Subgroups — C₅×#81637 #14437779

Order 1920.

800 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5688	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5668	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#488	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5068	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5056	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4804	C₂	1	2	yes	maximal, complemented
7	C₅×#4792	C₂	1	2	yes	maximal, complemented
8	C₅×#4772	C₂	1	2	yes	maximal, complemented
9	C₅×#4760	C₂	1	2	yes	maximal, complemented
10	C₅×#4697	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₅×D₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3131	—	3	1	no	maximal, Hall
13	C₂×C₅×#239	C₂²	1	1	yes	characteristic
14	C₂×C₅×#237	C₂²	1	1	yes	characteristic
15	C₃×C₅×#125	C₂²	1	1	yes	characteristic
16	C₃×C₅×#124	C₂²	1	1	yes	characteristic
17	C₅×#944	C₂²	1	1	yes	characteristic
18	C₅×#940	C₂²	1	1	yes	characteristic
19	C₂×C₅×D₃×C₈	C₂²	1	2	yes	—
20	C₅×#896	—	2	2	no	—
21	C₅×#892	C₂²	1	2	yes	—
22	C₅×#888	C₂²	1	2	yes	—
23	C₅×#887	—	2	2	no	—
24	C₅×#884	—	2	2	no	—
25	C₅×#67⋊C₄	—	2	2	no	—
26	C₅×#875	C₂²	1	1	yes	characteristic
27	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
28	C₅×#870	C₂²	1	1	yes	characteristic
29	C₃×C₅×#103	C₂²	1	2	yes	—
30	C₃×C₅×#102	C₂²	1	2	yes	—
31	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
32	C₅×#835	C₂²	1	2	yes	—
33	C₅×#832	C₂²	1	2	yes	—
34	C₅×#821	C₂²	1	2	yes	—
35	C₅×#816	C₂²	1	2	yes	—
36	C₅×C₈×Dic₃	C₂²	1	2	yes	—
37	C₅×#810	C₂²	1	2	yes	—
38	C₅×#809	C₂²	1	2	yes	—
39	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
40	#81637	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
41	C₅×#533	—	3	1	no	—
42	C₅×#532	—	3	1	no	—
43	C₅×#488	—	3	1	no	—
44	C₅×#488	—	3	1	no	—
45	C₅×#488	—	3	1	no	—
46	C₅×#488	D₃	1	1	yes	characteristic, complemented
47	C₅×#487	—	3	2	no	—
48	C₅×#486	—	3	2	no	—
49	C₅×#416	—	3	2	no	—
50	C₅×#416	—	3	2	no	—
51	C₂×C₄×C₅×C₈	—	3	1	no	—
52	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
53	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
54	C₂×C₅×#67	—	2	1	no	—
55	C₂×C₅×#67	—	2	2	no	—
56	C₂²×C₅×Dic₃	—	2	1	no	—
57	C₅×#239	—	2	4	no	—
58	C₅×#237	—	2	4	no	—
59	C₂×C₅×D₁₂	—	2	1	no	—
60	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
61	C₂×C₄×C₅×D₃	—	2	1	no	—
62	C₂×C₄×C₅×D₃	D₄	1	2	yes	—
63	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
64	C₂×C₅×Dic₆	—	2	2	no	—
65	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
66	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
67	C₃×C₅×C₄⋊C₄	—	2	2	no	—
