Subgroups — C₅×#68760 #14301525

Order 1920.

888 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×#5521	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#874	C₂	1	1	yes	maximal, characteristic
3	C₅×#5131	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#823	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5001	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#339	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4523	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1887	—	3	1	no	maximal, Hall
9	C₂²×C₅×D₁₂	—	2	2	no	—
10	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
11	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
13	C₃×C₅×#117	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
15	C₅×#926	C₂²	1	1	yes	characteristic
16	C₂×C₅×#208	C₂²	1	1	yes	characteristic
17	C₅×#893	—	2	2	no	—
18	C₅×D₃×C₂²⋊C₄	—	2	2	no	—
19	C₅×#874	—	2	2	no	—
20	C₅×#874	C₄	1	4	yes	complemented
21	C₄×C₅×D₁₂	—	2	2	no	—
22	C₅×#823	—	2	2	no	—
23	C₅×#821	—	2	2	no	—
24	C₅×#809	—	2	2	no	—
25	#68760	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
26	C₂×C₅×#127	—	3	1	no	—
27	C₅×#518	—	3	1	no	—
28	C₅×#418	—	3	1	no	—
29	C₅×#418	—	3	1	no	—
30	C₂×C₅×#100	—	3	1	no	—
31	C₅×#339	—	3	1	no	—
32	C₅×#339	D₃	1	1	yes	characteristic, complemented
33	C₂³×C₅×D₃	—	2	1	no	—
34	C₂³×C₅×D₃	D₄	1	2	yes	—
35	C₂²×C₃×C₄×C₅	—	2	1	no	—
36	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
37	C₂×C₅×D₁₂	—	2	1	no	—
38	C₂×C₅×D₁₂	—	2	1	no	—
39	C₂×C₅×D₁₂	—	2	1	no	—
40	C₂×C₅×D₁₂	—	2	1	no	—
41	C₂×C₅×D₁₂	—	2	1	no	—
42	C₂×C₅×D₁₂	—	2	1	no	—
43	C₂×C₅×D₁₂	—	2	1	no	—
44	C₂×C₅×D₁₂	—	2	1	no	—
45	C₂×C₅×D₁₂	—	2	8	no	—
46	C₂×C₅×D₁₂	—	2	1	no	—
47	C₂×C₅×D₁₂	—	4	8	no	—
48	C₂×C₅×D₁₂	C₂×C₄	1	2	yes	—
49	C₂×C₅×D₁₂	C₂×C₄	1	2	yes	complemented
50	C₂×C₅×D₁₂	D₄	1	2	yes	—
51	C₂×C₄×C₅×D₃	—	2	4	no	—
52	C₃×C₅×M₁₆	—	2	1	no	—
53	C₃×C₅×M₁₆	—	2	1	no	—
54	C₂×C₃×C₅×C₈	—	2	1	no	—
55	C₃×C₅×C₄⋊C₄	D₄	1	2	yes	complemented
56	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
57	C₃×C₄²×C₅	—	2	1	no	—
58	C₃×C₄²×C₅	—	2	1	no	—
59	C₃×C₄²×C₅	C₂×C₄	1	2	yes	complemented
60	C₅×#217	—	2	1	no	—
61	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
62	C₅×C₄⋊Dic₃	D₄	1	2	yes	complemented
63	C₄×C₅×Dic₃	—	2	1	no	—
64	C₅×#208	—	2	1	no	—
65	C₅×#208	—	2	1	no	—
66	C₂×C₅×C₃⋊C₈	—	2	1	no	—
67	#5521	C₂×C₅	1	1	yes	characteristic, complemented
68	C₂×#874	C₂×C₅	1	1	yes	characteristic
69	#5131	C₂×C₅	1	1	yes	characteristic, complemented
70	C₂×#823	C₂×C₅	1	1	yes	characteristic, complemented
71	#5001	C₂×C₅	1	1	yes	characteristic, complemented
