Subgroups — C₅×#64314 #13089327

Order 1440.

718 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₄×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×#237	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×D₃×D₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#3811	C₂	1	2	yes	maximal, complemented
5	C₅×D₃×#67	C₂	1	2	yes	maximal, complemented
6	C₂×C₅×#626	C₂	1	2	yes	maximal, complemented
7	C₅×#3804	C₂	1	2	yes	maximal, complemented
8	C₅×D₃×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#3799	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#3798	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#3796	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1009	—	3	1	no	maximal
13	C₅×#1004	—	3	1	no	maximal
14	C₂²×C₅×C₃⋊D₃	C₂²	1	2	yes	complemented
15	C₂²×C₃×C₅×D₃	C₂²	1	2	yes	complemented
16	C₂×C₅×D₃²	C₂²	1	2	yes	complemented
17	C₃²×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
18	C₅×#638	C₂²	1	2	yes	complemented
19	C₅×C₄⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic, complemented
20	C₄×C₅×C₃⋊D₃	C₂²	1	1	yes	characteristic, complemented
21	C₃×C₅×#67	C₂²	1	2	yes	complemented
22	C₃×C₅×#67	C₂²	1	2	yes	complemented
23	C₂×C₃×C₅×Dic₃	C₂²	1	2	yes	complemented
24	C₃×C₅×D₁₂	C₂²	1	1	yes	characteristic, complemented
25	C₃×C₄×C₅×D₃	C₂²	1	1	yes	characteristic, complemented
26	C₃×C₄×C₅×D₃	C₂²	1	1	yes	characteristic, complemented
27	C₃×C₅×Dic₆	C₂²	1	1	yes	characteristic, complemented
28	C₅×#627	C₂²	1	1	yes	characteristic, complemented
29	C₅×#626	C₂²	1	2	yes	complemented
30	C₅×#626	C₂²	1	1	yes	characteristic, complemented
31	C₅×#626	C₂²	1	1	yes	characteristic, complemented
32	C₅×#626	C₂²	1	2	yes	complemented
33	C₅×#626	C₂²	1	2	yes	complemented
34	C₅×#625	C₂²	1	1	yes	characteristic, complemented
35	C₅×#624	C₂²	1	2	yes	complemented
36	C₅×D₃×Dic₃	C₂²	1	2	yes	complemented
37	#64314	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
38	C₃×C₅×#41	—	3	1	no	—
39	C₂×C₃×C₅×D₄	—	3	1	no	—
40	C₂×C₅×#67	—	3	2	no	—
41	C₂×C₅×#67	—	3	2	no	—
42	C₅×#239	—	3	1	no	—
43	C₅×#239	—	3	1	no	—
44	C₅×#237	—	3	2	no	—
45	C₅×#237	—	3	1	no	—
46	C₅×#237	D₃	1	1	yes	characteristic, complemented
47	C₅×D₃×D₄	—	3	2	no	—
48	C₅×D₃×D₄	—	3	1	no	—
49	C₅×D₃×D₄	—	3	1	no	—
50	C₅×D₃×D₄	—	3	2	no	—
51	C₅×D₃×D₄	—	3	2	no	—
52	C₅×D₃×D₄	—	3	1	no	—