68	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
69	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
70	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
71	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
72	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
73	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
74	C₅×Dic₃⋊C₄	—	2	2	no	—
75	C₅×Dic₃⋊C₄	—	2	2	no	—
76	C₅×Dic₃⋊C₄	—	2	2	no	—
77	C₄×C₅×Dic₃	—	2	2	no	—
78	C₄×C₅×Dic₃	D₄	1	2	yes	—
79	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
80	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
81	C₅×D₃×C₈	—	2	4	no	—
82	#5688	C₂×C₅	1	1	yes	characteristic, complemented
83	#5668	C₂×C₅	1	1	yes	characteristic
84	C₃×#488	C₂×C₅	1	1	yes	characteristic, complemented
85	#5068	C₂×C₅	1	1	yes	characteristic, complemented
86	#5056	C₂×C₅	1	1	yes	characteristic, complemented
87	#4804	C₂×C₅	1	2	yes	complemented
88	#4792	C₂×C₅	1	2	yes	complemented
89	#4772	C₂×C₅	1	2	yes	complemented
90	#4760	C₂×C₅	1	2	yes	complemented
91	#4697	C₂×C₅	1	1	yes	characteristic, complemented
92	C₄×D₃×C₈	C₂×C₅	1	1	yes	characteristic, complemented
93	C₂×C₅×#41	—	3	1	no	—
94	C₂×C₅×#41	—	3	1	no	—
95	C₂²×C₅×C₈	—	3	2	no	—
96	C₅×C₄⋊Q₈	—	3	2	no	—
97	C₅×C₄⋊Q₈	—	3	1	no	—
98	C₅×#127	—	3	1	no	—
99	C₅×#125	—	3	1	no	—
100	C₅×#125	C₂×D₃	1	1	yes	characteristic
101	C₅×#124	—	3	1	no	—
102	C₅×#124	C₂×D₃	1	1	yes	characteristic
103	C₅×C₂²⋊Q₈	—	6	2	no	—
104	C₅×#121	—	6	2	no	—
105	C₄×C₅×Q₈	—	6	2	no	—
106	C₄×C₅×D₄	—	6	2	no	—
107	C₅×#117	—	3	2	no	—
108	C₂×C₄²×C₅	—	3	1	no	—
109	C₅×#103	—	3	2	no	—
110	C₅×#103	—	3	2	no	—
111	C₅×#103	—	3	2	no	—
112	C₅×#103	C₂×D₃	1	2	yes	—
113	C₅×#102	—	3	2	no	—
114	C₅×#102	—	3	2	no	—
115	C₅×#102	—	3	2	no	—
116	C₅×#102	C₂×D₃	1	2	yes	—
117	C₄×C₅×C₈	—	3	2	no	—
118	C₄×C₅×C₈	—	3	1	no	—
119	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
120	#3131	—	3	1	no	Sylow
121	C₂³×C₃×C₅	—	2	1	no	—
122	C₂²×C₅×D₃	—	2	1	no	—
123	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
124	C₃×C₅×Q₈	—	2	2	no	—
125	C₃×C₅×D₄	—	2	2	no	—
126	C₂×C₃×C₄×C₅	—	2	2	no	—
127	C₂×C₃×C₄×C₅	—	2	1	no	—
128	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
129	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
130	C₅×#67	—	4	2	no	—
131	C₅×#67	—	4	4	no	—
132	C₂×C₅×Dic₃	—	2	2	no	—
133	C₂×C₅×Dic₃	—	2	1	no	—
134	C₂×C₅×Dic₃	—	4	2	no	—
135	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
136	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
137	C₅×D₁₂	—	2	2	no	—
138	C₅×D₁₂	—	4	2	no	—
139	C₄×C₅×D₃	—	2	4	no	—
140	C₄×C₅×D₃	—	4	2	no	—
141	C₄×C₅×D₃	#41	1	4	yes	—
