Subgroups — C₅×#70064 #14306113

Order 1920.

792 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#940	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×#100	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#833	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	C₅×#5118	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×Dic₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1965	—	3	1	no	maximal, Hall
9	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
10	C₂²×C₅×#67	C₄	1	4	yes	—
11	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
14	C₅×#940	—	2	1	no	—
15	C₅×#940	—	2	2	no	—
16	C₅×#940	—	2	1	no	—
17	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
18	C₂×C₅×#208	C₂²	1	1	yes	characteristic
19	C₂×C₅×#208	C₂²	1	1	yes	characteristic
20	C₃×C₅×#100	—	2	2	no	—
21	C₅×#833	—	2	2	no	—
22	C₅×#823	—	2	2	no	—
23	C₅×#823	—	2	2	no	—
24	C₅×#815	—	2	1	no	—
25	C₅×Dic₃⋊C₈	—	2	2	no	—
26	C₅×C₈×Dic₃	—	2	1	no	—
27	#70064	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
28	C₂×C₅×#127	—	3	1	no	—
29	C₅×#423	—	3	1	no	—
30	C₂×C₅×#100	—	3	1	no	—
31	C₂×C₅×#100	—	3	1	no	—
32	C₂×C₅×#100	—	3	1	no	—
33	C₂×C₅×#100	D₃	1	1	yes	characteristic, complemented
34	C₄×C₅×M₁₆	—	3	1	no	—
35	C₂⁴×C₃×C₅	C₂×C₄	1	2	yes	—
36	C₂³×C₅×D₃	C₂×C₄	1	2	yes	—
37	C₂×C₃×C₅×D₄	—	2	1	no	—
38	C₂×C₃×C₅×D₄	—	2	1	no	—
39	C₂×C₃×C₅×D₄	—	2	1	no	—
40	C₂×C₃×C₅×D₄	—	2	1	no	—
41	C₂×C₃×C₅×D₄	—	2	1	no	—
42	C₂×C₃×C₅×D₄	—	2	1	no	—
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₂×C₅×#67	—	2	4	no	—
45	C₂×C₅×#67	—	2	4	no	—
46	C₂×C₅×#67	—	4	8	no	—
47	C₂²×C₅×Dic₃	C₂×C₄	1	2	yes	—
48	C₂×C₅×D₁₂	—	2	1	no	—
49	C₂×C₅×D₁₂	—	2	1	no	—
50	C₂×C₅×D₁₂	—	2	1	no	—
51	C₂×C₅×D₁₂	—	2	1	no	—
52	C₂×C₅×D₁₂	—	2	1	no	—
53	C₂×C₅×D₁₂	—	2	1	no	—
54	C₃×C₅×M₁₆	—	2	1	no	—
55	C₃×C₅×M₁₆	—	2	1	no	—
56	C₃×C₅×M₁₆	—	2	1	no	—
57	C₃×C₅×M₁₆	D₄	1	2	yes	complemented
58	C₂×C₃×C₅×C₈	—	2	1	no	—
59	C₂×C₃×C₅×C₈	—	2	1	no	—
60	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
61	C₄×C₅×Dic₃	D₄	1	2	yes	—
62	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
63	C₅×#208	—	2	1	no	—
64	C₅×#208	—	2	1	no	—
65	C₅×#208	—	2	1	no	—
66	C₅×#208	D₄	1	2	yes	complemented
67	C₂×C₅×C₃⋊C₈	—	2	1	no	—
68	C₂×C₅×C₃⋊C₈	—	2	1	no	—
69	C₂×#940	C₂×C₅	1	1	yes	characteristic
70	C₂×C₃×#100	C₂×C₅	1	1	yes	characteristic, complemented
71	C₂×#833	C₂×C₅	1	1	yes	characteristic, complemented
72	C₂×#823	C₂×C₅	1	1	yes	characteristic, complemented
73	C₂×#823	C₂×C₅	1	1	yes	characteristic, complemented
74	#5118	C₂×C₅	1	1	yes	characteristic, complemented