72	C₃×#339	C₂×C₅	1	1	yes	characteristic, complemented
73	#4523	C₂×C₅	1	1	yes	characteristic, complemented
74	C₂²×C₅×D₄	—	3	1	no	—
75	C₂²×C₅×D₄	—	3	1	no	—
76	C₂²×C₅×D₄	—	6	2	no	—
77	C₂×C₅×M₁₆	—	3	1	no	—
78	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
79	C₅×#127	—	3	4	no	—
80	C₅×#127	—	6	2	no	—
81	C₄×C₅×D₄	—	6	2	no	—
82	C₄×C₅×D₄	—	6	2	no	—
83	C₅×#117	—	3	1	no	—
84	C₅×#117	C₂×D₃	1	1	yes	characteristic
85	C₂×C₅×C₂²⋊C₄	—	6	2	no	—
86	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
87	C₅×#102	—	6	2	no	—
88	C₅×#102	—	6	2	no	—
89	C₅×#100	—	6	2	no	—
90	#1887	—	3	1	no	Sylow
91	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₅×D₃	—	2	2	no	—
93	C₂²×C₅×D₃	—	2	2	no	—
94	C₂²×C₅×D₃	—	2	2	no	—
95	C₂²×C₅×D₃	—	4	4	no	—
96	C₂²×C₅×D₃	—	4	4	no	—
97	C₂²×C₅×D₃	—	4	1	no	—
98	C₂²×C₅×D₃	—	4	1	no	—
99	C₂²×C₅×D₃	C₂²⋊C₄	1	4	yes	—
100	C₂×C₃×C₄×C₅	—	2	4	no	—
101	C₂×C₃×C₄×C₅	—	2	2	no	—
102	C₂×C₃×C₄×C₅	—	2	2	no	—
103	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
105	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
106	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
107	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
108	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
109	C₂×C₅×Dic₃	—	2	2	no	—
110	C₅×D₁₂	—	2	2	no	—
111	C₅×D₁₂	—	2	2	no	—
112	C₅×D₁₂	—	2	2	no	—
113	C₅×D₁₂	—	2	2	no	—
114	C₅×D₁₂	—	2	2	no	—
115	C₅×D₁₂	—	2	2	no	—
116	C₅×D₁₂	—	4	16	no	—
117	C₅×D₁₂	—	4	1	no	—
118	C₅×D₁₂	—	4	1	no	—
119	C₄×C₅×D₃	—	8	4	no	—
120	C₃×C₅×C₈	—	4	1	no	—
121	C₅×C₃⋊C₈	—	4	1	no	—
122	C₂²×D₁₂	—	2	2	no	—
123	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
124	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
125	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
126	C₃×#117	C₂²×C₅	1	1	yes	characteristic
127	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
128	#926	C₂²×C₅	1	1	yes	characteristic
129	C₂×#208	C₂²×C₅	1	1	yes	characteristic
130	#893	—	2	2	no	—
131	D₃×C₂²⋊C₄	—	2	2	no	—
132	#874	—	2	2	no	—
133	#874	C₄×C₅	1	4	yes	complemented
134	C₄×D₁₂	—	2	2	no	—
135	#823	—	2	2	no	—
136	#821	—	2	2	no	—
137	#809	—	2	2	no	—
138	C₂⁴×C₅	—	3	2	no	—
139	C₂⁴×C₅	—	6	1	no	—
140	C₂×C₅×D₄	—	3	2	no	—
141	C₂×C₅×D₄	—	3	2	no	—
142	C₂×C₅×D₄	—	3	2	no	—
143	C₂×C₅×D₄	—	6	8	no	—
144	C₂×C₅×D₄	—	6	1	no	—
145	C₂×C₅×D₄	—	6	1	no	—
146	C₂×C₅×D₄	—	6	1	no	—
147	C₂×C₅×D₄	—	6	1	no	—
148	C₂×C₅×D₄	—	6	1	no	—
149	C₂×C₅×D₄	—	6	1	no	—
150	C₂×C₅×D₄	—	6	1	no	—
151	C₂×C₅×D₄	—	6	1	no	—
152	C₂×C₅×D₄	—	6	1	no	—
153	C₂×C₅×D₄	—	12	8	no	—
154	C₂²×C₄×C₅	—	2	1	no	—
155	C₂²×C₄×C₅	—	6	4	no	—