142	C₅×Dic₆	—	2	2	no	—
143	C₅×Dic₆	—	4	4	no	—
144	C₃×C₅×C₈	—	2	2	no	—
145	C₅×C₃⋊C₈	—	2	2	no	—
146	C₂×#239	C₂²×C₅	1	1	yes	characteristic
147	C₂×#237	C₂²×C₅	1	1	yes	characteristic
148	C₃×#125	C₂²×C₅	1	1	yes	characteristic
149	C₃×#124	C₂²×C₅	1	1	yes	characteristic
150	#944	C₂²×C₅	1	1	yes	characteristic
151	#940	C₂²×C₅	1	1	yes	characteristic
152	C₂×D₃×C₈	C₂²×C₅	1	2	yes	—
153	#896	—	2	2	no	—
154	#892	C₂²×C₅	1	2	yes	—
155	#888	C₂²×C₅	1	2	yes	—
156	#887	—	2	2	no	—
157	#884	—	2	2	no	—
158	#67⋊C₄	—	2	2	no	—
159	#875	C₂²×C₅	1	1	yes	characteristic
160	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
161	#870	C₂²×C₅	1	1	yes	characteristic
162	C₃×#103	C₂²×C₅	1	2	yes	—
163	C₃×#102	C₂²×C₅	1	2	yes	—
164	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
165	#835	C₂²×C₅	1	2	yes	—
166	#832	C₂²×C₅	1	2	yes	—
167	#821	C₂²×C₅	1	2	yes	—
168	#816	C₂²×C₅	1	2	yes	—
169	C₈×Dic₃	C₂²×C₅	1	2	yes	—
170	#810	C₂²×C₅	1	2	yes	—
171	#809	C₂²×C₅	1	2	yes	—
172	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
173	C₅×#41	—	6	4	no	—
174	C₅×#41	—	6	4	no	—
175	C₂×C₅×Q₈	—	3	1	no	—
176	C₂×C₅×Q₈	—	6	2	no	—
177	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
178	C₂×C₅×D₄	—	3	1	no	—
179	C₂×C₅×D₄	—	6	1	no	—
180	C₂×C₅×D₄	—	6	2	no	—
181	C₂×C₅×D₄	—	6	1	no	—
182	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
183	C₂²×C₄×C₅	—	3	1	no	—
184	C₂²×C₄×C₅	—	3	2	no	—
185	C₂²×C₄×C₅	—	6	1	no	—
186	C₂²×C₄×C₅	—	6	1	no	—
187	C₂×C₅×C₈	—	3	2	no	—
188	C₂×C₅×C₈	—	6	4	no	—
189	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
190	C₅×C₄⋊C₄	—	2	2	no	—
191	C₅×C₄⋊C₄	—	3	2	no	—
192	C₅×C₄⋊C₄	—	6	2	no	—
193	C₅×C₄⋊C₄	—	6	2	no	—
194	C₅×C₄⋊C₄	—	6	2	no	—
195	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
196	C₅×C₂²⋊C₄	—	2	2	no	—
197	C₅×C₂²⋊C₄	—	6	2	no	—
198	C₅×C₂²⋊C₄	—	6	2	no	—
199	C₄²×C₅	—	3	2	no	—
200	C₄²×C₅	—	3	1	no	—
201	C₄²×C₅	—	6	2	no	—
202	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
203	#533	—	3	1	no	—
204	#532	—	3	1	no	—
205	#488	—	3	1	no	—
206	#488	—	3	1	no	—
207	#488	—	3	1	no	—
208	#488	C₅×D₃	1	1	yes	characteristic, complemented
209	#487	—	3	2	no	—
210	#486	—	3	2	no	—
211	#416	—	3	2	no	—
212	#416	—	3	2	no	—
213	C₂×C₄×C₈	—	3	1	no	—
214	C₂²×C₃×C₅	—	4	1	no	—
215	C₂²×C₃×C₅	—	4	2	no	—
216	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
217	C₂×C₅×D₃	—	2	2	no	—
218	C₂×C₅×D₃	—	4	1	no	—
219	C₂×C₅×D₃	—	4	2	no	—
220	C₂×C₅×D₃	#124	1	2	yes	—
221	C₃×C₄×C₅	—	2	2	no	—
222	C₃×C₄×C₅	—	4	1	no	—
223	C₃×C₄×C₅	—	4	2	no	—
224	C₃×C₄×C₅	C₂×#41	1	2	yes	—
225	C₅×Dic₃	—	4	1	no	—
226	C₅×Dic₃	—	4	2	no	—
227	C₅×Dic₃	#124	1	2	yes	—
