Subgroups — C₅×#81870 #14439204

Order 1920.

1104 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#918	C₂	1	2	yes	maximal, complemented
2	C₂×C₅×#915	C₂	1	2	yes	maximal, complemented
3	C₅×D₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5668	C₂	1	1	yes	maximal, characteristic
5	C₃×C₅×#497	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5183	C₂	1	2	yes	maximal, complemented
7	C₅×#5175	C₂	1	2	yes	maximal, complemented
8	C₅×#5086	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#5060	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4715	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4707	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3152	—	3	1	no	maximal, Hall
13	C₂×C₅×#239	C₂²	1	1	yes	characteristic
14	C₂×C₅×D₃×Q₈	C₂²	1	2	yes	—
15	C₂×C₅×#237	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×Q₁₆	C₂²	1	2	yes	—
17	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
18	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₃×C₅×#124	C₂²	1	1	yes	characteristic
20	C₅×#944	C₂²	1	2	yes	—
21	C₅×#944	C₂²	1	1	yes	characteristic
22	C₂×C₅×#216	C₂²	1	2	yes	—
23	C₂×C₅×#216	C₂²	1	2	yes	—
24	C₂×C₅×#215	C₂²	1	2	yes	—
25	C₅×#940	C₂²	1	1	yes	characteristic
26	C₂×C₅×#214	C₂²	1	2	yes	—
27	C₅×#918	—	2	8	no	—
28	C₅×#915	—	2	8	no	—
29	C₂×C₅×Dic₁₂	C₂²	1	2	yes	—
30	C₂×C₅×#204	C₂²	1	2	yes	—
31	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	—
32	C₅×D₃×C₄⋊C₄	—	2	2	no	—
33	C₅×#888	—	2	2	no	—
34	C₅×#884	—	2	2	no	—
35	C₅×#67⋊C₄	—	2	2	no	—
36	C₅×#875	C₂²	1	1	yes	characteristic
37	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
38	C₅×#869	C₂²	1	1	yes	characteristic
39	C₃×C₅×#97	C₂²	1	1	yes	characteristic
40	C₅×C₈×Dic₃	C₂²	1	2	yes	—
41	C₅×#803	C₂²	1	1	yes	characteristic
42	#81870	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
43	C₂×C₅×#137	—	3	2	no	—
44	C₂×C₅×#137	—	3	2	no	—
45	C₅×#532	—	3	1	no	—
46	C₂×C₅×C₄⋊Q₈	—	3	1	no	—
47	C₅×#497	—	3	1	no	—
48	C₅×#497	—	3	1	no	—
49	C₅×#497	—	3	1	no	—
50	C₅×#497	D₃	1	1	yes	characteristic, complemented
51	C₅×#494	—	3	2	no	—
52	C₅×#492	—	3	2	no	—
53	C₄×C₅×M₁₆	—	3	1	no	—
54	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
55	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
56	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
57	C₂×C₅×#67	—	2	1	no	—
58	C₂×C₅×#67	—	2	2	no	—
59	C₂²×C₅×Dic₃	—	2	1	no	—
60	C₅×#239	—	2	4	no	—
61	C₅×D₃×Q₈	—	2	4	no	—
62	C₅×D₃×Q₈	—	2	4	no	—
63	C₅×#237	—	2	4	no	—
64	C₂×C₅×D₁₂	—	2	1	no	—