156	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
157	C₅×M₁₆	—	2	1	no	—
158	C₅×M₁₆	—	2	1	no	—
159	C₅×M₁₆	—	6	1	no	—
160	C₅×M₁₆	—	6	1	no	—
161	C₂×C₅×C₈	—	2	1	no	—
162	C₂×C₅×C₈	—	6	1	no	—
163	C₅×C₄⋊C₄	—	3	2	no	—
164	C₅×C₄⋊C₄	D₁₂	1	2	yes	complemented
165	C₅×C₂²⋊C₄	—	2	1	no	—
166	C₅×C₂²⋊C₄	—	6	4	no	—
167	C₅×C₂²⋊C₄	—	6	1	no	—
168	C₄²×C₅	—	2	1	no	—
169	C₄²×C₅	—	2	1	no	—
170	C₄²×C₅	—	6	1	no	—
171	C₄²×C₅	C₄×D₃	1	2	yes	complemented
172	C₂×#127	—	3	1	no	—
173	#518	—	3	1	no	—
174	#418	—	3	1	no	—
175	#418	—	3	1	no	—
176	C₂×#100	—	3	1	no	—
177	#339	—	3	1	no	—
178	#339	C₅×D₃	1	1	yes	characteristic, complemented
179	C₂²×C₃×C₅	—	2	2	no	—
180	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
181	C₂²×C₃×C₅	#120	1	1	yes	characteristic
182	C₂²×C₃×C₅	#123	1	1	yes	characteristic
183	C₂×C₅×D₃	—	2	4	no	—
184	C₂×C₅×D₃	—	4	4	no	—
185	C₂×C₅×D₃	—	4	4	no	—
186	C₂×C₅×D₃	—	4	4	no	—
187	C₂×C₅×D₃	—	4	2	no	—
188	C₂×C₅×D₃	—	8	2	no	—
189	C₂×C₅×D₃	—	8	2	no	—
190	C₂×C₅×D₃	—	8	2	no	—
191	C₃×C₄×C₅	—	2	4	no	—
192	C₃×C₄×C₅	—	4	2	no	—
193	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
194	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
195	C₃×C₄×C₅	#121	1	1	yes	characteristic
196	C₃×C₄×C₅	#121	1	1	yes	characteristic
197	C₅×Dic₃	—	4	2	no	—
198	C₂³×D₃	—	2	1	no	—
199	C₂³×D₃	C₅×D₄	1	2	yes	—
200	C₂²×C₃×C₄	—	2	1	no	—
201	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
202	C₂×D₁₂	—	2	1	no	—
203	C₂×D₁₂	—	2	1	no	—
204	C₂×D₁₂	—	2	1	no	—
205	C₂×D₁₂	—	2	1	no	—
206	C₂×D₁₂	—	2	1	no	—
207	C₂×D₁₂	—	2	1	no	—
208	C₂×D₁₂	—	2	1	no	—
209	C₂×D₁₂	—	2	1	no	—
210	C₂×D₁₂	—	2	8	no	—
211	C₂×D₁₂	—	2	1	no	—
212	C₂×D₁₂	—	4	8	no	—
213	C₂×D₁₂	C₂×C₄×C₅	1	2	yes	—
214	C₂×D₁₂	C₂×C₄×C₅	1	2	yes	complemented
215	C₂×D₁₂	C₅×D₄	1	2	yes	—
216	C₂×C₄×D₃	—	2	4	no	—
217	C₃×M₁₆	—	2	1	no	—
218	C₃×M₁₆	—	2	1	no	—
219	C₂×C₃×C₈	—	2	1	no	—
220	C₃×C₄⋊C₄	C₅×D₄	1	2	yes	complemented
221	C₃×C₂²⋊C₄	—	2	1	no	—
222	C₃×C₄²	—	2	1	no	—
223	C₃×C₄²	—	2	1	no	—
224	C₃×C₄²	C₂×C₄×C₅	1	2	yes	complemented
225	#217	—	2	1	no	—
226	(C₂×D₃)⋊C₄	—	2	4	no	—
227	C₄⋊Dic₃	C₅×D₄	1	2	yes	complemented
228	C₄×Dic₃	—	2	1	no	—
229	#208	—	2	1	no	—
230	#208	—	2	1	no	—
231	C₂×C₃⋊C₈	—	2	1	no	—
232	C₂³×C₅	—	3	4	no	—
233	C₂³×C₅	—	6	2	no	—
234	C₂³×C₅	—	6	2	no	—
235	C₂³×C₅	—	6	2	no	—
236	C₂³×C₅	—	12	4	no	—
237	C₂³×C₅	—	12	4	no	—
238	C₂³×C₅	—	12	1	no	—
239	C₂³×C₅	—	12	1	no	—
240	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
241	C₅×D₄	—	6	2	no	—
242	C₅×D₄	—	6	2	no	—
243	C₅×D₄	—	6	2	no	—
244	C₅×D₄	—	6	2	no	—
245	C₅×D₄	—	6	2	no	—
246	C₅×D₄	—	6	2	no	—