228	C₅×Dic₃	#135	1	4	yes	—
229	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
230	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
231	C₂×#67	—	2	1	no	—
232	C₂×#67	—	2	2	no	—
233	C₂²×Dic₃	—	2	1	no	—
234	#239	—	2	4	no	—
235	#237	—	2	4	no	—
236	C₂×D₁₂	—	2	1	no	—
237	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
238	C₂×C₄×D₃	—	2	1	no	—
239	C₂×C₄×D₃	C₅×D₄	1	2	yes	—
240	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
241	C₂×Dic₆	—	2	2	no	—
242	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
243	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
244	C₃×C₄⋊C₄	—	2	2	no	—
245	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
246	C₃×C₂²⋊C₄	—	2	2	no	—
247	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
248	(C₂×D₃)⋊C₄	—	2	2	no	—
249	(C₂×D₃)⋊C₄	—	2	2	no	—
250	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
251	Dic₃⋊C₄	—	2	2	no	—
252	Dic₃⋊C₄	—	2	2	no	—
253	Dic₃⋊C₄	—	2	2	no	—
254	C₄×Dic₃	—	2	2	no	—
255	C₄×Dic₃	C₅×D₄	1	2	yes	—
256	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
257	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
258	D₃×C₈	—	2	4	no	—
259	C₂³×C₅	—	2	1	no	—
260	C₂³×C₅	—	3	1	no	—
261	C₂³×C₅	—	6	1	no	—
262	C₅×Q₈	—	2	2	no	—
263	C₅×Q₈	—	6	2	no	—
264	C₅×Q₈	—	12	4	no	—
265	C₅×D₄	—	2	2	no	—
266	C₅×D₄	—	6	2	no	—
267	C₅×D₄	—	12	4	no	—
268	C₅×D₄	—	12	2	no	—
269	C₅×D₄	—	12	2	no	—
270	C₂×C₄×C₅	—	2	2	no	—
271	C₂×C₄×C₅	—	2	1	no	—
272	C₂×C₄×C₅	—	3	1	no	—
273	C₂×C₄×C₅	—	3	2	no	—
274	C₂×C₄×C₅	—	3	4	no	—
275	C₂×C₄×C₅	—	6	4	no	—
276	C₂×C₄×C₅	—	6	2	no	—
277	C₂×C₄×C₅	—	6	1	no	—
278	C₂×C₄×C₅	—	12	2	no	—
279	C₂×C₄×C₅	—	12	2	no	—
280	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
281	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
282	C₅×C₈	—	2	2	no	—
283	C₅×C₈	—	6	2	no	—
284	C₂×#41	—	3	1	no	—
285	C₂×#41	—	3	1	no	—
286	C₂²×C₈	—	3	2	no	—
287	C₄⋊Q₈	—	3	2	no	—
288	C₄⋊Q₈	—	3	1	no	—
289	#127	—	3	1	no	—
290	#125	—	3	1	no	—
291	#125	C₂×C₅×D₃	1	1	yes	characteristic
292	#124	—	3	1	no	—
293	#124	C₂×C₅×D₃	1	1	yes	characteristic
294	C₂²⋊Q₈	—	6	2	no	—
295	#121	—	6	2	no	—
296	C₄×Q₈	—	6	2	no	—
297	C₄×D₄	—	6	2	no	—
298	#117	—	3	2	no	—
299	C₂×C₄²	—	3	1	no	—
300	#103	—	3	2	no	—
301	#103	—	3	2	no	—
302	#103	—	3	2	no	—
303	#103	C₂×C₅×D₃	1	2	yes	—
304	#102	—	3	2	no	—
305	#102	—	3	2	no	—
306	#102	—	3	2	no	—
307	#102	C₂×C₅×D₃	1	2	yes	—
308	C₄×C₈	—	3	2	no	—
309	C₄×C₈	—	3	1	no	—
310	C₄×C₈	C₂×C₅×D₃	1	1	yes	characteristic
311	C₂×C₃×C₅	—	8	1	no	—
312	C₂×C₃×C₅	C₂×#124	1	1	yes	characteristic
313	C₂×C₃×C₅	C₂×#135	1	2	yes	—
314	C₅×D₃	—	2	2	no	—
315	C₅×D₃	—	8	1	no	—
