	—	10	2	no	—
316	C₂×Dic₃	—	10	2	no	—
317	C₂×Dic₃	—	10	2	no	—
318	C₂×Dic₃	—	20	4	no	—
319	C₂×Dic₃	D₄×D₅	1	1	yes	characteristic
320	C₂×Dic₃	D₄×D₅	1	1	yes	characteristic
321	C₃×C₈	—	5	2	no	—
322	C₃×C₈	Q₈×D₅	1	2	yes	—
323	C₃⋊C₈	—	5	2	no	—
324	C₃⋊C₈	Q₈×D₅	1	2	yes	—
325	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
326	C₂×D₅	#888	1	2	yes	—
327	C₂×D₅	#912	1	2	yes	—
328	C₂×D₅	#919	1	2	yes	—
329	C₄×C₅	—	4	2	no	—
330	C₄×C₅	—	6	1	no	—
331	C₄×C₅	—	6	1	no	—
332	C₄×C₅	—	12	2	no	—
333	C₄×C₅	C₂²×Dic₆	1	1	yes	characteristic
334	C₄×C₅	C₂×D₃×Q₈	1	1	yes	characteristic
335	Dic₅	—	4	2	no	—
336	Dic₅	—	6	1	no	—
337	Dic₅	—	6	1	no	—
338	Dic₅	—	12	2	no	—
339	Dic₅	#888	1	2	yes	—
340	C₂²×C₄	—	5	1	no	—
341	C₂²×C₄	—	10	2	no	—
342	C₂²×C₄	—	15	1	no	—
343	C₂²×C₄	—	15	1	no	—
344	C₂²×C₄	—	30	2	no	—
345	C₂×C₈	—	3	1	no	—
346	C₂×C₈	—	5	1	no	—
347	C₂×C₈	—	5	4	no	—
348	C₂×C₈	—	15	4	no	—
349	C₂×C₈	—	15	1	no	—
350	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
351	C₄⋊C₄	—	3	2	no	—
352	C₄⋊C₄	—	5	2	no	—
353	C₄⋊C₄	—	6	2	no	—
354	C₄⋊C₄	—	6	2	no	—
355	C₄⋊C₄	—	10	2	no	—
356	C₄⋊C₄	—	15	2	no	—
357	C₄⋊C₄	—	30	2	no	—
358	C₄⋊C₄	—	30	2	no	—
359	C₄⋊C₄	—	30	2	no	—
360	C₄⋊C₄	—	30	2	no	—
361	C₄⋊C₄	—	30	2	no	—
362	C₄⋊C₄	—	30	2	no	—
363	C₄⋊C₄	—	30	2	no	—
364	C₄⋊C₄	C₂×D₃×D₅	1	2	yes	—
365	C₄²	—	3	1	no	—
366	C₄²	—	15	1	no	—
367	C₄²	—	15	1	no	—
368	C₄²	—	15	1	no	—
369	C₃×C₅	C₂×#499	1	1	yes	characteristic, complemented, Hall
370	C₂²×C₃	—	5	2	no	—
371	C₂²×C₃	—	5	2	no	—
372	C₂²×C₃	—	5	2	no	—
373	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
374	C₃×C₄	—	4	2	no	—
375	C₃×C₄	—	5	2	no	—
376	C₃×C₄	—	20	2	no	—
377	C₃×C₄	C₂×Q₈×D₅	1	1	yes	characteristic
378	C₃×C₄	C₂×Q₈×D₅	1	1	yes	characteristic
379	Dic₃	—	2	1	no	—
380	Dic₃	—	2	1	no	—
381	Dic₃	—	4	2	no	—
382	Dic₃	—	10	1	no	—
383	Dic₃	—	10	1	no	—
384	Dic₃	—	20	2	no	—
385	C₂×C₅	C₂×#888	1	1	yes	characteristic
386	C₂×C₅	C₂×#912	1	1	yes	characteristic
387	C₂×C₅	C₂×#919	1	1	yes	characteristic
388	D₅	#4878	1	4	yes	direct product factor
389	C₂³	—	5	1	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	3	1	no	—
392	C₂×C₄	—	3	1	no	—
393	C₂×C₄	—	5	1	no	—
394	C₂×C₄	—	5	2	no	—
395	C₂×C₄	—	5	2	no	—
396	C₂×C₄	—	6	2	no	—
397	C₂×C₄	—	10	2	no	—
398	C₂×C₄	—	15	1	no	—
399	C₂×C₄	—	15	1	no	—
400	C₂×C₄	—	20	4	no	—
401	C₂×C₄	—	30	2	no	—
402	C₂×C₄	—	30	2	no	—
403	C₂×C₄	—	30	2	no	—
404	C₂×C₄	—	60	4	no	—
405	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
406	C₈	—	3	2	no	—
407	C₈	—	5	2	no	—
408	C₈	—	15	2	no	—
409	C₈	D₅×Dic₆	1	2	yes	—
410	C₂×C₃	—	5	4	no	—
411	C₂×C₃	D₅×C₄⋊Q₈	1	1	yes	characteristic
412	C₂×C₃	D₅×#135	1	1	yes	characteristic
413	C₂×C₃	D₅×#135	1	1	yes	characteristic
414	C₅	C₂×#4878	1	1	yes	characteristic, complemented, Sylow
415	C₂²	—	5	2	no	—
416	C₂²	—	5	2	no	—
417	C₂²	—	5	2	no	—
418	C₂²	D₃×D₄×D₅	1	1	yes	characteristic
419	C₄	—	4	2	no	—
420	C₄	—	5	2	no	—
421	C₄	—	6	1	no	—
422	C₄	—	6	1	no	—
423	C₄	—	12	2	no	—
424	C₄	—	20	2	no	—
425	C₄	—	30	1	no	—
426	C₄	—	30	1	no	—
427	C₄	—	60	2	no	—
428	C₄	C₂×D₅×Dic₆	1	1	yes	characteristic
429	C₄	D₃×Q₈×D₅	1	1	yes	characteristic
430	C₃	D₅×#499	1	1	yes	characteristic, complemented, Sylow
431	C₂	—	5	4	no	—
432	C₂	D₅×#888	1	1	yes	characteristic
433	C₂	D₅×#912	1	1	yes	characteristic
434	C₂	D₅×#919	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×#499
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. #11750979	C₂	semidirect
3. C₅×#4878	C₂	semidirect
5. #11747992	C₂	semidirect
6. #11747989	C₂	semidirect
10. #11747151	C₂	semidirect
11. #11747148	C₂	semidirect
91. #4878	D₅	direct (N × H)
303. C₃×D₅	#499	semidirect
369. C₃×C₅	C₂×#499	semidirect
388. D₅	#4878	direct (N × H)
414. C₅	C₂×#4878	semidirect
430. C₃	D₅×#499	semidirect

Maximal subgroups

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

subgroup	index
D₅×#890	2
#11750979	2
C₅×#4878	2
C₃×D₅×#107	2
#11747992	2
#11747989	2
D₅×#818	2
C₈×D₅×Dic₃	2
D₅×#808	2
#11747151	2
#11747148	2
D₅×#499	3
C₂×#4878	5

Subgroups — D5×#4878 #14439798

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×#4878 #14439798