Subgroups — C₅×#79889 #14418104

Order 1920.

916 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5768	C₂	1	1	yes	maximal, characteristic
2	C₅×#5750	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#443	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5197	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5145	C₂	1	2	yes	maximal, complemented
6	C₅×#4894	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4893	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4824	C₂	1	2	yes	maximal, complemented
9	C₅×D₃×#104	C₂	1	2	yes	maximal, complemented
10	C₅×#4700	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₅×ΓL(1,𝔽₂₅)	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#2956	—	3	1	no	maximal, Hall
13	C₅×D₃×#41	C₂²	1	2	yes	—
14	C₃×C₅×#135	C₂²	1	1	yes	characteristic
15	C₃×C₅×#131	C₂²	1	2	yes	complemented
16	C₅×#950	C₂²	1	2	yes	—
17	C₅×#948	C₂²	1	2	yes	complemented
18	C₅×#918	C₄	1	2	yes	complemented
19	C₅×#915	C₄	1	2	yes	complemented
20	C₅×#914	C₄	1	2	yes	complemented
21	C₅×#911	C₄	1	2	yes	complemented
22	C₅×#907	—	2	2	no	—
23	C₅×#907	C₂²	1	2	yes	complemented
24	C₅×D₃×M₁₆	—	2	2	no	—
25	C₅×D₃×M₁₆	C₂²	1	2	yes	—
26	C₅×#904	C₂²	1	1	yes	characteristic
27	C₅×#901	—	2	2	no	—
28	C₅×#901	C₂²	1	2	yes	complemented
29	C₂×C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
30	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
31	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
32	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
33	C₃×C₅×#108	C₂²	1	1	yes	characteristic, complemented
34	C₃×C₅×#104	C₂²	1	2	yes	complemented
35	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
36	C₅×#837	C₂²	1	2	yes	complemented
37	C₅×#825	C₂²	1	2	yes	complemented
38	C₅×#822	C₂²	1	2	yes	complemented
39	C₅×#819	C₂²	1	1	yes	characteristic, complemented
40	C₅×#815	C₂²	1	1	yes	characteristic, complemented
41	C₅×#815	C₂²	1	1	yes	characteristic, complemented
42	C₅×#805	C₂²	1	2	yes	complemented
43	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
44	#79889	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
45	C₅×#575	—	3	1	no	—
46	C₅×#568	—	3	2	no	—
47	C₅×#444	—	3	1	no	—
48	C₅×#444	—	3	1	no	—
49	C₅×#444	—	3	2	no	—
50	C₅×#443	—	3	2	no	—
51	C₅×#443	—	3	1	no	—
52	C₅×#443	D₃	1	1	yes	characteristic, complemented
53	C₅×#430	—	3	1	no	—
54	C₂×C₅×#104	—	3	2	no	—
55	C₄×C₅×M₁₆	—	3	1	no	—
56	C₃×C₅×#41	C₂³	1	2	yes	—
57	C₅×#239	C₂×C₄	1	2	yes	—
58	C₅×D₃×Q₈	C₂×C₄	1	2	yes	—
59	C₅×#237	—	2	2	no	—
60	C₅×#237	C₂×C₄	1	2	yes	—
61	C₅×D₃×D₄	—	2	2	no	—
62	C₅×D₃×D₄	C₂×C₄	1	2	yes	—
63	C₅×#235	—	2	2	no	—
64	C₅×#235	C₂³	1	2	yes	—
65	C₂×C₄×C₅×D₃	—	2	2	no	—
66	C₂×C₄×C₅×D₃	—	2	1	no	—
67	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
68	C₃×C₅×Q₁₆	C₂×C₄	1	1	yes	characteristic, complemented
69	C₃×C₅×SD₁₆	C₂×C₄	1	2	yes	complemented
70	C₃×C₅×D₈	C₂×C₄	1	1	yes	characteristic, complemented