247	C₅×D₄	—	12	16	no	—
248	C₅×D₄	—	12	1	no	—
249	C₅×D₄	—	12	1	no	—
250	C₂×C₄×C₅	—	2	4	no	—
251	C₂×C₄×C₅	—	2	2	no	—
252	C₂×C₄×C₅	—	2	2	no	—
253	C₂×C₄×C₅	—	6	2	no	—
254	C₂×C₄×C₅	—	24	4	no	—
255	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
256	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
257	C₂×C₄×C₅	#235	1	1	yes	characteristic
258	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
259	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
260	C₂×C₄×C₅	#239	1	1	yes	characteristic
261	C₅×C₈	—	4	1	no	—
262	C₅×C₈	—	12	1	no	—
263	C₂²×D₄	—	3	1	no	—
264	C₂²×D₄	—	3	1	no	—
265	C₂²×D₄	—	6	2	no	—
266	C₂×M₁₆	—	3	1	no	—
267	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
268	#127	—	3	4	no	—
269	#127	—	6	2	no	—
270	C₄×D₄	—	6	2	no	—
271	C₄×D₄	—	6	2	no	—
272	#117	—	3	1	no	—
273	#117	C₂×C₅×D₃	1	1	yes	characteristic
274	C₂×C₂²⋊C₄	—	6	2	no	—
275	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
276	#102	—	6	2	no	—
277	#102	—	6	2	no	—
278	#100	—	6	2	no	—
279	C₂×C₃×C₅	—	2	1	no	—
280	C₂×C₃×C₅	—	2	1	no	—
281	C₂×C₃×C₅	#386	1	1	yes	characteristic
282	C₂×C₃×C₅	#453	1	2	yes	—
283	C₅×D₃	—	4	4	no	—
284	C₅×D₃	—	8	2	no	—
285	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
286	C₂²×D₃	—	2	2	no	—
287	C₂²×D₃	—	2	2	no	—
288	C₂²×D₃	—	2	2	no	—
289	C₂²×D₃	—	4	4	no	—
290	C₂²×D₃	—	4	4	no	—
291	C₂²×D₃	—	4	1	no	—
292	C₂²×D₃	—	4	1	no	—
293	C₂²×D₃	C₅×C₂²⋊C₄	1	4	yes	—
294	C₂×C₃×C₄	—	2	4	no	—
295	C₂×C₃×C₄	—	2	2	no	—
296	C₂×C₃×C₄	—	2	2	no	—
297	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
298	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
299	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
300	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
301	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
302	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
303	C₂×Dic₃	—	2	2	no	—
304	D₁₂	—	2	2	no	—
305	D₁₂	—	2	2	no	—
306	D₁₂	—	2	2	no	—
307	D₁₂	—	2	2	no	—
308	D₁₂	—	2	2	no	—
309	D₁₂	—	2	2	no	—
310	D₁₂	—	4	16	no	—
311	D₁₂	—	4	1	no	—
312	D₁₂	—	4	1	no	—
313	C₄×D₃	—	8	4	no	—
314	C₃×C₈	—	4	1	no	—
315	C₃⋊C₈	—	4	1	no	—
316	C₂²×C₅	—	2	2	no	—
317	C₂²×C₅	—	6	4	no	—
318	C₂²×C₅	—	12	4	no	—
319	C₂²×C₅	—	12	4	no	—
320	C₂²×C₅	—	12	4	no	—
321	C₂²×C₅	—	12	2	no	—
322	C₂²×C₅	—	24	2	no	—
323	C₂²×C₅	—	24	2	no	—
324	C₂²×C₅	—	24	2	no	—
325	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
326	C₂²×C₅	#882	1	1	yes	characteristic
327	C₂²×C₅	#894	1	1	yes	characteristic
328	C₄×C₅	—	2	4	no	—
329	C₄×C₅	—	4	2	no	—
330	C₄×C₅	—	12	2	no	—
331	C₄×C₅	C₄×D₁₂	1	1	yes	characteristic
