Subgroups — C₅×#69040 #14303034

Order 1920.

680 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×#5745	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5525	C₂	1	1	yes	maximal, characteristic
3	C₅×#5132	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#823	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#823	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#344	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4533	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1914	—	3	1	no	maximal, Hall
9	C₂×C₅×#235	C₂²	1	1	yes	characteristic
10	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₅×M₁₆	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×C₅×#208	C₂²	1	1	yes	characteristic
15	C₂×C₅×#208	C₂²	1	1	yes	characteristic
16	C₅×#907	—	2	2	no	—
17	C₅×D₃×M₁₆	—	2	2	no	—
18	C₅×#901	—	2	2	no	—
19	C₅×#895	—	2	2	no	—
20	C₅×#882	C₄	1	4	yes	—
21	C₅×#875	—	2	1	no	—
22	C₅×#874	—	2	1	no	—
23	C₅×#824	—	2	1	no	—
24	C₅×#823	—	2	1	no	—
25	C₅×#823	—	2	2	no	—
26	C₅×#823	—	2	2	no	—
27	#69040	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
28	C₅×#568	—	3	1	no	—
29	C₅×#535	—	3	1	no	—
30	C₅×#413	—	3	1	no	—
31	C₂×C₅×#100	—	3	1	no	—
32	C₂×C₅×#100	—	3	1	no	—
33	C₅×#344	—	3	1	no	—
34	C₅×#344	D₃	1	1	yes	characteristic, complemented
35	C₂³×C₅×D₃	C₂×C₄	1	2	yes	—
36	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
37	C₂×C₅×#67	C₂×C₄	1	2	yes	—
38	C₅×#235	—	2	1	no	—
39	C₅×#235	—	2	1	no	—
40	C₅×#235	—	2	1	no	—
41	C₅×#235	—	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	1	no	—
46	C₂×C₅×D₁₂	—	2	1	no	—
47	C₂×C₅×D₁₂	—	2	1	no	—
48	C₂×C₅×D₁₂	—	2	4	no	—
49	C₂×C₅×D₁₂	D₄	1	1	yes	characteristic
50	C₂×C₄×C₅×D₃	D₄	1	2	yes	—
51	C₂×C₅×Dic₆	D₄	1	1	yes	characteristic
52	C₃×C₅×M₁₆	—	2	1	no	—
53	C₃×C₅×M₁₆	—	2	1	no	—
54	C₃×C₅×M₁₆	—	2	1	no	—
55	C₃×C₅×M₁₆	D₄	1	2	yes	complemented
56	C₂×C₃×C₅×C₈	—	2	1	no	—
57	C₂×C₃×C₅×C₈	—	2	1	no	—
58	C₃×C₅×C₄⋊C₄	—	2	1	no	—
59	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
60	C₃×C₄²×C₅	—	2	1	no	—
61	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
62	C₅×#208	—	2	1	no	—
63	C₅×#208	—	2	1	no	—
64	C₅×#208	—	2	1	no	—
65	C₅×#208	D₄	1	2	yes	complemented
66	C₂×C₅×C₃⋊C₈	—	2	1	no	—
67	C₂×C₅×C₃⋊C₈	—	2	1	no	—
68	C₅×ΓL(1,𝔽₂₅)	—	2	4	no	—
69	C₅×D₃×C₈	—	2	4	no	—
70	#5745	C₂×C₅	1	1	yes	characteristic, complemented
71	#5525	C₂×C₅	1	1	yes	characteristic
72	#5132	C₂×C₅	1	1	yes	characteristic, complemented