71	C₃×C₅×M₁₆	—	2	2	no	—
72	C₃×C₅×M₁₆	C₂³	1	2	yes	—
73	C₂×C₃×C₅×C₈	—	2	2	no	—
74	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
75	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
76	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
77	C₅×#216	C₂×C₄	1	2	yes	complemented
78	C₅×#215	C₂×C₄	1	2	yes	complemented
79	C₅×#214	C₂×C₄	1	2	yes	complemented
80	C₅×#213	C₂×C₄	1	2	yes	complemented
81	C₄×C₅×Dic₃	—	2	1	no	—
82	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
83	C₅×#208	—	2	2	no	—
84	C₅×#208	C₂³	1	2	yes	—
85	C₂×C₅×C₃⋊C₈	—	2	2	no	—
86	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
87	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
88	C₅×Dic₁₂	C₂×C₄	1	1	yes	characteristic, complemented
89	C₅×D₂₄	C₂×C₄	1	1	yes	characteristic, complemented
90	C₅×#204	C₂×C₄	1	2	yes	complemented
91	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
92	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
93	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
94	C₅×ΓL(1,𝔽₂₅)	C₂×C₄	1	2	yes	—
95	C₅×ΓL(1,𝔽₂₅)	C₂×C₄	1	2	yes	—
96	C₅×ΓL(1,𝔽₂₅)	D₄	1	2	yes	—
97	C₅×ΓL(1,𝔽₂₅)	D₄	1	2	yes	—
98	C₅×D₃×C₈	—	2	2	no	—
99	C₅×D₃×C₈	—	2	2	no	—
100	C₅×D₃×C₈	—	2	2	no	—
101	#5768	C₂×C₅	1	1	yes	characteristic
102	#5750	C₂×C₅	1	2	yes	complemented
103	C₃×#443	C₂×C₅	1	1	yes	characteristic, complemented
104	#5197	C₂×C₅	1	1	yes	characteristic, complemented
105	#5145	C₂×C₅	1	2	yes	complemented
106	#4894	C₂×C₅	1	1	yes	characteristic, complemented
107	#4893	C₂×C₅	1	1	yes	characteristic, complemented
108	#4824	C₂×C₅	1	2	yes	complemented
109	D₃×#104	C₂×C₅	1	2	yes	complemented
110	#4700	C₂×C₅	1	1	yes	characteristic, complemented
111	C₄×ΓL(1,𝔽₂₅)	C₂×C₅	1	1	yes	characteristic, complemented
112	C₂×C₅×#41	—	3	2	no	—
113	C₅×#137	—	3	2	no	—
114	C₅×#137	—	3	2	no	—
115	C₅×AGL(1,ℤ/8)	—	3	2	no	—
116	C₅×AGL(1,ℤ/8)	—	3	2	no	—
117	C₅×#135	—	3	2	no	—
118	C₅×#135	—	3	1	no	—
119	C₅×#135	C₂×D₃	1	1	yes	characteristic
120	C₅×#131	—	3	2	no	—
121	C₅×#131	—	3	2	no	—
122	C₅×#131	—	3	2	no	—
123	C₅×#131	—	6	2	no	—
124	C₅×#131	—	6	2	no	—
125	C₅×#131	C₂×D₃	1	2	yes	complemented
126	C₂×C₅×M₁₆	—	3	1	no	—
127	C₂×C₅×M₁₆	—	3	1	no	—
128	C₂×C₅×M₁₆	—	3	2	no	—
129	C₂×C₅×M₁₆	—	6	2	no	—
130	C₂×C₅×M₁₆	—	6	2	no	—
131	C₂×C₄²×C₅	—	3	1	no	—
132	C₅×#108	—	3	2	no	—
133	C₅×#108	—	3	1	no	—
134	C₅×#108	C₂×D₃	1	1	yes	characteristic, complemented
135	C₅×#104	—	3	2	no	—
136	C₅×#104	—	3	2	no	—
137	C₅×#104	—	3	2	no	—
138	C₅×#104	C₂×D₃	1	2	yes	complemented
139	C₅×#97	—	3	1	no	—
140	C₅×#97	—	3	1	no	—
141	C₄×C₅×C₈	—	3	1	no	—
142	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic, complemented
143	#2956	—	3	1	no	Sylow
144	C₂²×C₅×D₃	—	2	2	no	—
145	C₂²×C₅×D₃	#41	1	1	yes	characteristic
146	C₃×C₅×Q₈	C₂²×C₄	1	2	yes	—
147	C₃×C₅×D₄	—	2	2	no	—
148	C₃×C₅×D₄	C₂²×C₄	1	2	yes	—
149	C₂×C₃×C₄×C₅	—	2	1	no	—
150	C₂×C₃×C₄×C₅	—	2	2	no	—