53	C₅×D₃×D₄	—	6	1	no	—
54	C₅×D₃×D₄	D₃	1	1	yes	characteristic, complemented
55	C₅×#235	—	3	2	no	—
56	C₅×#235	—	3	1	no	—
57	C₅×#235	—	3	1	no	—
58	C₅×#235	—	3	1	no	—
59	C₂×C₅×D₁₂	—	3	2	no	—
60	C₂×C₅×D₁₂	—	3	1	no	—
61	C₂²×C₃²×C₅	C₂³	1	2	yes	—
62	C₂×C₅×C₃⋊D₃	—	4	2	no	—
63	C₂×C₅×C₃⋊D₃	C₂³	1	2	yes	—
64	C₂×C₅×C₃⋊D₃	C₂³	1	1	yes	characteristic
65	C₂×C₃×C₅×D₃	—	4	2	no	—
66	C₂×C₃×C₅×D₃	C₂³	1	2	yes	—
67	C₂×C₃×C₅×D₃	C₂³	1	1	yes	characteristic
68	C₂×C₃×C₅×D₃	C₂³	1	1	yes	characteristic
69	C₅×D₃²	—	4	2	no	—
70	C₃²×C₄×C₅	C₂³	1	1	yes	characteristic
71	C₅×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
72	C₃×C₅×Dic₃	C₂³	1	2	yes	—
73	C₃×C₅×Dic₃	C₂³	1	1	yes	characteristic
74	C₃×C₅×Dic₃	C₂³	1	1	yes	characteristic
75	C₅×H(5,𝔽₂)	—	9	1	no	Hall
76	D₄×C₃⋊D₃	C₂×C₅	1	1	yes	characteristic, complemented
77	C₃×#237	C₂×C₅	1	1	yes	characteristic, complemented
78	C₃×D₃×D₄	C₂×C₅	1	1	yes	characteristic, complemented
79	#3811	C₂×C₅	1	2	yes	complemented
80	D₃×#67	C₂×C₅	1	2	yes	complemented
81	C₂×#626	C₂×C₅	1	2	yes	complemented
82	#3804	C₂×C₅	1	2	yes	complemented
83	D₃×D₁₂	C₂×C₅	1	1	yes	characteristic, complemented
84	#3799	C₂×C₅	1	1	yes	characteristic, complemented
85	#3798	C₂×C₅	1	1	yes	characteristic, complemented
86	#3796	C₂×C₅	1	1	yes	characteristic, complemented
87	C₂³×C₃×C₅	—	3	2	no	—
88	C₂²×C₅×D₃	—	3	2	no	—
89	C₂²×C₅×D₃	—	3	2	no	—
90	C₂²×C₅×D₃	—	3	2	no	—
91	C₂²×C₅×D₃	—	3	2	no	—
92	C₂²×C₅×D₃	—	6	2	no	—
93	C₂²×C₅×D₃	C₂×D₃	1	2	yes	complemented
94	C₃×C₅×Q₈	—	3	1	no	—
95	C₃×C₅×D₄	—	2	1	no	—
96	C₃×C₅×D₄	—	3	2	no	—
97	C₃×C₅×D₄	—	3	2	no	—
98	C₃×C₅×D₄	—	3	1	no	—
99	C₃×C₅×D₄	C₂×D₃	1	1	yes	characteristic, complemented
100	C₃×C₅×D₄	C₂×D₃	1	1	yes	characteristic, complemented
101	C₂×C₃×C₄×C₅	—	3	2	no	—
102	C₂×C₃×C₄×C₅	—	3	1	no	—
103	C₂×C₃×C₄×C₅	—	3	1	no	—
104	C₅×#67	—	3	2	no	—
105	C₅×#67	—	3	2	no	—
106	C₅×#67	—	3	1	no	—
107	C₅×#67	—	3	1	no	—
108	C₅×#67	—	3	1	no	—
109	C₅×#67	—	3	1	no	—
110	C₅×#67	—	3	2	no	—
111	C₅×#67	—	3	2	no	—
112	C₅×#67	—	3	2	no	—
113	C₅×#67	—	6	2	no	—
114	C₅×#67	C₂×D₃	1	2	yes	complemented
115	C₅×#67	C₂×D₃	1	2	yes	complemented
116	C₂×C₅×Dic₃	—	3	2	no	—
117	C₂×C₅×Dic₃	C₂×D₃	1	2	yes	complemented
118	C₅×D₁₂	—	3	2	no	—
119	C₅×D₁₂	—	3	1	no	—
120	C₅×D₁₂	—	3	2	no	—
121	C₅×D₁₂	—	3	2	no	—
122	C₅×D₁₂	—	3	1	no	—
123	C₅×D₁₂	—	3	1	no	—
124	C₅×D₁₂	—	3	1	no	—
125	C₅×D₁₂	—	6	1	no	—