65	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
66	C₂×C₄×C₅×D₃	—	2	2	no	—
67	C₂×C₄×C₅×D₃	—	2	1	no	—
68	C₂×C₄×C₅×D₃	D₄	1	2	yes	—
69	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
70	C₂×C₅×Dic₆	—	2	2	no	—
71	C₂×C₅×Dic₆	C₂³	1	2	yes	—
72	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
73	C₃×C₅×Q₁₆	—	2	4	no	—
74	C₃×C₅×SD₁₆	—	2	4	no	—
75	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
76	C₃×C₅×C₄⋊C₄	—	2	2	no	—
77	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
78	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
79	C₅×#216	—	2	4	no	—
80	C₅×#216	—	2	4	no	—
81	C₅×#215	—	2	4	no	—
82	C₅×#214	—	2	4	no	—
83	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
84	C₅×C₄⋊Dic₃	—	2	2	no	—
85	C₅×Dic₃⋊C₄	—	2	2	no	—
86	C₅×Dic₃⋊C₄	—	2	4	no	—
87	C₄×C₅×Dic₃	D₄	1	2	yes	—
88	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
89	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
90	C₅×Dic₁₂	—	2	4	no	—
91	C₅×#204	—	2	4	no	—
92	C₅×ΓL(1,𝔽₂₅)	D₄	1	8	yes	complemented
93	C₂×#918	C₂×C₅	1	2	yes	complemented
94	C₂×#915	C₂×C₅	1	2	yes	complemented
95	D₃×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
96	#5668	C₂×C₅	1	1	yes	characteristic
97	C₃×#497	C₂×C₅	1	1	yes	characteristic, complemented
98	#5183	C₂×C₅	1	2	yes	complemented
99	#5175	C₂×C₅	1	2	yes	complemented
100	#5086	C₂×C₅	1	1	yes	characteristic, complemented
101	#5060	C₂×C₅	1	1	yes	characteristic, complemented
102	#4715	C₂×C₅	1	1	yes	characteristic, complemented
103	#4707	C₂×C₅	1	1	yes	characteristic, complemented
104	C₂×C₅×#41	—	3	1	no	—
105	C₂×C₅×#41	—	3	1	no	—
106	C₂²×C₅×Q₈	—	3	2	no	—
107	C₅×#137	—	6	8	no	—
108	C₅×#137	—	6	8	no	—
109	C₂×C₅×Q₁₆	—	3	2	no	—
110	C₂×C₅×Q₁₆	—	3	2	no	—
111	C₂×C₅×Q₁₆	—	3	2	no	—
112	C₂×C₅×Q₁₆	C₂×D₃	1	2	yes	—
113	C₂×C₅×SD₁₆	—	3	2	no	—
114	C₂×C₅×SD₁₆	—	3	2	no	—
115	C₂×C₅×SD₁₆	—	3	2	no	—
116	C₂×C₅×SD₁₆	C₂×D₃	1	2	yes	—
117	C₂×C₅×M₁₆	—	3	2	no	—
118	C₅×C₄⋊Q₈	—	3	2	no	—
119	C₅×C₄⋊Q₈	—	3	1	no	—
120	C₅×C₄⋊Q₈	—	3	1	no	—
121	C₅×C₄⋊Q₈	—	6	2	no	—
122	C₅×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic
123	C₅×#127	—	3	1	no	—
124	C₅×#124	—	3	1	no	—
125	C₅×#124	C₂×D₃	1	1	yes	characteristic
126	C₅×#121	—	6	2	no	—
127	C₄×C₅×D₄	—	6	2	no	—
128	C₂×C₅×C₄⋊C₄	—	6	2	no	—
129	C₂×C₄²×C₅	—	3	1	no	—
130	C₅×#97	—	3	1	no	—
131	C₅×#97	C₂×D₃	1	1	yes	characteristic
132	C₄×C₅×C₈	—	3	2	no	—
133	#3152	—	3	1	no	Sylow
134	C₂³×C₃×C₅	—	2	1	no	—
135	C₂²×C₅×D₃	—	2	1	no	—
136	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