151	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
152	C₅×#67	—	2	2	no	—
153	C₅×#67	—	2	2	no	—
154	C₅×#67	—	2	2	no	—
155	C₂×C₅×Dic₃	—	2	2	no	—
156	C₂×C₅×Dic₃	—	2	1	no	—
157	C₂×C₅×Dic₃	#41	1	1	yes	characteristic
158	C₅×D₁₂	—	2	2	no	—
159	C₅×D₁₂	C₂²×C₄	1	2	yes	—
160	C₄×C₅×D₃	—	2	2	no	—
161	C₄×C₅×D₃	—	2	2	no	—
162	C₄×C₅×D₃	—	2	2	no	—
163	C₄×C₅×D₃	—	4	2	no	—
164	C₄×C₅×D₃	C₂²×C₄	1	2	yes	—
165	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
166	C₅×Dic₆	—	2	2	no	—
167	C₅×Dic₆	C₂²×C₄	1	2	yes	—
168	C₃×C₅×C₈	—	2	2	no	—
169	C₃×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
170	C₃×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
171	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
172	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
173	C₅×C₃⋊C₈	—	2	2	no	—
174	C₅×C₃⋊C₈	C₂²×C₄	1	2	yes	—
175	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	—
176	D₃×#41	C₂²×C₅	1	2	yes	—
177	C₃×#135	C₂²×C₅	1	1	yes	characteristic
178	C₃×#131	C₂²×C₅	1	2	yes	complemented
179	#950	C₂²×C₅	1	2	yes	—
180	#948	C₂²×C₅	1	2	yes	complemented
181	#918	C₄×C₅	1	2	yes	complemented
182	#915	C₄×C₅	1	2	yes	complemented
183	#914	C₄×C₅	1	2	yes	complemented
184	#911	C₄×C₅	1	2	yes	complemented
185	#907	—	2	2	no	—
186	#907	C₂²×C₅	1	2	yes	complemented
187	D₃×M₁₆	—	2	2	no	—
188	D₃×M₁₆	C₂²×C₅	1	2	yes	—
189	#904	C₂²×C₅	1	1	yes	characteristic
190	#901	—	2	2	no	—
191	#901	C₂²×C₅	1	2	yes	complemented
192	C₂×ΓL(1,𝔽₂₅)	—	2	2	no	—
193	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	1	yes	characteristic
194	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	1	yes	characteristic
195	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
196	C₃×#108	C₂²×C₅	1	1	yes	characteristic, complemented
197	C₃×#104	C₂²×C₅	1	2	yes	complemented
198	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
199	#837	C₂²×C₅	1	2	yes	complemented
200	#825	C₂²×C₅	1	2	yes	complemented
201	#822	C₂²×C₅	1	2	yes	complemented
202	#819	C₂²×C₅	1	1	yes	characteristic, complemented
203	#815	C₂²×C₅	1	1	yes	characteristic, complemented
204	#815	C₂²×C₅	1	1	yes	characteristic, complemented
205	#805	C₂²×C₅	1	2	yes	complemented
206	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
207	C₅×#41	—	3	2	no	—
208	C₅×#41	—	3	2	no	—
209	C₅×#41	—	3	2	no	—
210	C₅×#41	—	6	2	no	—
211	C₅×#41	—	6	2	no	—
212	C₅×#41	C₂²×D₃	1	2	yes	—
213	C₂×C₅×Q₈	—	3	2	no	—
214	C₂×C₅×D₄	—	3	2	no	—
215	C₂×C₅×D₄	—	6	2	no	—
216	C₂²×C₄×C₅	—	3	1	no	—
217	C₂²×C₄×C₅	—	6	2	no	—
218	C₂²×C₄×C₅	—	6	1	no	—
219	C₅×Q₁₆	—	3	2	no	—
220	C₅×Q₁₆	—	3	1	no	—
221	C₅×Q₁₆	C₄×D₃	1	1	yes	characteristic, complemented
222	C₅×SD₁₆	—	3	2	no	—
223	C₅×SD₁₆	—	3	2	no	—
224	C₅×SD₁₆	—	3	2	no	—
225	C₅×SD₁₆	C₄×D₃	1	2	yes	complemented
226	C₅×D₈	—	3	2	no	—
227	C₅×D₈	—	3	1	no	—
228	C₅×D₈	C₄×D₃	1	1	yes	characteristic, complemented
229	C₅×M₁₆	—	2	2	no	—
230	C₅×M₁₆	—	3	2	no	—
231	C₅×M₁₆	—	3	2	no	—
232	C₅×M₁₆	—	3	2	no	—