75	Dic₃×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
76	C₂²×C₅×D₄	—	3	4	no	—
77	C₂²×C₅×D₄	—	3	1	no	—
78	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
79	C₂×C₅×M₁₆	—	3	1	no	—
80	C₂×C₅×M₁₆	—	3	1	no	—
81	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
82	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
83	C₅×#127	—	6	1	no	—
84	C₅×#127	—	6	1	no	—
85	C₅×#127	—	6	2	no	—
86	C₂×C₄²×C₅	—	3	1	no	—
87	C₅×C₄⋊C₈	—	6	2	no	—
88	C₅×#100	—	2	2	no	—
89	C₅×#100	—	6	2	no	—
90	C₅×#100	—	6	2	no	—
91	C₅×#100	—	6	2	no	—
92	C₅×#97	—	6	1	no	—
93	C₄×C₅×C₈	—	6	1	no	—
94	#1965	—	3	1	no	Sylow
95	C₂³×C₃×C₅	—	2	2	no	—
96	C₂³×C₃×C₅	—	2	2	no	—
97	C₂³×C₃×C₅	—	2	2	no	—
98	C₂³×C₃×C₅	—	4	4	no	—
99	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₅×D₃	—	2	2	no	—
101	C₂²×C₅×D₃	—	2	2	no	—
102	C₂²×C₅×D₃	—	2	2	no	—
103	C₂²×C₅×D₃	—	4	4	no	—
104	C₃×C₅×D₄	—	4	1	no	—
105	C₃×C₅×D₄	—	4	1	no	—
106	C₃×C₅×D₄	—	4	1	no	—
107	C₃×C₅×D₄	—	4	1	no	—
108	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
109	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
110	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
111	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
112	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
113	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
114	C₅×#67	—	4	8	no	—
115	C₅×#67	—	4	8	no	—
116	C₂×C₅×Dic₃	—	2	4	no	—
117	C₂×C₅×Dic₃	C₂²⋊C₄	1	2	yes	—
118	C₂×C₅×Dic₃	C₂²⋊C₄	1	2	yes	—
119	C₅×D₁₂	—	4	1	no	—
120	C₅×D₁₂	—	4	1	no	—
121	C₅×D₁₂	—	4	1	no	—
122	C₅×D₁₂	—	4	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	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
128	C₂²×#67	C₄×C₅	1	4	yes	—
129	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
130	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
131	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
132	#940	—	2	1	no	—
133	#940	—	2	2	no	—
134	#940	—	2	1	no	—
135	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
136	C₂×#208	C₂²×C₅	1	1	yes	characteristic
137	C₂×#208	C₂²×C₅	1	1	yes	characteristic
138	C₃×#100	—	2	2	no	—
139	#833	—	2	2	no	—
140	#823	—	2	2	no	—
141	#823	—	2	2	no	—
142	#815	—	2	1	no	—
143	Dic₃⋊C₈	—	2	2	no	—
144	C₈×Dic₃	—	2	1	no	—
145	C₂⁴×C₅	—	3	2	no	—
146	C₂⁴×C₅	C₄×D₃	1	2	yes	—
147	C₂×C₅×D₄	—	2	1	no	—
148	C₂×C₅×D₄	—	2	1	no	—
149	C₂×C₅×D₄	—	2	1	no	—
150	C₂×C₅×D₄	—	2	1	no	—
151	C₂×C₅×D₄	—	2	1	no	—
152	C₂×C₅×D₄	—	2	1	no	—
153	C₂×C₅×D₄	—	6	4	no	—
154	C₂×C₅×D₄	—	6	4	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	C₂×C₅×D₄	—	6	1	no	—