126	C₅×D₁₂	C₂×D₃	1	1	yes	characteristic, complemented
127	C₄×C₅×D₃	—	3	2	no	—
128	C₄×C₅×D₃	—	3	1	no	—
129	C₄×C₅×D₃	—	3	1	no	—
130	C₄×C₅×D₃	—	3	2	no	—
131	C₄×C₅×D₃	—	3	2	no	—
132	C₄×C₅×D₃	—	6	1	no	—
133	C₄×C₅×D₃	C₂×D₃	1	1	yes	characteristic, complemented
134	C₄×C₅×D₃	C₂×D₃	1	1	yes	characteristic, complemented
135	C₅×Dic₆	—	3	1	no	—
136	C₅×Dic₆	—	3	1	no	—
137	C₅×Dic₆	C₂×D₃	1	1	yes	characteristic, complemented
138	#1009	—	3	1	no	—
139	#1004	—	3	1	no	—
140	C₂×C₃²×C₅	—	2	2	no	—
141	C₂×C₃²×C₅	C₂⁴	1	1	yes	characteristic
142	C₅×C₃⋊D₃	—	2	1	no	—
143	C₅×C₃⋊D₃	—	2	2	no	—
144	C₃×C₅×D₃	—	2	1	no	—
145	C₃×C₅×D₃	—	2	2	no	—
146	C₃×C₅×D₃	—	2	1	no	—
147	C₅×#41	—	3	1	no	—
148	C₅×#41	—	9	1	no	—
149	C₅×#41	—	9	2	no	—
150	C₅×#41	—	9	1	no	—
151	C₅×#41	—	9	1	no	—
152	C₂×C₅×D₄	—	3	1	no	—
153	C₂×C₅×D₄	—	9	1	no	—
154	C₂×C₅×D₄	—	9	2	no	—
155	C₂×C₅×D₄	—	9	2	no	—
156	C₂×C₅×D₄	—	9	2	no	—
157	C₂×C₅×D₄	—	9	1	no	—
158	C₂²×C₃⋊D₃	C₂²×C₅	1	2	yes	complemented
159	C₂²×C₃×D₃	C₂²×C₅	1	2	yes	complemented
160	C₂×D₃²	C₂²×C₅	1	2	yes	complemented
161	C₃²×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
162	#638	C₂²×C₅	1	2	yes	complemented
163	C₄⋊(C₃⋊D₃)	C₂²×C₅	1	1	yes	characteristic, complemented
164	C₄×C₃⋊D₃	C₂²×C₅	1	1	yes	characteristic, complemented
165	C₃×#67	C₂²×C₅	1	2	yes	complemented
166	C₃×#67	C₂²×C₅	1	2	yes	complemented
167	C₂×C₃×Dic₃	C₂²×C₅	1	2	yes	complemented
168	C₃×D₁₂	C₂²×C₅	1	1	yes	characteristic, complemented
169	C₃×C₄×D₃	C₂²×C₅	1	1	yes	characteristic, complemented
170	C₃×C₄×D₃	C₂²×C₅	1	1	yes	characteristic, complemented
171	C₃×Dic₆	C₂²×C₅	1	1	yes	characteristic, complemented
172	#627	C₂²×C₅	1	1	yes	characteristic, complemented
173	#626	C₂²×C₅	1	2	yes	complemented
174	#626	C₂²×C₅	1	1	yes	characteristic, complemented
175	#626	C₂²×C₅	1	1	yes	characteristic, complemented
176	#626	C₂²×C₅	1	2	yes	complemented
177	#626	C₂²×C₅	1	2	yes	complemented
178	#625	C₂²×C₅	1	1	yes	characteristic, complemented
179	#624	C₂²×C₅	1	2	yes	complemented
180	D₃×Dic₃	C₂²×C₅	1	2	yes	complemented
181	C₂²×C₃×C₅	—	2	2	no	—
182	C₂²×C₃×C₅	—	3	2	no	—
183	C₂²×C₃×C₅	—	3	1	no	—
184	C₂²×C₃×C₅	—	3	1	no	—
185	C₂²×C₃×C₅	—	12	2	no	—
186	C₂²×C₃×C₅	C₂²×D₃	1	2	yes	—
187	C₂²×C₃×C₅	C₂²×D₃	1	2	yes	—
188	C₂×C₅×D₃	—	3	2	no	—
189	C₂×C₅×D₃	—	3	1	no	—
190	C₂×C₅×D₃	—	3	2	no	—
191	C₂×C₅×D₃	—	3	1	no	—