73	C₂×#823	C₂×C₅	1	1	yes	characteristic, complemented
74	C₂×#823	C₂×C₅	1	1	yes	characteristic, complemented
75	C₃×#344	C₂×C₅	1	1	yes	characteristic, complemented
76	#4533	C₂×C₅	1	1	yes	characteristic, complemented
77	C₂×C₅×#41	—	3	1	no	—
78	C₂²×C₅×D₄	—	3	1	no	—
79	C₅×#131	—	6	2	no	—
80	C₅×#131	—	6	2	no	—
81	C₂×C₅×M₁₆	—	3	1	no	—
82	C₂×C₅×M₁₆	—	3	1	no	—
83	C₂×C₅×M₁₆	—	6	2	no	—
84	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
85	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
86	C₅×#127	—	6	1	no	—
87	C₅×#124	—	6	1	no	—
88	C₅×#121	—	6	2	no	—
89	C₅×#120	—	3	4	no	—
90	C₅×#117	C₂×D₃	1	1	yes	characteristic
91	C₅×#101	—	6	1	no	—
92	C₅×#100	—	6	2	no	—
93	C₅×#100	—	6	1	no	—
94	C₅×#100	—	6	2	no	—
95	#1914	—	3	1	no	Sylow
96	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₅×D₃	—	2	2	no	—
98	C₂²×C₅×D₃	—	2	2	no	—
99	C₂²×C₅×D₃	—	2	2	no	—
100	C₂²×C₅×D₃	—	8	2	no	—
101	C₂²×C₅×D₃	C₂²⋊C₄	1	2	yes	—
102	C₂×C₃×C₄×C₅	—	2	2	no	—
103	C₂×C₃×C₄×C₅	C₂×D₄	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	C₅×#67	—	2	2	no	—
110	C₅×#67	—	2	2	no	—
111	C₂×C₅×Dic₃	C₂²⋊C₄	1	2	yes	—
112	C₅×D₁₂	—	2	1	no	—
113	C₅×D₁₂	—	2	1	no	—
114	C₅×D₁₂	—	4	1	no	—
115	C₅×D₁₂	—	4	1	no	—
116	C₅×D₁₂	—	4	1	no	—
117	C₅×D₁₂	—	4	1	no	—
118	C₅×D₁₂	—	8	4	no	—
119	C₄×C₅×D₃	—	2	2	no	—
120	C₄×C₅×D₃	—	2	2	no	—
121	C₅×Dic₆	—	2	1	no	—
122	C₅×Dic₆	—	2	1	no	—
123	C₃×C₅×C₈	—	2	2	no	—
124	C₃×C₅×C₈	—	4	1	no	—
125	C₅×C₃⋊C₈	—	2	2	no	—
126	C₅×C₃⋊C₈	—	4	1	no	—
127	C₂×#235	C₂²×C₅	1	1	yes	characteristic
128	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
129	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
130	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
131	C₃×#117	C₂²×C₅	1	1	yes	characteristic
132	C₂×#208	C₂²×C₅	1	1	yes	characteristic
133	C₂×#208	C₂²×C₅	1	1	yes	characteristic
134	#907	—	2	2	no	—
135	D₃×M₁₆	—	2	2	no	—
136	#901	—	2	2	no	—
137	#895	—	2	2	no	—
138	#882	C₄×C₅	1	4	yes	—
139	#875	—	2	1	no	—
140	#874	—	2	1	no	—
141	#824	—	2	1	no	—
142	#823	—	2	1	no	—
143	#823	—	2	2	no	—
144	#823	—	2	2	no	—
145	C₂⁴×C₅	—	3	2	no	—
146	C₅×#41	—	6	1	no	—
147	C₅×#41	—	6	1	no	—
148	C₅×#41	—	6	1	no	—
149	C₅×#41	—	6	1	no	—
150	C₂×C₅×Q₈	—	3	1	no	—
151	C₂×C₅×D₄	—	3	2	no	—
152	C₂×C₅×D₄	—	3	1	no	—
153	C₂×C₅×D₄	—	6	4	no	—
154	C₂×C₅×D₄	—	6	1	no	—
155	C₂×C₅×D₄	—	6	1	no	—
156	C₂×C₅×D₄	—	6	1	no	—
157	C₂×C₅×D₄	—	6	1	no	—
158	C₂×C₅×D₄	—	6	1	no	—
159	C₂×C₅×D₄	—	6	1	no	—
160	C₂²×C₄×C₅	—	3	2	no	—