161	C₂×C₅×D₄	—	12	8	no	—
162	C₂²×C₄×C₅	—	3	2	no	—
163	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
164	C₅×M₁₆	—	2	1	no	—
165	C₅×M₁₆	—	2	1	no	—
166	C₅×M₁₆	—	2	1	no	—
167	C₅×M₁₆	—	3	2	no	—
168	C₅×M₁₆	—	6	1	no	—
169	C₅×M₁₆	—	6	1	no	—
170	C₅×M₁₆	—	6	1	no	—
171	C₅×M₁₆	#67	1	2	yes	complemented
172	C₂×C₅×C₈	—	2	1	no	—
173	C₂×C₅×C₈	—	2	1	no	—
174	C₂×C₅×C₈	—	6	1	no	—
175	C₂×C₅×C₈	—	6	1	no	—
176	C₄²×C₅	—	3	1	no	—
177	C₄²×C₅	—	3	1	no	—
178	C₄²×C₅	—	3	2	no	—
179	C₂×#127	—	3	1	no	—
180	#423	—	3	1	no	—
181	C₂×#100	—	3	1	no	—
182	C₂×#100	—	3	1	no	—
183	C₂×#100	—	3	1	no	—
184	C₂×#100	C₅×D₃	1	1	yes	characteristic, complemented
185	C₄×M₁₆	—	3	1	no	—
186	C₂²×C₃×C₅	—	2	2	no	—
187	C₂²×C₃×C₅	—	4	2	no	—
188	C₂²×C₃×C₅	—	4	4	no	—
189	C₂²×C₃×C₅	—	8	2	no	—
190	C₂²×C₃×C₅	—	8	2	no	—
191	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
192	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
193	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
194	C₂×C₅×D₃	—	4	2	no	—
195	C₂×C₅×D₃	—	4	4	no	—
196	C₂×C₅×D₃	—	8	2	no	—
197	C₂×C₅×D₃	—	8	2	no	—
198	C₃×C₄×C₅	#121	1	1	yes	characteristic
199	C₃×C₄×C₅	#121	1	1	yes	characteristic
200	C₃×C₄×C₅	#124	1	1	yes	characteristic
201	C₃×C₄×C₅	#127	1	1	yes	characteristic
202	C₅×Dic₃	—	2	2	no	—
203	C₅×Dic₃	#100	1	4	yes	complemented
204	C₂⁴×C₃	C₂×C₄×C₅	1	2	yes	—
205	C₂³×D₃	C₂×C₄×C₅	1	2	yes	—
206	C₂×C₃×D₄	—	2	1	no	—
207	C₂×C₃×D₄	—	2	1	no	—
208	C₂×C₃×D₄	—	2	1	no	—
209	C₂×C₃×D₄	—	2	1	no	—
210	C₂×C₃×D₄	—	2	1	no	—
211	C₂×C₃×D₄	—	2	1	no	—
212	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
213	C₂×#67	—	2	4	no	—
214	C₂×#67	—	2	4	no	—
215	C₂×#67	—	4	8	no	—
216	C₂²×Dic₃	C₂×C₄×C₅	1	2	yes	—
217	C₂×D₁₂	—	2	1	no	—
218	C₂×D₁₂	—	2	1	no	—
219	C₂×D₁₂	—	2	1	no	—
220	C₂×D₁₂	—	2	1	no	—
221	C₂×D₁₂	—	2	1	no	—
222	C₂×D₁₂	—	2	1	no	—
223	C₃×M₁₆	—	2	1	no	—
224	C₃×M₁₆	—	2	1	no	—
225	C₃×M₁₆	—	2	1	no	—
226	C₃×M₁₆	C₅×D₄	1	2	yes	complemented
227	C₂×C₃×C₈	—	2	1	no	—
228	C₂×C₃×C₈	—	2	1	no	—
229	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
230	C₄×Dic₃	C₅×D₄	1	2	yes	—
231	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
232	#208	—	2	1	no	—
233	#208	—	2	1	no	—
234	#208	—	2	1	no	—
235	#208	C₅×D₄	1	2	yes	complemented
236	C₂×C₃⋊C₈	—	2	1	no	—
237	C₂×C₃⋊C₈	—	2	1	no	—
238	C₂³×C₅	—	2	2	no	—
239	C₂³×C₅	—	2	2	no	—
240	C₂³×C₅	—	2	2	no	—
241	C₂³×C₅	—	4	4	no	—
242	C₂³×C₅	—	6	2	no	—
243	C₂³×C₅	—	6	2	no	—
244	C₂³×C₅	—	6	2	no	—
245	C₂³×C₅	—	12	4	no	—
246	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