332	C₄×C₅	#884	1	1	yes	characteristic
333	C₄×C₅	#893	1	1	yes	characteristic
334	C₄×C₅	#895	1	1	yes	characteristic
335	C₂⁴	—	3	2	no	—
336	C₂⁴	—	6	1	no	—
337	C₂×D₄	—	3	2	no	—
338	C₂×D₄	—	3	2	no	—
339	C₂×D₄	—	3	2	no	—
340	C₂×D₄	—	6	8	no	—
341	C₂×D₄	—	6	1	no	—
342	C₂×D₄	—	6	1	no	—
343	C₂×D₄	—	6	1	no	—
344	C₂×D₄	—	6	1	no	—
345	C₂×D₄	—	6	1	no	—
346	C₂×D₄	—	6	1	no	—
347	C₂×D₄	—	6	1	no	—
348	C₂×D₄	—	6	1	no	—
349	C₂×D₄	—	6	1	no	—
350	C₂×D₄	—	12	8	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	6	4	no	—
353	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
354	M₁₆	—	2	1	no	—
355	M₁₆	—	2	1	no	—
356	M₁₆	—	6	1	no	—
357	M₁₆	—	6	1	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	6	1	no	—
360	C₄⋊C₄	—	3	2	no	—
361	C₄⋊C₄	C₅×D₁₂	1	2	yes	complemented
362	C₂²⋊C₄	—	2	1	no	—
363	C₂²⋊C₄	—	6	4	no	—
364	C₂²⋊C₄	—	6	1	no	—
365	C₄²	—	2	1	no	—
366	C₄²	—	2	1	no	—
367	C₄²	—	6	1	no	—
368	C₄²	C₄×C₅×D₃	1	2	yes	complemented
369	C₃×C₅	#1887	1	1	yes	characteristic, complemented, Hall
370	C₂²×C₃	—	2	2	no	—
371	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
372	C₂²×C₃	C₅×#120	1	1	yes	characteristic
373	C₂²×C₃	C₅×#123	1	1	yes	characteristic
374	C₂×D₃	—	2	4	no	—
375	C₂×D₃	—	4	4	no	—
376	C₂×D₃	—	4	4	no	—
377	C₂×D₃	—	4	4	no	—
378	C₂×D₃	—	4	2	no	—
379	C₂×D₃	—	8	2	no	—
380	C₂×D₃	—	8	2	no	—
381	C₂×D₃	—	8	2	no	—
382	C₃×C₄	—	2	4	no	—
383	C₃×C₄	—	4	2	no	—
384	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
385	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
386	C₃×C₄	C₅×#121	1	1	yes	characteristic
387	C₃×C₄	C₅×#121	1	1	yes	characteristic
388	Dic₃	—	4	2	no	—
389	C₂×C₅	—	2	1	no	—
390	C₂×C₅	—	2	1	no	—
391	C₂×C₅	—	12	4	no	—
392	C₂×C₅	—	24	2	no	—
393	C₂×C₅	#4665	1	1	yes	characteristic
394	C₂×C₅	#4822	1	2	yes	—
395	C₂³	—	3	4	no	—
396	C₂³	—	6	2	no	—
397	C₂³	—	6	2	no	—
398	C₂³	—	6	2	no	—
399	C₂³	—	12	4	no	—
400	C₂³	—	12	4	no	—
401	C₂³	—	12	1	no	—
402	C₂³	—	12	1	no	—
403	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
404	D₄	—	6	2	no	—
405	D₄	—	6	2	no	—
406	D₄	—	6	2	no	—
407	D₄	—	6	2	no	—
408	D₄	—	6	2	no	—
409	D₄	—	6	2	no	—
410	D₄	—	12	16	no	—
411	D₄	—	12	1	no	—
412	D₄	—	12	1	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	6	2	no	—
417	C₂×C₄	—	24	4	no	—
418	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
419	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
420	C₂×C₄	C₅×#235	1	1	yes	characteristic
421	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
422	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
423	C₂×C₄	C₅×#239	1	1	yes	characteristic
424	C₈	—	4	1	no	—