192	C₂×C₅×D₃	—	4	2	no	—
193	C₂×C₅×D₃	—	6	1	no	—
194	C₂×C₅×D₃	—	6	2	no	—
195	C₂×C₅×D₃	—	12	2	no	—
196	C₂×C₅×D₃	—	12	2	no	—
197	C₂×C₅×D₃	—	12	2	no	—
198	C₂×C₅×D₃	—	12	2	no	—
199	C₂×C₅×D₃	—	12	4	no	—
200	C₂×C₅×D₃	C₂²×D₃	1	2	yes	—
201	C₂×C₅×D₃	C₂²×D₃	1	1	yes	characteristic
202	C₂×C₅×D₃	C₂²×D₃	1	1	yes	characteristic
203	C₃×C₄×C₅	—	2	1	no	—
204	C₃×C₄×C₅	—	3	1	no	—
205	C₃×C₄×C₅	—	3	1	no	—
206	C₃×C₄×C₅	—	3	2	no	—
207	C₃×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
208	C₃×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
209	C₅×Dic₃	—	3	1	no	—
210	C₅×Dic₃	—	3	1	no	—
211	C₅×Dic₃	—	6	1	no	—
212	C₅×Dic₃	C₂²×D₃	1	1	yes	characteristic
213	C₅×Dic₃	C₂²×D₃	1	1	yes	characteristic
214	C₅×Dic₃	C₂²×D₃	1	2	yes	—
215	C₃×#41	—	3	1	no	—
216	C₂×C₃×D₄	—	3	1	no	—
217	C₂×#67	—	3	2	no	—
218	C₂×#67	—	3	2	no	—
219	#239	—	3	1	no	—
220	#239	—	3	1	no	—
221	#237	—	3	2	no	—
222	#237	—	3	1	no	—
223	#237	C₅×D₃	1	1	yes	characteristic, complemented
224	D₃×D₄	—	3	2	no	—
225	D₃×D₄	—	3	1	no	—
226	D₃×D₄	—	3	1	no	—
227	D₃×D₄	—	3	2	no	—
228	D₃×D₄	—	3	2	no	—
229	D₃×D₄	—	3	1	no	—
230	D₃×D₄	—	6	1	no	—
231	D₃×D₄	C₅×D₃	1	1	yes	characteristic, complemented
232	#235	—	3	2	no	—
233	#235	—	3	1	no	—
234	#235	—	3	1	no	—
235	#235	—	3	1	no	—
236	C₂×D₁₂	—	3	2	no	—
237	C₂×D₁₂	—	3	1	no	—
238	C₃²×C₅	H(5,𝔽₂)	1	1	yes	characteristic, complemented, Hall
239	C₂³×C₅	—	3	2	no	—
240	C₂³×C₅	—	9	2	no	—
241	C₂³×C₅	—	9	2	no	—
242	C₅×Q₈	—	3	1	no	—
243	C₅×Q₈	—	9	1	no	—
244	C₅×D₄	—	3	2	no	—
245	C₅×D₄	—	3	2	no	—
246	C₅×D₄	—	3	1	no	—
247	C₅×D₄	—	9	1	no	—
248	C₅×D₄	—	9	2	no	—
249	C₅×D₄	—	9	1	no	—
250	C₅×D₄	—	9	2	no	—
251	C₅×D₄	—	9	2	no	—
252	C₅×D₄	—	9	1	no	—
253	C₅×D₄	—	9	2	no	—
254	C₅×D₄	—	9	1	no	—
255	C₅×D₄	D₃²	1	1	yes	characteristic, complemented
256	C₂×C₄×C₅	—	3	2	no	—
257	C₂×C₄×C₅	—	3	1	no	—
258	C₂×C₄×C₅	—	3	1	no	—
259	C₂×C₄×C₅	—	9	2	no	—
260	C₂×C₄×C₅	—	9	2	no	—
261	C₂×C₄×C₅	—	9	1	no	—
262	C₂²×C₃²	C₂³×C₅	1	2	yes	—
263	C₂×C₃⋊D₃	—	4	2	no	—
264	C₂×C₃⋊D₃	C₂³×C₅	1	2	yes	—
265	C₂×C₃⋊D₃	C₂³×C₅	1	1	yes	characteristic
266	C₂×C₃×D₃	—	4	2	no	—
267	C₂×C₃×D₃	C₂³×C₅	1	2	yes	—
268	C₂×C₃×D₃	C₂³×C₅	1	1	yes	characteristic
269	C₂×C₃×D₃	C₂³×C₅	1	1	yes	characteristic
270	D₃²	—	4	2	no	—
271	C₃²×C₄	C₂³×C₅	1	1	yes	characteristic
272	C₃⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
273	C₃×Dic₃	C₂³×C₅	1	2	yes	—