161	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
162	C₅×M₁₆	—	2	1	no	—
163	C₅×M₁₆	—	2	1	no	—
164	C₅×M₁₆	—	2	1	no	—
165	C₅×M₁₆	—	3	2	no	—
166	C₅×M₁₆	—	6	4	no	—
167	C₅×M₁₆	—	6	1	no	—
168	C₅×M₁₆	—	6	1	no	—
169	C₅×M₁₆	—	6	1	no	—
170	C₅×M₁₆	D₁₂	1	2	yes	complemented
171	C₂×C₅×C₈	—	2	1	no	—
172	C₂×C₅×C₈	—	2	1	no	—
173	C₂×C₅×C₈	—	6	4	no	—
174	C₂×C₅×C₈	—	6	1	no	—
175	C₂×C₅×C₈	—	6	1	no	—
176	C₅×C₄⋊C₄	—	2	1	no	—
177	C₅×C₂²⋊C₄	—	6	4	no	—
178	C₅×C₂²⋊C₄	C₄×D₃	1	2	yes	—
179	C₄²×C₅	—	2	1	no	—
180	#568	—	3	1	no	—
181	#535	—	3	1	no	—
182	#413	—	3	1	no	—
183	C₂×#100	—	3	1	no	—
184	C₂×#100	—	3	1	no	—
185	#344	—	3	1	no	—
186	#344	C₅×D₃	1	1	yes	characteristic, complemented
187	C₂²×C₃×C₅	—	4	1	no	—
188	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
189	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
190	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
191	C₂×C₅×D₃	—	2	2	no	—
192	C₂×C₅×D₃	—	4	2	no	—
193	C₂×C₅×D₃	—	4	4	no	—
194	C₂×C₅×D₃	—	4	2	no	—
195	C₂×C₅×D₃	—	8	2	no	—
196	C₂×C₅×D₃	—	8	2	no	—
197	C₃×C₄×C₅	—	4	2	no	—
198	C₃×C₄×C₅	#120	1	1	yes	characteristic
199	C₃×C₄×C₅	#121	1	1	yes	characteristic
200	C₃×C₄×C₅	#121	1	1	yes	characteristic
201	C₃×C₄×C₅	#123	1	1	yes	characteristic
202	C₅×Dic₃	—	2	2	no	—
203	C₂³×D₃	C₂×C₄×C₅	1	2	yes	—
204	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
205	C₂×#67	C₂×C₄×C₅	1	2	yes	—
206	#235	—	2	1	no	—
207	#235	—	2	1	no	—
208	#235	—	2	1	no	—
209	#235	—	2	1	no	—
210	C₂×D₁₂	—	2	1	no	—
211	C₂×D₁₂	—	2	1	no	—
212	C₂×D₁₂	—	2	1	no	—
213	C₂×D₁₂	—	2	1	no	—
214	C₂×D₁₂	—	2	1	no	—
215	C₂×D₁₂	—	2	1	no	—
216	C₂×D₁₂	—	2	4	no	—
217	C₂×D₁₂	C₅×D₄	1	1	yes	characteristic
218	C₂×C₄×D₃	C₅×D₄	1	2	yes	—
219	C₂×Dic₆	C₅×D₄	1	1	yes	characteristic
220	C₃×M₁₆	—	2	1	no	—
221	C₃×M₁₆	—	2	1	no	—
222	C₃×M₁₆	—	2	1	no	—
223	C₃×M₁₆	C₅×D₄	1	2	yes	complemented
224	C₂×C₃×C₈	—	2	1	no	—
225	C₂×C₃×C₈	—	2	1	no	—
226	C₃×C₄⋊C₄	—	2	1	no	—
227	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
228	C₃×C₄²	—	2	1	no	—
229	(C₂×D₃)⋊C₄	—	2	4	no	—
230	#208	—	2	1	no	—
231	#208	—	2	1	no	—
232	#208	—	2	1	no	—
233	#208	C₅×D₄	1	2	yes	complemented
234	C₂×C₃⋊C₈	—	2	1	no	—
235	C₂×C₃⋊C₈	—	2	1	no	—
236	ΓL(1,𝔽₂₅)	—	2	4	no	—
237	D₃×C₈	—	2	4	no	—
238	C₂³×C₅	—	3	2	no	—
239	C₂³×C₅	—	6	2	no	—
240	C₂³×C₅	—	6	2	no	—
241	C₂³×C₅	—	6	2	no	—
242	C₂³×C₅	—	24	2	no	—
243	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
244	C₅×Q₈	—	6	1	no	—
245	C₅×Q₈	—	6	1	no	—