137	C₃×C₅×Q₈	—	2	2	no	—
138	C₃×C₅×Q₈	—	2	2	no	—
139	C₃×C₅×Q₈	—	2	2	no	—
140	C₃×C₅×D₄	—	2	2	no	—
141	C₂×C₃×C₄×C₅	—	2	1	no	—
142	C₂×C₃×C₄×C₅	—	2	2	no	—
143	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
144	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
145	C₅×#67	—	4	2	no	—
146	C₅×#67	—	4	4	no	—
147	C₂×C₅×Dic₃	—	2	2	no	—
148	C₂×C₅×Dic₃	—	2	1	no	—
149	C₂×C₅×Dic₃	—	4	2	no	—
150	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
151	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
152	C₅×D₁₂	—	2	2	no	—
153	C₅×D₁₂	—	4	2	no	—
154	C₄×C₅×D₃	—	2	4	no	—
155	C₄×C₅×D₃	—	4	4	no	—
156	C₄×C₅×D₃	—	4	2	no	—
157	C₄×C₅×D₃	C₂×D₄	1	4	yes	—
158	C₅×Dic₆	—	2	2	no	—
159	C₅×Dic₆	—	2	2	no	—
160	C₅×Dic₆	—	2	2	no	—
161	C₅×Dic₆	—	4	4	no	—
162	C₃×C₅×C₈	C₂×D₄	1	4	yes	—
163	C₅×C₃⋊C₈	C₂×D₄	1	4	yes	—
164	C₂×#239	C₂²×C₅	1	1	yes	characteristic
165	C₂×D₃×Q₈	C₂²×C₅	1	2	yes	—
166	C₂×#237	C₂²×C₅	1	1	yes	characteristic
167	C₂×C₃×Q₁₆	C₂²×C₅	1	2	yes	—
168	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
169	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
170	C₃×#124	C₂²×C₅	1	1	yes	characteristic
171	#944	C₂²×C₅	1	1	yes	characteristic
172	#944	C₂²×C₅	1	2	yes	—
173	C₂×#216	C₂²×C₅	1	2	yes	—
174	C₂×#216	C₂²×C₅	1	2	yes	—
175	C₂×#215	C₂²×C₅	1	2	yes	—
176	#940	C₂²×C₅	1	1	yes	characteristic
177	C₂×#214	C₂²×C₅	1	2	yes	—
178	#918	—	2	8	no	—
179	#915	—	2	8	no	—
180	C₂×Dic₁₂	C₂²×C₅	1	2	yes	—
181	C₂×#204	C₂²×C₅	1	2	yes	—
182	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	2	yes	—
183	D₃×C₄⋊C₄	—	2	2	no	—
184	#888	—	2	2	no	—
185	#884	—	2	2	no	—
186	#67⋊C₄	—	2	2	no	—
187	#875	C₂²×C₅	1	1	yes	characteristic
188	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
189	#869	C₂²×C₅	1	1	yes	characteristic
190	C₃×#97	C₂²×C₅	1	1	yes	characteristic
191	C₈×Dic₃	C₂²×C₅	1	2	yes	—
192	#803	C₂²×C₅	1	1	yes	characteristic
193	C₅×#41	—	6	4	no	—
194	C₅×#41	—	6	4	no	—
195	C₂×C₅×Q₈	—	3	1	no	—
196	C₂×C₅×Q₈	—	3	2	no	—
197	C₂×C₅×Q₈	—	6	2	no	—
198	C₂×C₅×Q₈	—	6	4	no	—
199	C₂×C₅×Q₈	—	6	4	no	—
200	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
201	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
202	C₂×C₅×D₄	—	3	1	no	—
203	C₂×C₅×D₄	—	6	1	no	—
204	C₂×C₅×D₄	—	6	2	no	—
205	C₂×C₅×D₄	—	6	1	no	—
206	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
207	C₂²×C₄×C₅	—	3	1	no	—
208	C₂²×C₄×C₅	—	3	2	no	—
209	C₂²×C₄×C₅	—	6	1	no	—
210	C₂²×C₄×C₅	—	6	2	no	—
211	C₂²×C₄×C₅	—	6	1	no	—
212	C₅×Q₁₆	—	2	4	no	—