274	C₃×Dic₃	C₂³×C₅	1	1	yes	characteristic
275	C₃×Dic₃	C₂³×C₅	1	1	yes	characteristic
276	H(5,𝔽₂)	—	9	1	no	Sylow
277	C₂×C₃×C₅	—	2	2	no	—
278	C₂×C₃×C₅	—	2	2	no	—
279	C₂×C₃×C₅	—	2	1	no	—
280	C₂×C₃×C₅	—	4	2	no	—
281	C₂×C₃×C₅	—	6	1	no	—
282	C₂×C₃×C₅	—	6	2	no	—
283	C₂×C₃×C₅	—	6	1	no	—
284	C₂×C₃×C₅	C₂³×D₃	1	1	yes	characteristic
285	C₂×C₃×C₅	C₂³×D₃	1	1	yes	characteristic
286	C₅×D₃	—	2	1	no	—
287	C₅×D₃	—	2	2	no	—
288	C₅×D₃	—	2	1	no	—
289	C₅×D₃	—	6	2	no	—
290	C₅×D₃	—	6	1	no	—
291	C₅×D₃	—	6	2	no	—
292	C₅×D₃	—	6	1	no	—
293	C₅×D₃	—	6	2	no	—
294	C₅×D₃	—	12	2	no	—
295	C₂³×C₃	—	3	2	no	—
296	C₂²×D₃	—	3	2	no	—
297	C₂²×D₃	—	3	2	no	—
298	C₂²×D₃	—	3	2	no	—
299	C₂²×D₃	—	3	2	no	—
300	C₂²×D₃	—	6	2	no	—
301	C₂²×D₃	C₂×C₅×D₃	1	2	yes	complemented
302	C₃×Q₈	—	3	1	no	—
303	C₃×D₄	—	2	1	no	—
304	C₃×D₄	—	3	2	no	—
305	C₃×D₄	—	3	2	no	—
306	C₃×D₄	—	3	1	no	—
307	C₃×D₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
308	C₃×D₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
309	C₂×C₃×C₄	—	3	2	no	—
310	C₂×C₃×C₄	—	3	1	no	—
311	C₂×C₃×C₄	—	3	1	no	—
312	#67	—	3	2	no	—
313	#67	—	3	2	no	—
314	#67	—	3	1	no	—
315	#67	—	3	1	no	—
316	#67	—	3	1	no	—
317	#67	—	3	1	no	—
318	#67	—	3	2	no	—
319	#67	—	3	2	no	—
320	#67	—	3	2	no	—
321	#67	—	6	2	no	—
322	#67	C₂×C₅×D₃	1	2	yes	complemented
323	#67	C₂×C₅×D₃	1	2	yes	complemented
324	C₂×Dic₃	—	3	2	no	—
325	C₂×Dic₃	C₂×C₅×D₃	1	2	yes	complemented
326	D₁₂	—	3	2	no	—
327	D₁₂	—	3	1	no	—
328	D₁₂	—	3	2	no	—
329	D₁₂	—	3	2	no	—
330	D₁₂	—	3	1	no	—
331	D₁₂	—	3	1	no	—
332	D₁₂	—	3	1	no	—
333	D₁₂	—	6	1	no	—
334	D₁₂	C₂×C₅×D₃	1	1	yes	characteristic, complemented
335	C₄×D₃	—	3	2	no	—
336	C₄×D₃	—	3	1	no	—
337	C₄×D₃	—	3	1	no	—
338	C₄×D₃	—	3	2	no	—
339	C₄×D₃	—	3	2	no	—
340	C₄×D₃	—	6	1	no	—
341	C₄×D₃	C₂×C₅×D₃	1	1	yes	characteristic, complemented
342	C₄×D₃	C₂×C₅×D₃	1	1	yes	characteristic, complemented
343	Dic₆	—	3	1	no	—
344	Dic₆	—	3	1	no	—
345	Dic₆	C₂×C₅×D₃	1	1	yes	characteristic, complemented
346	C₂²×C₅	—	3	1	no	—
347	C₂²×C₅	—	3	1	no	—
348	C₂²×C₅	—	3	2	no	—
349	C₂²×C₅	—	9	1	no	—
350	C₂²×C₅	—	9	2	no	—
351	C₂²×C₅	—	12	2	no	—
352	C₂²×C₅	—	36	2	no	—
353	C₂²×C₅	—	36	2	no	—
354	C₂²×C₅	C₂×D₃²	1	2	yes	—
355	C₄×C₅	—	3	1	no	—
356	C₄×C₅	—	3	1	no	—
357	C₄×C₅	—	3	2	no	—
358	C₄×C₅	—	9	1	no	—
359	C₄×C₅	C₂×D₃²	1	1	yes	characteristic
360	C₂×C₃²	—	2	2	no	—