246	C₅×D₄	—	6	2	no	—
247	C₅×D₄	—	6	2	no	—
248	C₅×D₄	—	6	1	no	—
249	C₅×D₄	—	6	1	no	—
250	C₅×D₄	—	12	1	no	—
251	C₅×D₄	—	12	1	no	—
252	C₅×D₄	—	12	1	no	—
253	C₅×D₄	—	12	1	no	—
254	C₅×D₄	—	24	4	no	—
255	C₂×C₄×C₅	—	2	2	no	—
256	C₂×C₄×C₅	—	3	2	no	—
257	C₂×C₄×C₅	—	6	2	no	—
258	C₂×C₄×C₅	—	6	2	no	—
259	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
260	C₂×C₄×C₅	#235	1	1	yes	characteristic
261	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
262	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
263	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
264	C₂×C₄×C₅	#239	1	1	yes	characteristic
265	C₅×C₈	—	2	2	no	—
266	C₅×C₈	—	4	1	no	—
267	C₅×C₈	—	6	2	no	—
268	C₅×C₈	—	12	1	no	—
269	C₂×#41	—	3	1	no	—
270	C₂²×D₄	—	3	1	no	—
271	#131	—	6	2	no	—
272	#131	—	6	2	no	—
273	C₂×M₁₆	—	3	1	no	—
274	C₂×M₁₆	—	3	1	no	—
275	C₂×M₁₆	—	6	2	no	—
276	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
277	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
278	#127	—	6	1	no	—
279	#124	—	6	1	no	—
280	#121	—	6	2	no	—
281	#120	—	3	4	no	—
282	#117	C₂×C₅×D₃	1	1	yes	characteristic
283	#101	—	6	1	no	—
284	#100	—	6	2	no	—
285	#100	—	6	1	no	—
286	#100	—	6	2	no	—
287	C₂×C₃×C₅	—	2	1	no	—
288	C₂×C₃×C₅	—	2	1	no	—
289	C₂×C₃×C₅	—	2	1	no	—
290	C₂×C₃×C₅	#386	1	1	yes	characteristic
291	C₅×D₃	—	4	2	no	—
292	C₅×D₃	—	8	2	no	—
293	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
294	C₂²×D₃	—	2	2	no	—
295	C₂²×D₃	—	2	2	no	—
296	C₂²×D₃	—	2	2	no	—
297	C₂²×D₃	—	8	2	no	—
298	C₂²×D₃	C₅×C₂²⋊C₄	1	2	yes	—
299	C₂×C₃×C₄	—	2	2	no	—
300	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
301	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
302	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
303	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
304	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
305	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
306	#67	—	2	2	no	—
307	#67	—	2	2	no	—
308	C₂×Dic₃	C₅×C₂²⋊C₄	1	2	yes	—
309	D₁₂	—	2	1	no	—
310	D₁₂	—	2	1	no	—
311	D₁₂	—	4	1	no	—
312	D₁₂	—	4	1	no	—
313	D₁₂	—	4	1	no	—
314	D₁₂	—	4	1	no	—
315	D₁₂	—	8	4	no	—
316	C₄×D₃	—	2	2	no	—
317	C₄×D₃	—	2	2	no	—
318	Dic₆	—	2	1	no	—
319	Dic₆	—	2	1	no	—
320	C₃×C₈	—	2	2	no	—
321	C₃×C₈	—	4	1	no	—
322	C₃⋊C₈	—	2	2	no	—
323	C₃⋊C₈	—	4	1	no	—
324	C₂²×C₅	—	4	1	no	—
325	C₂²×C₅	—	6	2	no	—
326	C₂²×C₅	—	12	2	no	—
327	C₂²×C₅	—	12	4	no	—
328	C₂²×C₅	—	12	2	no	—
329	C₂²×C₅	—	24	2	no	—