213	C₅×Q₁₆	—	6	4	no	—
214	C₅×Q₁₆	—	6	4	no	—
215	C₅×Q₁₆	—	6	4	no	—
216	C₅×SD₁₆	—	2	4	no	—
217	C₅×SD₁₆	—	6	4	no	—
218	C₅×SD₁₆	—	6	4	no	—
219	C₅×SD₁₆	—	6	4	no	—
220	C₅×M₁₆	—	3	8	no	—
221	C₂×C₅×C₈	—	3	2	no	—
222	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
223	C₅×C₄⋊C₄	—	2	2	no	—
224	C₅×C₄⋊C₄	—	6	4	no	—
225	C₅×C₄⋊C₄	—	6	2	no	—
226	C₅×C₄⋊C₄	—	6	2	no	—
227	C₅×C₂²⋊C₄	—	2	2	no	—
228	C₅×C₂²⋊C₄	—	6	2	no	—
229	C₄²×C₅	—	3	2	no	—
230	C₄²×C₅	—	3	1	no	—
231	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
232	C₂×#137	—	3	2	no	—
233	C₂×#137	—	3	2	no	—
234	#532	—	3	1	no	—
235	C₂×C₄⋊Q₈	—	3	1	no	—
236	#497	—	3	1	no	—
237	#497	—	3	1	no	—
238	#497	—	3	1	no	—
239	#497	C₅×D₃	1	1	yes	characteristic, complemented
240	#494	—	3	2	no	—
241	#492	—	3	2	no	—
242	C₄×M₁₆	—	3	1	no	—
243	C₂²×C₃×C₅	—	4	1	no	—
244	C₂²×C₃×C₅	—	4	2	no	—
245	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
246	C₂×C₅×D₃	—	2	2	no	—
247	C₂×C₅×D₃	—	4	1	no	—
248	C₂×C₅×D₃	—	4	2	no	—
249	C₂×C₅×D₃	#127	1	2	yes	—
250	C₃×C₄×C₅	—	2	2	no	—
251	C₃×C₄×C₅	—	4	2	no	—
252	C₃×C₄×C₅	—	4	1	no	—
253	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
254	C₅×Dic₃	—	4	2	no	—
255	C₅×Dic₃	—	4	1	no	—
256	C₅×Dic₃	#127	1	2	yes	—
257	C₅×Dic₃	#137	1	4	yes	complemented
258	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
259	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
260	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
261	C₂×#67	—	2	1	no	—
262	C₂×#67	—	2	2	no	—
263	C₂²×Dic₃	—	2	1	no	—
264	#239	—	2	4	no	—
265	D₃×Q₈	—	2	4	no	—
266	D₃×Q₈	—	2	4	no	—
267	#237	—	2	4	no	—
268	C₂×D₁₂	—	2	1	no	—
269	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
270	C₂×C₄×D₃	—	2	2	no	—
271	C₂×C₄×D₃	—	2	1	no	—
272	C₂×C₄×D₃	C₅×D₄	1	2	yes	—
273	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
274	C₂×Dic₆	—	2	2	no	—
275	C₂×Dic₆	C₂³×C₅	1	2	yes	—
276	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
277	C₃×Q₁₆	—	2	4	no	—
278	C₃×SD₁₆	—	2	4	no	—
279	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
280	C₃×C₄⋊C₄	—	2	2	no	—
281	C₃×C₂²⋊C₄	—	2	2	no	—
282	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
283	#216	—	2	4	no	—
284	#216	—	2	4	no	—
285	#215	—	2	4	no	—
286	#214	—	2	4	no	—
287	(C₂×D₃)⋊C₄	—	2	2	no	—
288	C₄⋊Dic₃	—	2	2	no	—
289	Dic₃⋊C₄	—	2	2	no	—
290	Dic₃⋊C₄	—	2	4	no	—
291	C₄×Dic₃	C₅×D₄	1	2	yes	—
292	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
293	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
294	Dic₁₂	—	2	4	no	—