361	C₂×C₃²	C₂⁴×C₅	1	1	yes	characteristic
362	C₃⋊D₃	—	2	1	no	—
363	C₃⋊D₃	—	2	2	no	—
364	C₃×D₃	—	2	1	no	—
365	C₃×D₃	—	2	2	no	—
366	C₃×D₃	—	2	1	no	—
367	#41	—	3	1	no	—
368	#41	—	9	1	no	—
369	#41	—	9	2	no	—
370	#41	—	9	1	no	—
371	#41	—	9	1	no	—
372	C₂×D₄	—	3	1	no	—
373	C₂×D₄	—	9	1	no	—
374	C₂×D₄	—	9	2	no	—
375	C₂×D₄	—	9	2	no	—
376	C₂×D₄	—	9	2	no	—
377	C₂×D₄	—	9	1	no	—
378	C₃×C₅	—	2	1	no	—
379	C₃×C₅	#1004	1	1	yes	characteristic, complemented
380	C₃×C₅	#1009	1	1	yes	characteristic, complemented
381	C₂²×C₃	—	2	2	no	—
382	C₂²×C₃	—	3	2	no	—
383	C₂²×C₃	—	3	1	no	—
384	C₂²×C₃	—	3	1	no	—
385	C₂²×C₃	—	12	2	no	—
386	C₂²×C₃	C₂²×C₅×D₃	1	2	yes	—
387	C₂²×C₃	C₂²×C₅×D₃	1	2	yes	—
388	C₂×D₃	—	3	1	no	—
389	C₂×D₃	—	3	2	no	—
390	C₂×D₃	—	3	1	no	—
391	C₂×D₃	—	3	2	no	—
392	C₂×D₃	—	4	2	no	—
393	C₂×D₃	—	6	1	no	—
394	C₂×D₃	—	6	2	no	—
395	C₂×D₃	—	12	2	no	—
396	C₂×D₃	—	12	2	no	—
397	C₂×D₃	—	12	2	no	—
398	C₂×D₃	—	12	2	no	—
399	C₂×D₃	—	12	4	no	—
400	C₂×D₃	C₂²×C₅×D₃	1	2	yes	—
401	C₂×D₃	C₂²×C₅×D₃	1	1	yes	characteristic
402	C₂×D₃	C₂²×C₅×D₃	1	1	yes	characteristic
403	C₃×C₄	—	2	1	no	—
404	C₃×C₄	—	3	1	no	—
405	C₃×C₄	—	3	1	no	—
406	C₃×C₄	—	3	2	no	—
407	C₃×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
408	C₃×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
409	Dic₃	—	3	1	no	—
410	Dic₃	—	3	1	no	—
411	Dic₃	—	6	1	no	—
412	Dic₃	C₂²×C₅×D₃	1	1	yes	characteristic
413	Dic₃	C₂²×C₅×D₃	1	1	yes	characteristic
414	Dic₃	C₂²×C₅×D₃	1	2	yes	—
415	C₂×C₅	—	2	2	no	—
416	C₂×C₅	—	6	1	no	—
417	C₂×C₅	—	6	2	no	—
418	C₂×C₅	—	6	1	no	—
419	C₂×C₅	—	18	1	no	—
420	C₂×C₅	—	18	2	no	—
421	C₂×C₅	C₂²×D₃²	1	1	yes	characteristic
422	C₃²	C₅×H(5,𝔽₂)	1	1	yes	characteristic, complemented, Sylow
423	C₂³	—	3	2	no	—
424	C₂³	—	9	2	no	—
425	C₂³	—	9	2	no	—
426	Q₈	—	3	1	no	—
427	Q₈	—	9	1	no	—
428	D₄	—	3	2	no	—
429	D₄	—	3	2	no	—
430	D₄	—	3	1	no	—
431	D₄	—	9	1	no	—
432	D₄	—	9	2	no	—
433	D₄	—	9	1	no	—
434	D₄	—	9	2	no	—
435	D₄	—	9	2	no	—
436	D₄	—	9	1	no	—
437	D₄	—	9	2	no	—
438	D₄	—	9	1	no	—
439	D₄	C₅×D₃²	1	1	yes	characteristic, complemented
440	C₂×C₄	—	3	2	no	—
441	C₂×C₄	—	3	1	no	—
442	C₂×C₄	—	3	1	no	—
443	C₂×C₄	—	9	2	no	—
444	C₂×C₄	—	9	2	no	—
445	C₂×C₄	—	9	1	no	—
446	C₂×C₃	—	2	2	no	—
447	C₂×C₃	—	2	2	no	—
448	C₂×C₃	—	2	1	no	—
449	C₂×C₃	—	4	2	no	—
450	C₂×C₃	—	6	1	no	—
451	C₂×C₃	—	6	2	no	—
452	C₂×C₃	—	6	1	no	—