330	C₂²×C₅	—	24	2	no	—
331	C₂²×C₅	C₄×D₁₂	1	1	yes	characteristic
332	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
333	C₂²×C₅	#893	1	1	yes	characteristic
334	C₄×C₅	—	4	2	no	—
335	C₄×C₅	—	6	2	no	—
336	C₄×C₅	#882	1	1	yes	characteristic
337	C₄×C₅	#884	1	1	yes	characteristic
338	C₄×C₅	#894	1	1	yes	characteristic
339	C₄×C₅	#895	1	1	yes	characteristic
340	C₂⁴	—	3	2	no	—
341	#41	—	6	1	no	—
342	#41	—	6	1	no	—
343	#41	—	6	1	no	—
344	#41	—	6	1	no	—
345	C₂×Q₈	—	3	1	no	—
346	C₂×D₄	—	3	2	no	—
347	C₂×D₄	—	3	1	no	—
348	C₂×D₄	—	6	4	no	—
349	C₂×D₄	—	6	1	no	—
350	C₂×D₄	—	6	1	no	—
351	C₂×D₄	—	6	1	no	—
352	C₂×D₄	—	6	1	no	—
353	C₂×D₄	—	6	1	no	—
354	C₂×D₄	—	6	1	no	—
355	C₂²×C₄	—	3	2	no	—
356	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
357	M₁₆	—	2	1	no	—
358	M₁₆	—	2	1	no	—
359	M₁₆	—	2	1	no	—
360	M₁₆	—	3	2	no	—
361	M₁₆	—	6	4	no	—
362	M₁₆	—	6	1	no	—
363	M₁₆	—	6	1	no	—
364	M₁₆	—	6	1	no	—
365	M₁₆	C₅×D₁₂	1	2	yes	complemented
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	—	2	1	no	—
368	C₂×C₈	—	6	4	no	—
369	C₂×C₈	—	6	1	no	—
370	C₂×C₈	—	6	1	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₂²⋊C₄	—	6	4	no	—
373	C₂²⋊C₄	C₄×C₅×D₃	1	2	yes	—
374	C₄²	—	2	1	no	—
375	C₃×C₅	#1914	1	1	yes	characteristic, complemented, Hall
376	C₂²×C₃	—	4	1	no	—
377	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
378	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
379	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
380	C₂×D₃	—	2	2	no	—
381	C₂×D₃	—	4	2	no	—
382	C₂×D₃	—	4	4	no	—
383	C₂×D₃	—	4	2	no	—
384	C₂×D₃	—	8	2	no	—
385	C₂×D₃	—	8	2	no	—
386	C₃×C₄	—	4	2	no	—
387	C₃×C₄	C₅×#120	1	1	yes	characteristic
388	C₃×C₄	C₅×#121	1	1	yes	characteristic
389	C₃×C₄	C₅×#121	1	1	yes	characteristic
390	C₃×C₄	C₅×#123	1	1	yes	characteristic
391	Dic₃	—	2	2	no	—
392	C₂×C₅	—	2	1	no	—
393	C₂×C₅	—	2	1	no	—
394	C₂×C₅	—	2	1	no	—
395	C₂×C₅	—	12	2	no	—
396	C₂×C₅	—	24	2	no	—
397	C₂×C₅	#4665	1	1	yes	characteristic
398	C₂³	—	3	2	no	—
399	C₂³	—	6	2	no	—
400	C₂³	—	6	2	no	—
401	C₂³	—	6	2	no	—
402	C₂³	—	24	2	no	—
403	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
404	Q₈	—	6	1	no	—
405	Q₈	—	6	1	no	—
406	D₄	—	6	2	no	—
407	D₄	—	6	2	no	—
408	D₄	—	6	1	no	—
409	D₄	—	6	1	no	—
410	D₄	—	12	1	no	—
411	D₄	—	12	1	no	—
412	D₄	—	12	1	no	—
413	D₄	—	12	1	no	—
414	D₄	—	24	4	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	3	2	no	—
417	C₂×C₄	—	6	2	no	—
418	C₂×C₄	—	6	2	no	—