295	#204	—	2	4	no	—
296	ΓL(1,𝔽₂₅)	C₅×D₄	1	8	yes	complemented
297	C₂³×C₅	—	2	1	no	—
298	C₂³×C₅	—	3	1	no	—
299	C₂³×C₅	—	6	1	no	—
300	C₅×Q₈	—	2	2	no	—
301	C₅×Q₈	—	2	2	no	—
302	C₅×Q₈	—	2	2	no	—
303	C₅×Q₈	—	6	2	no	—
304	C₅×Q₈	—	6	2	no	—
305	C₅×Q₈	—	6	2	no	—
306	C₅×Q₈	—	12	4	no	—
307	C₅×D₄	—	2	2	no	—
308	C₅×D₄	—	6	2	no	—
309	C₅×D₄	—	12	4	no	—
310	C₅×D₄	—	12	2	no	—
311	C₅×D₄	—	12	2	no	—
312	C₂×C₄×C₅	—	2	1	no	—
313	C₂×C₄×C₅	—	2	2	no	—
314	C₂×C₄×C₅	—	3	2	no	—
315	C₂×C₄×C₅	—	3	1	no	—
316	C₂×C₄×C₅	—	3	4	no	—
317	C₂×C₄×C₅	—	6	4	no	—
318	C₂×C₄×C₅	—	6	1	no	—
319	C₂×C₄×C₅	—	6	2	no	—
320	C₂×C₄×C₅	—	12	2	no	—
321	C₂×C₄×C₅	—	12	2	no	—
322	C₂×C₄×C₅	—	12	4	no	—
323	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
324	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
325	C₅×C₈	—	3	4	no	—
326	C₅×C₈	D₃×D₄	1	4	yes	—
327	C₂×#41	—	3	1	no	—
328	C₂×#41	—	3	1	no	—
329	C₂²×Q₈	—	3	2	no	—
330	#137	—	6	8	no	—
331	#137	—	6	8	no	—
332	C₂×Q₁₆	—	3	2	no	—
333	C₂×Q₁₆	—	3	2	no	—
334	C₂×Q₁₆	—	3	2	no	—
335	C₂×Q₁₆	C₂×C₅×D₃	1	2	yes	—
336	C₂×SD₁₆	—	3	2	no	—
337	C₂×SD₁₆	—	3	2	no	—
338	C₂×SD₁₆	—	3	2	no	—
339	C₂×SD₁₆	C₂×C₅×D₃	1	2	yes	—
340	C₂×M₁₆	—	3	2	no	—
341	C₄⋊Q₈	—	3	2	no	—
342	C₄⋊Q₈	—	3	1	no	—
343	C₄⋊Q₈	—	3	1	no	—
344	C₄⋊Q₈	—	6	2	no	—
345	C₄⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic
346	#127	—	3	1	no	—
347	#124	—	3	1	no	—
348	#124	C₂×C₅×D₃	1	1	yes	characteristic
349	#121	—	6	2	no	—
350	C₄×D₄	—	6	2	no	—
351	C₂×C₄⋊C₄	—	6	2	no	—
352	C₂×C₄²	—	3	1	no	—
353	#97	—	3	1	no	—
354	#97	C₂×C₅×D₃	1	1	yes	characteristic
355	C₄×C₈	—	3	2	no	—
356	C₂×C₃×C₅	—	8	1	no	—
357	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
358	C₂×C₃×C₅	C₂×#137	1	2	yes	—
359	C₅×D₃	—	2	2	no	—
360	C₅×D₃	—	8	1	no	—
361	C₂³×C₃	—	2	1	no	—
362	C₂²×D₃	—	2	1	no	—
363	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
364	C₃×Q₈	—	2	2	no	—
365	C₃×Q₈	—	2	2	no	—
366	C₃×Q₈	—	2	2	no	—
367	C₃×D₄	—	2	2	no	—
368	C₂×C₃×C₄	—	2	1	no	—
369	C₂×C₃×C₄	—	2	2	no	—
370	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
371	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
372	#67	—	4	2	no	—
373	#67	—	4	4	no	—
374	C₂×Dic₃	—	2	2	no	—
375	C₂×Dic₃	—	2	1	no	—
376	C₂×Dic₃	—	4	2	no	—
377	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
378	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
379	D₁₂	—	2	2	no	—
380	D₁₂	—	4	2	no	—
381	C₄×D₃	—	2	4	no	—
382	C₄×D₃	—	4	4	no	—
383	C₄×D₃	—	4	2	no	—
384	C₄×D₃	C₂×C₅×D₄	1	4	yes	—
385	Dic₆	—	2	2	no	—
386	Dic₆	—	2	2	no	—