453	C₂×C₃	C₂³×C₅×D₃	1	1	yes	characteristic
454	C₂×C₃	C₂³×C₅×D₃	1	1	yes	characteristic
455	D₃	—	2	1	no	—
456	D₃	—	2	2	no	—
457	D₃	—	2	1	no	—
458	D₃	—	6	2	no	—
459	D₃	—	6	1	no	—
460	D₃	—	6	2	no	—
461	D₃	—	6	1	no	—
462	D₃	—	6	2	no	—
463	D₃	—	12	2	no	—
464	C₅	#64314	1	1	yes	characteristic, direct product factor, Sylow
465	C₂²	—	3	1	no	—
466	C₂²	—	3	1	no	—
467	C₂²	—	3	2	no	—
468	C₂²	—	9	1	no	—
469	C₂²	—	9	2	no	—
470	C₂²	—	12	2	no	—
471	C₂²	—	36	2	no	—
472	C₂²	—	36	2	no	—
473	C₂²	C₂×C₅×D₃²	1	2	yes	—
474	C₄	—	3	1	no	—
475	C₄	—	3	1	no	—
476	C₄	—	3	2	no	—
477	C₄	—	9	1	no	—
478	C₄	C₂×C₅×D₃²	1	1	yes	characteristic
479	C₃	—	2	1	no	—
480	C₃	C₅×#1004	1	1	yes	characteristic, complemented
481	C₃	C₅×#1009	1	1	yes	characteristic, complemented
482	C₂	—	2	2	no	—
483	C₂	—	6	1	no	—
484	C₂	—	6	2	no	—
485	C₂	—	6	1	no	—
486	C₂	—	18	1	no	—
487	C₂	—	18	2	no	—
488	C₂	C₂²×C₅×D₃²	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅	C₂²×D₃²
commutator, cosocle	C₂×C₃²	C₂⁴×C₅
Frattini	C₂	C₂²×C₅×D₃²
Fitting	C₃²×C₅×D₄	C₂²
socle	C₂×C₃²×C₅	C₂⁴
hypercenter	C₅×D₄	D₃²
hypocenter	C₃²	C₅×H(5,𝔽₂)
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₅ ◁ C₅×D₄

Complements

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

N	H ≅ G/N	type
1. C₅×D₄×C₃⋊D₃	C₂	semidirect
2. C₃×C₅×#237	C₂	semidirect
3. C₃×C₅×D₃×D₄	C₂	semidirect
4. C₅×#3811	C₂	semidirect
5. C₅×D₃×#67	C₂	semidirect
6. C₂×C₅×#626	C₂	semidirect
7. C₅×#3804	C₂	semidirect
8. C₅×D₃×D₁₂	C₂	semidirect
9. C₅×#3799	C₂	semidirect
10. C₅×#3798	C₂	semidirect
11. C₅×#3796	C₂	semidirect
14. C₂²×C₅×C₃⋊D₃	C₂²	semidirect
15. C₂²×C₃×C₅×D₃	C₂²	semidirect
16. C₂×C₅×D₃²	C₂²	semidirect
17. C₃²×C₅×D₄	C₂²	semidirect
18. C₅×#638	C₂²	semidirect
19. C₅×C₄⋊(C₃⋊D₃)	C₂²	semidirect
20. C₄×C₅×C₃⋊D₃	C₂²	semidirect
21. C₃×C₅×#67	C₂²	semidirect
22. C₃×C₅×#67	C₂²	semidirect
23. C₂×C₃×C₅×Dic₃	C₂²	semidirect
24. C₃×C₅×D₁₂	C₂²	semidirect
25. C₃×C₄×C₅×D₃	C₂²	semidirect
26. C₃×C₄×C₅×D₃	C₂²	semidirect
27. C₃×C₅×Dic₆	C₂²	semidirect
28. C₅×#627	C₂²	semidirect
29. C₅×#626	C₂²	semidirect
30. C₅×#626	C₂²	semidirect
31. C₅×#626	C₂²	semidirect
32. C₅×#626	C₂²	semidirect
33. C₅×#626	C₂²	semidirect
34. C₅×#625	C₂²	semidirect
35. C₅×#624	C₂²	semidirect
36. C₅×D₃×Dic₃	C₂²	semidirect
37. #64314	C₅	direct (N × H)
46. C₅×#237	D₃	semidirect
54. C₅×D₃×D₄	D₃	semidirect