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×D₃×D₄	1	1	yes	characteristic
424	C₂×C₄	C₅×#239	1	1	yes	characteristic
425	C₈	—	2	2	no	—
426	C₈	—	4	1	no	—
427	C₈	—	6	2	no	—
428	C₈	—	12	1	no	—
429	C₂×C₃	—	2	1	no	—
430	C₂×C₃	—	2	1	no	—
431	C₂×C₃	—	2	1	no	—
432	C₂×C₃	C₅×#386	1	1	yes	characteristic
433	D₃	—	4	2	no	—
434	D₃	—	8	2	no	—
435	C₅	#69040	1	1	yes	characteristic, direct product factor, Sylow
436	C₂²	—	4	1	no	—
437	C₂²	—	6	2	no	—
438	C₂²	—	12	2	no	—
439	C₂²	—	12	4	no	—
440	C₂²	—	12	2	no	—
441	C₂²	—	24	2	no	—
442	C₂²	—	24	2	no	—
443	C₂²	C₄×C₅×D₁₂	1	1	yes	characteristic
444	C₂²	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
445	C₂²	C₅×#893	1	1	yes	characteristic
446	C₄	—	4	2	no	—
447	C₄	—	6	2	no	—
448	C₄	C₅×#882	1	1	yes	characteristic
449	C₄	C₅×#884	1	1	yes	characteristic
450	C₄	C₅×#894	1	1	yes	characteristic
451	C₄	C₅×#895	1	1	yes	characteristic
452	C₃	C₅×#1914	1	1	yes	characteristic, complemented, Sylow
453	C₂	—	2	1	no	—
454	C₂	—	2	1	no	—
455	C₂	—	2	1	no	—
456	C₂	—	12	2	no	—
457	C₂	—	24	2	no	—
458	C₂	C₅×#4665	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅	#4665
commutator	C₂³×C₃	C₂²×C₄×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₃×C₅×#344	C₂
socle	C₂×C₃×C₅	#386
prime radical	C₅×#5525	C₂
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₅×#344	D₃
hypocenter	C₃	C₅×#1914
LCS	G ▷ C₂³×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#344

Complements

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

N	H ≅ G/N	type
1. C₅×#5745	C₂	semidirect
3. C₅×#5132	C₂	semidirect
4. C₂×C₅×#823	C₂	semidirect
5. C₂×C₅×#823	C₂	semidirect
6. C₃×C₅×#344	C₂	semidirect
7. C₅×#4533	C₂	semidirect
27. #69040	C₅	direct (N × H)
34. C₅×#344	D₃	semidirect
55. C₃×C₅×M₁₆	D₄	semidirect
65. C₅×#208	D₄	semidirect
70. #5745	C₂×C₅	semidirect
72. #5132	C₂×C₅	semidirect
73. C₂×#823	C₂×C₅	semidirect
74. C₂×#823	C₂×C₅	semidirect
75. C₃×#344	C₂×C₅	semidirect
76. #4533	C₂×C₅	semidirect
170. C₅×M₁₆	D₁₂	semidirect
186. #344	C₅×D₃	semidirect
223. C₃×M₁₆	C₅×D₄	semidirect
233. #208	C₅×D₄	semidirect
365. M₁₆	C₅×D₁₂	semidirect
375. C₃×C₅	#1914	semidirect
435. C₅	#69040	direct (N × H)
452. C₃	C₅×#1914	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5745	2
C₅×#5525	2
C₅×#5132	2
C₂×C₅×#823	2
C₃×C₅×#344	2
C₅×#4533	2
C₅×#1914	3
#69040	5

Subgroups — C5×#69040 #14303034

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#69040 #14303034