387	Dic₆	—	2	2	no	—
388	Dic₆	—	4	4	no	—
389	C₃×C₈	C₂×C₅×D₄	1	4	yes	—
390	C₃⋊C₈	C₂×C₅×D₄	1	4	yes	—
391	C₂²×C₅	—	3	2	no	—
392	C₂²×C₅	—	4	1	no	—
393	C₂²×C₅	—	4	2	no	—
394	C₂²×C₅	—	6	2	no	—
395	C₂²×C₅	—	12	1	no	—
396	C₂²×C₅	—	12	2	no	—
397	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
398	C₄×C₅	—	2	2	no	—
399	C₄×C₅	—	3	2	no	—
400	C₄×C₅	—	3	4	no	—
401	C₄×C₅	—	4	1	no	—
402	C₄×C₅	—	4	2	no	—
403	C₄×C₅	—	12	1	no	—
404	C₄×C₅	—	12	2	no	—
405	C₄×C₅	C₂×D₃×D₄	1	2	yes	—
406	#41	—	6	4	no	—
407	#41	—	6	4	no	—
408	C₂×Q₈	—	3	1	no	—
409	C₂×Q₈	—	3	2	no	—
410	C₂×Q₈	—	6	2	no	—
411	C₂×Q₈	—	6	4	no	—
412	C₂×Q₈	—	6	4	no	—
413	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
414	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
415	C₂×D₄	—	3	1	no	—
416	C₂×D₄	—	6	1	no	—
417	C₂×D₄	—	6	2	no	—
418	C₂×D₄	—	6	1	no	—
419	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
420	C₂²×C₄	—	3	1	no	—
421	C₂²×C₄	—	3	2	no	—
422	C₂²×C₄	—	6	1	no	—
423	C₂²×C₄	—	6	2	no	—
424	C₂²×C₄	—	6	1	no	—
425	Q₁₆	—	2	4	no	—
426	Q₁₆	—	6	4	no	—
427	Q₁₆	—	6	4	no	—
428	Q₁₆	—	6	4	no	—
429	SD₁₆	—	2	4	no	—
430	SD₁₆	—	6	4	no	—
431	SD₁₆	—	6	4	no	—
432	SD₁₆	—	6	4	no	—
433	M₁₆	—	3	8	no	—
434	C₂×C₈	—	3	2	no	—
435	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
436	C₄⋊C₄	—	2	2	no	—
437	C₄⋊C₄	—	6	4	no	—
438	C₄⋊C₄	—	6	2	no	—
439	C₄⋊C₄	—	6	2	no	—
440	C₂²⋊C₄	—	2	2	no	—
441	C₂²⋊C₄	—	6	2	no	—
442	C₄²	—	3	2	no	—
443	C₄²	—	3	1	no	—
444	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
445	C₃×C₅	#3152	1	1	yes	characteristic, complemented, Hall
446	C₂²×C₃	—	4	1	no	—
447	C₂²×C₃	—	4	2	no	—
448	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
449	C₂×D₃	—	2	2	no	—
450	C₂×D₃	—	4	1	no	—
451	C₂×D₃	—	4	2	no	—
452	C₂×D₃	C₅×#127	1	2	yes	—
453	C₃×C₄	—	2	2	no	—
454	C₃×C₄	—	4	2	no	—
455	C₃×C₄	—	4	1	no	—
456	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
457	Dic₃	—	4	2	no	—
458	Dic₃	—	4	1	no	—
459	Dic₃	C₅×#127	1	2	yes	—
460	Dic₃	C₅×#137	1	4	yes	complemented
461	C₂×C₅	—	6	2	no	—
462	C₂×C₅	—	8	1	no	—
463	C₂×C₅	—	24	1	no	—
464	C₂×C₅	D₃×#127	1	1	yes	characteristic
465	C₂×C₅	D₃×#137	1	2	yes	—
466	C₂³	—	2	1	no	—
467	C₂³	—	3	1	no	—
468	C₂³	—	6	1	no	—
469	Q₈	—	2	2	no	—
470	Q₈	—	2	2	no	—
471	Q₈	—	2	2	no	—
472	Q₈	—	6	2	no	—
473	Q₈	—	6	2	no	—
474	Q₈	—	6	2	no	—
475	Q₈	—	12	4	no	—
476	D₄	—	2	2	no	—
477	D₄	—	6	2	no	—
478	D₄	—	12	4	no	—
479	D₄	—	12	2	no	—
480	D₄	—	12	2	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	3	2	no	—
484	C₂×C₄	—	3	1	no	—