425	C₈	—	12	1	no	—
426	C₂×C₃	—	2	1	no	—
427	C₂×C₃	—	2	1	no	—
428	C₂×C₃	C₅×#386	1	1	yes	characteristic
429	C₂×C₃	C₅×#453	1	2	yes	—
430	D₃	—	4	4	no	—
431	D₃	—	8	2	no	—
432	C₅	#68760	1	1	yes	characteristic, direct product factor, Sylow
433	C₂²	—	2	2	no	—
434	C₂²	—	6	4	no	—
435	C₂²	—	12	4	no	—
436	C₂²	—	12	4	no	—
437	C₂²	—	12	4	no	—
438	C₂²	—	12	2	no	—
439	C₂²	—	24	2	no	—
440	C₂²	—	24	2	no	—
441	C₂²	—	24	2	no	—
442	C₂²	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
443	C₂²	C₅×#882	1	1	yes	characteristic
444	C₂²	C₅×#894	1	1	yes	characteristic
445	C₄	—	2	4	no	—
446	C₄	—	4	2	no	—
447	C₄	—	12	2	no	—
448	C₄	C₄×C₅×D₁₂	1	1	yes	characteristic
449	C₄	C₅×#884	1	1	yes	characteristic
450	C₄	C₅×#893	1	1	yes	characteristic
451	C₄	C₅×#895	1	1	yes	characteristic
452	C₃	C₅×#1887	1	1	yes	characteristic, complemented, Sylow
453	C₂	—	2	1	no	—
454	C₂	—	2	1	no	—
455	C₂	—	12	4	no	—
456	C₂	—	24	2	no	—
457	C₂	C₅×#4665	1	1	yes	characteristic
458	C₂	C₅×#4822	1	2	yes	—

	subgroup	G/H
center	C₂²×C₅	#882
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₃×C₅×#339	C₂
socle	C₂²×C₃×C₅	#120
prime radical	C₂×C₅×#874	C₂
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₅×#339	D₃
hypocenter	C₃	C₅×#1887
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#339

Complements

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

N	H ≅ G/N	type
1. C₅×#5521	C₂	semidirect
3. C₅×#5131	C₂	semidirect
4. C₂×C₅×#823	C₂	semidirect
5. C₅×#5001	C₂	semidirect
6. C₃×C₅×#339	C₂	semidirect
7. C₅×#4523	C₂	semidirect
20. C₅×#874	C₄	semidirect
25. #68760	C₅	direct (N × H)
32. C₅×#339	D₃	semidirect
49. C₂×C₅×D₁₂	C₂×C₄	semidirect
55. C₃×C₅×C₄⋊C₄	D₄	semidirect
59. C₃×C₄²×C₅	C₂×C₄	semidirect
62. C₅×C₄⋊Dic₃	D₄	semidirect
67. #5521	C₂×C₅	semidirect
69. #5131	C₂×C₅	semidirect
70. C₂×#823	C₂×C₅	semidirect
71. #5001	C₂×C₅	semidirect
72. C₃×#339	C₂×C₅	semidirect
73. #4523	C₂×C₅	semidirect
133. #874	C₄×C₅	semidirect
164. C₅×C₄⋊C₄	D₁₂	semidirect
171. C₄²×C₅	C₄×D₃	semidirect
178. #339	C₅×D₃	semidirect
214. C₂×D₁₂	C₂×C₄×C₅	semidirect
220. C₃×C₄⋊C₄	C₅×D₄	semidirect
224. C₃×C₄²	C₂×C₄×C₅	semidirect
227. C₄⋊Dic₃	C₅×D₄	semidirect
361. C₄⋊C₄	C₅×D₁₂	semidirect
368. C₄²	C₄×C₅×D₃	semidirect
369. C₃×C₅	#1887	semidirect
432. C₅	#68760	direct (N × H)
452. C₃	C₅×#1887	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5521	2
C₂×C₅×#874	2
C₅×#5131	2
C₂×C₅×#823	2
C₅×#5001	2
C₃×C₅×#339	2
C₅×#4523	2
C₅×#1887	3
#68760	5

Subgroups — C5×#68760 #14301525

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#68760 #14301525