247	C₅×D₄	—	4	1	no	—
248	C₅×D₄	—	4	1	no	—
249	C₅×D₄	—	4	1	no	—
250	C₅×D₄	—	4	1	no	—
251	C₅×D₄	—	12	8	no	—
252	C₅×D₄	—	12	8	no	—
253	C₅×D₄	—	12	1	no	—
254	C₅×D₄	—	12	1	no	—
255	C₅×D₄	—	12	1	no	—
256	C₅×D₄	—	12	1	no	—
257	C₂×C₄×C₅	—	3	2	no	—
258	C₂×C₄×C₅	—	3	2	no	—
259	C₂×C₄×C₅	—	6	4	no	—
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	#237	1	1	yes	characteristic
265	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
266	C₅×C₈	—	2	2	no	—
267	C₅×C₈	—	4	1	no	—
268	C₅×C₈	—	6	2	no	—
269	C₅×C₈	—	12	1	no	—
270	C₂²×D₄	—	3	4	no	—
271	C₂²×D₄	—	3	1	no	—
272	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
273	C₂×M₁₆	—	3	1	no	—
274	C₂×M₁₆	—	3	1	no	—
275	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
276	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
277	#127	—	6	1	no	—
278	#127	—	6	1	no	—
279	#127	—	6	2	no	—
280	C₂×C₄²	—	3	1	no	—
281	C₄⋊C₈	—	6	2	no	—
282	#100	—	2	2	no	—
283	#100	—	6	2	no	—
284	#100	—	6	2	no	—
285	#100	—	6	2	no	—
286	#97	—	6	1	no	—
287	C₄×C₈	—	6	1	no	—
288	C₂×C₃×C₅	—	2	1	no	—
289	C₂×C₃×C₅	—	2	1	no	—
290	C₂×C₃×C₅	—	8	2	no	—
291	C₂×C₃×C₅	#390	1	1	yes	characteristic
292	C₂×C₃×C₅	C₂×#100	1	2	yes	—
293	C₅×D₃	—	8	2	no	—
294	C₂³×C₃	—	2	2	no	—
295	C₂³×C₃	—	2	2	no	—
296	C₂³×C₃	—	2	2	no	—
297	C₂³×C₃	—	4	4	no	—
298	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
299	C₂²×D₃	—	2	2	no	—
300	C₂²×D₃	—	2	2	no	—
301	C₂²×D₃	—	2	2	no	—
302	C₂²×D₃	—	4	4	no	—
303	C₃×D₄	—	4	1	no	—
304	C₃×D₄	—	4	1	no	—
305	C₃×D₄	—	4	1	no	—
306	C₃×D₄	—	4	1	no	—
307	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
308	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
309	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
310	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
311	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
312	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
313	#67	—	4	8	no	—
314	#67	—	4	8	no	—
315	C₂×Dic₃	—	2	4	no	—
316	C₂×Dic₃	C₅×C₂²⋊C₄	1	2	yes	—
317	C₂×Dic₃	C₅×C₂²⋊C₄	1	2	yes	—
318	D₁₂	—	4	1	no	—
319	D₁₂	—	4	1	no	—
320	D₁₂	—	4	1	no	—
321	D₁₂	—	4	1	no	—
322	C₃×C₈	—	2	2	no	—
323	C₃×C₈	—	4	1	no	—
324	C₃⋊C₈	—	2	2	no	—
325	C₃⋊C₈	—	4	1	no	—
326	C₂²×C₅	—	2	2	no	—
327	C₂²×C₅	—	4	2	no	—
328	C₂²×C₅	—	4	4	no	—
329	C₂²×C₅	—	8	2	no	—
330	C₂²×C₅	—	8	2	no	—
331	C₂²×C₅	—	12	2	no	—
332	C₂²×C₅	—	12	4	no	—
333	C₂²×C₅	—	24	2	no	—
334	C₂²×C₅	—	24	2	no	—
335	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
336	C₂²×C₅	#67⋊C₄	1	1	yes	characteristic
337	C₂²×C₅	C₄×#67	1	1	yes	characteristic