485	C₂×C₄	—	3	4	no	—
486	C₂×C₄	—	6	4	no	—
487	C₂×C₄	—	6	1	no	—
488	C₂×C₄	—	6	2	no	—
489	C₂×C₄	—	12	2	no	—
490	C₂×C₄	—	12	2	no	—
491	C₂×C₄	—	12	4	no	—
492	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
493	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
494	C₈	—	3	4	no	—
495	C₈	C₅×D₃×D₄	1	4	yes	—
496	C₂×C₃	—	8	1	no	—
497	C₂×C₃	C₂×C₅×#127	1	1	yes	characteristic
498	C₂×C₃	C₂×C₅×#137	1	2	yes	—
499	D₃	—	2	2	no	—
500	D₃	—	8	1	no	—
501	C₅	#81870	1	1	yes	characteristic, direct product factor, Sylow
502	C₂²	—	3	2	no	—
503	C₂²	—	4	1	no	—
504	C₂²	—	4	2	no	—
505	C₂²	—	6	2	no	—
506	C₂²	—	12	1	no	—
507	C₂²	—	12	2	no	—
508	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
509	C₄	—	2	2	no	—
510	C₄	—	3	2	no	—
511	C₄	—	3	4	no	—
512	C₄	—	4	1	no	—
513	C₄	—	4	2	no	—
514	C₄	—	12	1	no	—
515	C₄	—	12	2	no	—
516	C₄	C₂×C₅×D₃×D₄	1	2	yes	—
517	C₃	C₅×#3152	1	1	yes	characteristic, complemented, Sylow
518	C₂	—	6	2	no	—
519	C₂	—	8	1	no	—
520	C₂	—	24	1	no	—
521	C₂	C₅×D₃×#127	1	1	yes	characteristic
522	C₂	C₅×D₃×#137	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×#497	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₅×#5668	C₂
hypercenter	C₅×#497	D₃
hypocenter	C₃	C₅×#3152
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#497

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#918	C₂	semidirect
2. C₂×C₅×#915	C₂	semidirect
3. C₅×D₃×C₄⋊Q₈	C₂	semidirect
5. C₃×C₅×#497	C₂	semidirect
6. C₅×#5183	C₂	semidirect
7. C₅×#5175	C₂	semidirect
8. C₅×#5086	C₂	semidirect
9. C₅×#5060	C₂	semidirect
10. C₅×#4715	C₂	semidirect
11. C₅×#4707	C₂	semidirect
42. #81870	C₅	direct (N × H)
50. C₅×#497	D₃	semidirect
92. C₅×ΓL(1,𝔽₂₅)	D₄	semidirect
93. C₂×#918	C₂×C₅	semidirect
94. C₂×#915	C₂×C₅	semidirect
95. D₃×C₄⋊Q₈	C₂×C₅	semidirect
97. C₃×#497	C₂×C₅	semidirect
98. #5183	C₂×C₅	semidirect
99. #5175	C₂×C₅	semidirect
100. #5086	C₂×C₅	semidirect
101. #5060	C₂×C₅	semidirect
102. #4715	C₂×C₅	semidirect
103. #4707	C₂×C₅	semidirect
239. #497	C₅×D₃	semidirect
257. C₅×Dic₃	#137	semidirect
296. ΓL(1,𝔽₂₅)	C₅×D₄	semidirect
445. C₃×C₅	#3152	semidirect
460. Dic₃	C₅×#137	semidirect
501. C₅	#81870	direct (N × H)
517. C₃	C₅×#3152	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#918	2
C₂×C₅×#915	2
C₅×D₃×C₄⋊Q₈	2
C₅×#5668	2
C₃×C₅×#497	2
C₅×#5183	2
C₅×#5175	2
C₅×#5086	2
C₅×#5060	2
C₅×#4715	2
C₅×#4707	2
C₅×#3152	3
#81870	5

Subgroups — C5×#81870 #14439204

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#81870 #14439204