316	C₂³×C₃	—	2	1	no	—
317	C₂²×D₃	—	2	1	no	—
318	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
319	C₃×Q₈	—	2	2	no	—
320	C₃×D₄	—	2	2	no	—
321	C₂×C₃×C₄	—	2	2	no	—
322	C₂×C₃×C₄	—	2	1	no	—
323	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
324	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
325	#67	—	4	2	no	—
326	#67	—	4	4	no	—
327	C₂×Dic₃	—	2	2	no	—
328	C₂×Dic₃	—	2	1	no	—
329	C₂×Dic₃	—	4	2	no	—
330	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
331	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
332	D₁₂	—	2	2	no	—
333	D₁₂	—	4	2	no	—
334	C₄×D₃	—	2	4	no	—
335	C₄×D₃	—	4	2	no	—
336	C₄×D₃	C₅×#41	1	4	yes	—
337	Dic₆	—	2	2	no	—
338	Dic₆	—	4	4	no	—
339	C₃×C₈	—	2	2	no	—
340	C₃⋊C₈	—	2	2	no	—
341	C₂²×C₅	—	3	2	no	—
342	C₂²×C₅	—	4	1	no	—
343	C₂²×C₅	—	4	2	no	—
344	C₂²×C₅	—	6	2	no	—
345	C₂²×C₅	—	12	1	no	—
346	C₂²×C₅	—	12	2	no	—
347	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
348	C₄×C₅	—	2	2	no	—
349	C₄×C₅	—	3	2	no	—
350	C₄×C₅	—	3	4	no	—
351	C₄×C₅	—	4	1	no	—
352	C₄×C₅	—	4	2	no	—
353	C₄×C₅	—	12	1	no	—
354	C₄×C₅	—	12	2	no	—
355	C₄×C₅	D₃×#41	1	2	yes	—
356	#41	—	6	4	no	—
357	#41	—	6	4	no	—
358	C₂×Q₈	—	3	1	no	—
359	C₂×Q₈	—	6	2	no	—
360	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
361	C₂×D₄	—	3	1	no	—
362	C₂×D₄	—	6	1	no	—
363	C₂×D₄	—	6	2	no	—
364	C₂×D₄	—	6	1	no	—
365	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
366	C₂²×C₄	—	3	1	no	—
367	C₂²×C₄	—	3	2	no	—
368	C₂²×C₄	—	6	1	no	—
369	C₂²×C₄	—	6	1	no	—
370	C₂×C₈	—	3	2	no	—
371	C₂×C₈	—	6	4	no	—
372	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	3	2	no	—
375	C₄⋊C₄	—	6	2	no	—
376	C₄⋊C₄	—	6	2	no	—
377	C₄⋊C₄	—	6	2	no	—
378	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
379	C₂²⋊C₄	—	2	2	no	—
380	C₂²⋊C₄	—	6	2	no	—
381	C₂²⋊C₄	—	6	2	no	—
382	C₄²	—	3	2	no	—
383	C₄²	—	3	1	no	—
384	C₄²	—	6	2	no	—
385	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
386	C₃×C₅	#3131	1	1	yes	characteristic, complemented, Hall
387	C₂²×C₃	—	4	1	no	—
388	C₂²×C₃	—	4	2	no	—
389	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
390	C₂×D₃	—	2	2	no	—
391	C₂×D₃	—	4	1	no	—
392	C₂×D₃	—	4	2	no	—
393	C₂×D₃	C₅×#124	1	2	yes	—
394	C₃×C₄	—	2	2	no	—
395	C₃×C₄	—	4	1	no	—
396	C₃×C₄	—	4	2	no	—
397	C₃×C₄	C₂×C₅×#41	1	2	yes	—
398	Dic₃	—	4	1	no	—
399	Dic₃	—	4	2	no	—
400	Dic₃	C₅×#124	1	2	yes	—
401	Dic₃	C₅×#135	1	4	yes	—
402	C₂×C₅	—	6	2	no	—
403	C₂×C₅	—	8	1	no	—
404	C₂×C₅	—	24	1	no	—
405	C₂×C₅	D₃×#124	1	1	yes	characteristic
406	C₂×C₅	D₃×#135	1	2	yes	—
407	C₂³	—	2	1	no	—
408	C₂³	—	3	1	no	—
409	C₂³	—	6	1	no	—
410	Q₈	—	2	2	no	—
411	Q₈	—	6	2	no	—