338	C₄×C₅	—	3	4	no	—
339	C₄×C₅	—	6	2	no	—
340	C₄×C₅	#884	1	1	yes	characteristic
341	C₄×C₅	#885	1	1	yes	characteristic
342	C₄×C₅	#939	1	1	yes	characteristic
343	C₄×C₅	#940	1	1	yes	characteristic
344	C₂⁴	—	3	2	no	—
345	C₂⁴	C₄×C₅×D₃	1	2	yes	—
346	C₂×D₄	—	2	1	no	—
347	C₂×D₄	—	2	1	no	—
348	C₂×D₄	—	2	1	no	—
349	C₂×D₄	—	2	1	no	—
350	C₂×D₄	—	2	1	no	—
351	C₂×D₄	—	2	1	no	—
352	C₂×D₄	—	6	4	no	—
353	C₂×D₄	—	6	4	no	—
354	C₂×D₄	—	6	1	no	—
355	C₂×D₄	—	6	1	no	—
356	C₂×D₄	—	6	1	no	—
357	C₂×D₄	—	6	1	no	—
358	C₂×D₄	—	6	1	no	—
359	C₂×D₄	—	6	1	no	—
360	C₂×D₄	—	12	8	no	—
361	C₂²×C₄	—	3	2	no	—
362	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
363	M₁₆	—	2	1	no	—
364	M₁₆	—	2	1	no	—
365	M₁₆	—	2	1	no	—
366	M₁₆	—	3	2	no	—
367	M₁₆	—	6	1	no	—
368	M₁₆	—	6	1	no	—
369	M₁₆	—	6	1	no	—
370	M₁₆	C₅×#67	1	2	yes	complemented
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	—	6	1	no	—
374	C₂×C₈	—	6	1	no	—
375	C₄²	—	3	1	no	—
376	C₄²	—	3	1	no	—
377	C₄²	—	3	2	no	—
378	C₃×C₅	#1965	1	1	yes	characteristic, complemented, Hall
379	C₂²×C₃	—	2	2	no	—
380	C₂²×C₃	—	4	2	no	—
381	C₂²×C₃	—	4	4	no	—
382	C₂²×C₃	—	8	2	no	—
383	C₂²×C₃	—	8	2	no	—
384	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
385	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
386	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
387	C₂×D₃	—	4	2	no	—
388	C₂×D₃	—	4	4	no	—
389	C₂×D₃	—	8	2	no	—
390	C₂×D₃	—	8	2	no	—
391	C₃×C₄	C₅×#121	1	1	yes	characteristic
392	C₃×C₄	C₅×#121	1	1	yes	characteristic
393	C₃×C₄	C₅×#124	1	1	yes	characteristic
394	C₃×C₄	C₅×#127	1	1	yes	characteristic
395	Dic₃	—	2	2	no	—
396	Dic₃	C₅×#100	1	4	yes	complemented
397	C₂×C₅	—	2	1	no	—
398	C₂×C₅	—	2	1	no	—
399	C₂×C₅	—	8	2	no	—
400	C₂×C₅	—	24	2	no	—
401	C₂×C₅	D₃×#100	1	2	yes	—
402	C₂×C₅	#4957	1	1	yes	characteristic
403	C₂³	—	2	2	no	—
404	C₂³	—	2	2	no	—
405	C₂³	—	2	2	no	—
406	C₂³	—	4	4	no	—
407	C₂³	—	6	2	no	—
408	C₂³	—	6	2	no	—
409	C₂³	—	6	2	no	—
410	C₂³	—	12	4	no	—
411	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
412	D₄	—	4	1	no	—
413	D₄	—	4	1	no	—
414	D₄	—	4	1	no	—
415	D₄	—	4	1	no	—
416	D₄	—	12	8	no	—
417	D₄	—	12	8	no	—
418	D₄	—	12	1	no	—
419	D₄	—	12	1	no	—
420	D₄	—	12	1	no	—
421	D₄	—	12	1	no	—
422	C₂×C₄	—	3	2	no	—
423	C₂×C₄	—	3	2	no	—
424	C₂×C₄	—	6	4	no	—
425	C₂×C₄	C₅×#235	1	1	yes	characteristic
426	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
427	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
428	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
429	C₂×C₄	C₅×#237	1	1	yes	characteristic