76. D₄×C₃⋊D₃	C₂×C₅	semidirect
77. C₃×#237	C₂×C₅	semidirect
78. C₃×D₃×D₄	C₂×C₅	semidirect
79. #3811	C₂×C₅	semidirect
80. D₃×#67	C₂×C₅	semidirect
81. C₂×#626	C₂×C₅	semidirect
82. #3804	C₂×C₅	semidirect
83. D₃×D₁₂	C₂×C₅	semidirect
84. #3799	C₂×C₅	semidirect
85. #3798	C₂×C₅	semidirect
86. #3796	C₂×C₅	semidirect
93. C₂²×C₅×D₃	C₂×D₃	semidirect
99. C₃×C₅×D₄	C₂×D₃	semidirect
100. C₃×C₅×D₄	C₂×D₃	semidirect
114. C₅×#67	C₂×D₃	semidirect
115. C₅×#67	C₂×D₃	semidirect
117. C₂×C₅×Dic₃	C₂×D₃	semidirect
126. C₅×D₁₂	C₂×D₃	semidirect
133. C₄×C₅×D₃	C₂×D₃	semidirect
134. C₄×C₅×D₃	C₂×D₃	semidirect
137. C₅×Dic₆	C₂×D₃	semidirect
158. C₂²×C₃⋊D₃	C₂²×C₅	semidirect
159. C₂²×C₃×D₃	C₂²×C₅	semidirect
160. C₂×D₃²	C₂²×C₅	semidirect
161. C₃²×D₄	C₂²×C₅	semidirect
162. #638	C₂²×C₅	semidirect
163. C₄⋊(C₃⋊D₃)	C₂²×C₅	semidirect
164. C₄×C₃⋊D₃	C₂²×C₅	semidirect
165. C₃×#67	C₂²×C₅	semidirect
166. C₃×#67	C₂²×C₅	semidirect
167. C₂×C₃×Dic₃	C₂²×C₅	semidirect
168. C₃×D₁₂	C₂²×C₅	semidirect
169. C₃×C₄×D₃	C₂²×C₅	semidirect
170. C₃×C₄×D₃	C₂²×C₅	semidirect
171. C₃×Dic₆	C₂²×C₅	semidirect
172. #627	C₂²×C₅	semidirect
173. #626	C₂²×C₅	semidirect
174. #626	C₂²×C₅	semidirect
175. #626	C₂²×C₅	semidirect
176. #626	C₂²×C₅	semidirect
177. #626	C₂²×C₅	semidirect
178. #625	C₂²×C₅	semidirect
179. #624	C₂²×C₅	semidirect
180. D₃×Dic₃	C₂²×C₅	semidirect
223. #237	C₅×D₃	semidirect
231. D₃×D₄	C₅×D₃	semidirect
238. C₃²×C₅	H(5,𝔽₂)	semidirect
255. C₅×D₄	D₃²	semidirect
301. C₂²×D₃	C₂×C₅×D₃	semidirect
307. C₃×D₄	C₂×C₅×D₃	semidirect
308. C₃×D₄	C₂×C₅×D₃	semidirect
322. #67	C₂×C₅×D₃	semidirect
323. #67	C₂×C₅×D₃	semidirect
325. C₂×Dic₃	C₂×C₅×D₃	semidirect
334. D₁₂	C₂×C₅×D₃	semidirect
341. C₄×D₃	C₂×C₅×D₃	semidirect
342. C₄×D₃	C₂×C₅×D₃	semidirect
345. Dic₆	C₂×C₅×D₃	semidirect
379. C₃×C₅	#1004	semidirect
380. C₃×C₅	#1009	semidirect
422. C₃²	C₅×H(5,𝔽₂)	semidirect
439. D₄	C₅×D₃²	semidirect
464. C₅	#64314	direct (N × H)
480. C₃	C₅×#1004	semidirect
481. C₃	C₅×#1009	semidirect

Maximal subgroups

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

subgroup	index
C₅×D₄×C₃⋊D₃	2
C₃×C₅×#237	2
C₃×C₅×D₃×D₄	2
C₅×#3811	2
C₅×D₃×#67	2
C₂×C₅×#626	2
C₅×#3804	2
C₅×D₃×D₁₂	2
C₅×#3799	2
C₅×#3798	2
C₅×#3796	2
C₅×#1009	3
C₅×#1004	3
#64314	5

Subgroups — C5×#64314 #13089327

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#64314 #13089327