412	Q₈	—	12	4	no	—
413	D₄	—	2	2	no	—
414	D₄	—	6	2	no	—
415	D₄	—	12	4	no	—
416	D₄	—	12	2	no	—
417	D₄	—	12	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	3	1	no	—
421	C₂×C₄	—	3	2	no	—
422	C₂×C₄	—	3	4	no	—
423	C₂×C₄	—	6	4	no	—
424	C₂×C₄	—	6	2	no	—
425	C₂×C₄	—	6	1	no	—
426	C₂×C₄	—	12	2	no	—
427	C₂×C₄	—	12	2	no	—
428	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
429	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
430	C₈	—	2	2	no	—
431	C₈	—	6	2	no	—
432	C₂×C₃	—	8	1	no	—
433	C₂×C₃	C₂×C₅×#124	1	1	yes	characteristic
434	C₂×C₃	C₂×C₅×#135	1	2	yes	—
435	D₃	—	2	2	no	—
436	D₃	—	8	1	no	—
437	C₅	#81637	1	1	yes	characteristic, direct product factor, Sylow
438	C₂²	—	3	2	no	—
439	C₂²	—	4	1	no	—
440	C₂²	—	4	2	no	—
441	C₂²	—	6	2	no	—
442	C₂²	—	12	1	no	—
443	C₂²	—	12	2	no	—
444	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
445	C₄	—	2	2	no	—
446	C₄	—	3	2	no	—
447	C₄	—	3	4	no	—
448	C₄	—	4	1	no	—
449	C₄	—	4	2	no	—
450	C₄	—	12	1	no	—
451	C₄	—	12	2	no	—
452	C₄	C₅×D₃×#41	1	2	yes	—
453	C₃	C₅×#3131	1	1	yes	characteristic, complemented, Sylow
454	C₂	—	6	2	no	—
455	C₂	—	8	1	no	—
456	C₂	—	24	1	no	—
457	C₂	C₅×D₃×#124	1	1	yes	characteristic
458	C₂	C₅×D₃×#135	1	2	yes	—

	subgroup	G/H
center	C₂²×C₅	C₂×D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#488	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₅×#5668	C₂
hypercenter	C₅×#488	D₃
hypocenter	C₃	C₅×#3131
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#488

Complements

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

N	H ≅ G/N	type
1. C₅×#5688	C₂	semidirect
3. C₃×C₅×#488	C₂	semidirect
4. C₅×#5068	C₂	semidirect
5. C₅×#5056	C₂	semidirect
6. C₅×#4804	C₂	semidirect
7. C₅×#4792	C₂	semidirect
8. C₅×#4772	C₂	semidirect
9. C₅×#4760	C₂	semidirect
10. C₅×#4697	C₂	semidirect
11. C₄×C₅×D₃×C₈	C₂	semidirect
40. #81637	C₅	direct (N × H)
46. C₅×#488	D₃	semidirect
82. #5688	C₂×C₅	semidirect
84. C₃×#488	C₂×C₅	semidirect
85. #5068	C₂×C₅	semidirect
86. #5056	C₂×C₅	semidirect
87. #4804	C₂×C₅	semidirect
88. #4792	C₂×C₅	semidirect
89. #4772	C₂×C₅	semidirect
90. #4760	C₂×C₅	semidirect
91. #4697	C₂×C₅	semidirect
92. C₄×D₃×C₈	C₂×C₅	semidirect
208. #488	C₅×D₃	semidirect
386. C₃×C₅	#3131	semidirect
437. C₅	#81637	direct (N × H)
453. C₃	C₅×#3131	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5688	2
C₅×#5668	2
C₃×C₅×#488	2
C₅×#5068	2
C₅×#5056	2
C₅×#4804	2
C₅×#4792	2
C₅×#4772	2
C₅×#4760	2
C₅×#4697	2
C₄×C₅×D₃×C₈	2
C₅×#3131	3
#81637	5

Subgroups — C5×#81637 #14437779

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#81637 #14437779