430	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
431	C₈	—	2	2	no	—
432	C₈	—	4	1	no	—
433	C₈	—	6	2	no	—
434	C₈	—	12	1	no	—
435	C₂×C₃	—	2	1	no	—
436	C₂×C₃	—	2	1	no	—
437	C₂×C₃	—	8	2	no	—
438	C₂×C₃	C₅×#390	1	1	yes	characteristic
439	C₂×C₃	C₂×C₅×#100	1	2	yes	—
440	D₃	—	8	2	no	—
441	C₅	#70064	1	1	yes	characteristic, direct product factor, Sylow
442	C₂²	—	2	2	no	—
443	C₂²	—	4	2	no	—
444	C₂²	—	4	4	no	—
445	C₂²	—	8	2	no	—
446	C₂²	—	8	2	no	—
447	C₂²	—	12	2	no	—
448	C₂²	—	12	4	no	—
449	C₂²	—	24	2	no	—
450	C₂²	—	24	2	no	—
451	C₂²	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
452	C₂²	C₅×#67⋊C₄	1	1	yes	characteristic
453	C₂²	C₄×C₅×#67	1	1	yes	characteristic
454	C₄	—	3	4	no	—
455	C₄	—	6	2	no	—
456	C₄	C₅×#884	1	1	yes	characteristic
457	C₄	C₅×#885	1	1	yes	characteristic
458	C₄	C₅×#939	1	1	yes	characteristic
459	C₄	C₅×#940	1	1	yes	characteristic
460	C₃	C₅×#1965	1	1	yes	characteristic, complemented, Sylow
461	C₂	—	2	1	no	—
462	C₂	—	2	1	no	—
463	C₂	—	8	2	no	—
464	C₂	—	24	2	no	—
465	C₂	C₅×D₃×#100	1	2	yes	—
466	C₂	C₅×#4957	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	D₃×C₂²⋊C₄
commutator	C₂³×C₃	C₂²×C₄×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₂×C₃×C₅×#100	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂×C₅×#940	C₂
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₂×C₅×#100	D₃
hypocenter	C₃	C₅×#1965
LCS	G ▷ C₂³×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×#100

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₅×#100	C₂	semidirect
3. C₂×C₅×#833	C₂	semidirect
4. C₂×C₅×#823	C₂	semidirect
5. C₂×C₅×#823	C₂	semidirect
6. C₅×#5118	C₂	semidirect
7. C₅×Dic₃×M₁₆	C₂	semidirect
27. #70064	C₅	direct (N × H)
33. C₂×C₅×#100	D₃	semidirect
57. C₃×C₅×M₁₆	D₄	semidirect
66. C₅×#208	D₄	semidirect
70. C₂×C₃×#100	C₂×C₅	semidirect
71. C₂×#833	C₂×C₅	semidirect
72. C₂×#823	C₂×C₅	semidirect
73. C₂×#823	C₂×C₅	semidirect
74. #5118	C₂×C₅	semidirect
75. Dic₃×M₁₆	C₂×C₅	semidirect
171. C₅×M₁₆	#67	semidirect
184. C₂×#100	C₅×D₃	semidirect
203. C₅×Dic₃	#100	semidirect
226. C₃×M₁₆	C₅×D₄	semidirect
235. #208	C₅×D₄	semidirect
370. M₁₆	C₅×#67	semidirect
378. C₃×C₅	#1965	semidirect
396. Dic₃	C₅×#100	semidirect
441. C₅	#70064	direct (N × H)
460. C₃	C₅×#1965	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#940	2
C₂×C₃×C₅×#100	2
C₂×C₅×#833	2
C₂×C₅×#823	2
C₅×#5118	2
C₅×Dic₃×M₁₆	2
C₅×#1965	3
#70064	5

Subgroups — C5×#70064 #14306113

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#70064 #14306113