233	C₅×M₁₆	—	3	2	no	—
234	C₅×M₁₆	—	3	2	no	—
235	C₅×M₁₆	—	6	2	no	—
236	C₅×M₁₆	—	6	2	no	—
237	C₅×M₁₆	—	6	2	no	—
238	C₅×M₁₆	—	6	2	no	—
239	C₅×M₁₆	C₂²×D₃	1	2	yes	—
240	C₂×C₅×C₈	—	2	2	no	—
241	C₂×C₅×C₈	—	3	1	no	—
242	C₂×C₅×C₈	—	3	1	no	—
243	C₂×C₅×C₈	—	6	2	no	—
244	C₂×C₅×C₈	—	6	2	no	—
245	C₂×C₅×C₈	—	6	2	no	—
246	C₂×C₅×C₈	—	6	2	no	—
247	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
248	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
249	C₄²×C₅	—	3	1	no	—
250	C₄²×C₅	—	6	1	no	—
251	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
252	#575	—	3	1	no	—
253	#568	—	3	2	no	—
254	#444	—	3	1	no	—
255	#444	—	3	2	no	—
256	#444	—	3	1	no	—
257	#443	—	3	2	no	—
258	#443	—	3	1	no	—
259	#443	C₅×D₃	1	1	yes	characteristic, complemented
260	#430	—	3	1	no	—
261	C₂×#104	—	3	2	no	—
262	C₄×M₁₆	—	3	1	no	—
263	C₂²×C₃×C₅	—	2	2	no	—
264	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
265	C₂×C₅×D₃	—	2	2	no	—
266	C₂×C₅×D₃	—	4	1	no	—
267	C₂×C₅×D₃	—	8	2	no	—
268	C₂×C₅×D₃	C₄×D₄	1	2	yes	—
269	C₃×C₄×C₅	—	2	2	no	—
270	C₃×C₄×C₅	—	2	2	no	—
271	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
272	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
273	C₅×Dic₃	—	2	2	no	—
274	C₅×Dic₃	—	4	1	no	—
275	C₅×Dic₃	C₄×D₄	1	2	yes	—
276	C₃×#41	C₂³×C₅	1	2	yes	—
277	#239	C₂×C₄×C₅	1	2	yes	—
278	D₃×Q₈	C₂×C₄×C₅	1	2	yes	—
279	#237	—	2	2	no	—
280	#237	C₂×C₄×C₅	1	2	yes	—
281	D₃×D₄	—	2	2	no	—
282	D₃×D₄	C₂×C₄×C₅	1	2	yes	—
283	#235	—	2	2	no	—
284	#235	C₂³×C₅	1	2	yes	—
285	C₂×C₄×D₃	—	2	2	no	—
286	C₂×C₄×D₃	—	2	1	no	—
287	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
288	C₃×Q₁₆	C₂×C₄×C₅	1	1	yes	characteristic, complemented
289	C₃×SD₁₆	C₂×C₄×C₅	1	2	yes	complemented
290	C₃×D₈	C₂×C₄×C₅	1	1	yes	characteristic, complemented
291	C₃×M₁₆	—	2	2	no	—
292	C₃×M₁₆	C₂³×C₅	1	2	yes	—
293	C₂×C₃×C₈	—	2	2	no	—
294	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
295	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
296	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
297	#216	C₂×C₄×C₅	1	2	yes	complemented
298	#215	C₂×C₄×C₅	1	2	yes	complemented
299	#214	C₂×C₄×C₅	1	2	yes	complemented
300	#213	C₂×C₄×C₅	1	2	yes	complemented
301	C₄×Dic₃	—	2	1	no	—
302	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
303	#208	—	2	2	no	—
304	#208	C₂³×C₅	1	2	yes	—
305	C₂×C₃⋊C₈	—	2	2	no	—
306	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
307	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
308	Dic₁₂	C₂×C₄×C₅	1	1	yes	characteristic, complemented
309	D₂₄	C₂×C₄×C₅	1	1	yes	characteristic, complemented
310	#204	C₂×C₄×C₅	1	2	yes	complemented
311	ΓL(1,𝔽₂₅)	—	2	2	no	—
312	ΓL(1,𝔽₂₅)	—	2	2	no	—
313	ΓL(1,𝔽₂₅)	—	2	2	no	—
314	ΓL(1,𝔽₂₅)	C₂×C₄×C₅	1	2	yes	—
315	ΓL(1,𝔽₂₅)	C₂×C₄×C₅	1	2	yes	—
316	ΓL(1,𝔽₂₅)	C₅×D₄	1	2	yes	—
317	ΓL(1,𝔽₂₅)	C₅×D₄	1	2	yes	—
318	D₃×C₈	—	2	2	no	—
319	D₃×C₈	—	2	2	no	—
320	D₃×C₈	—	2	2	no	—
321	C₂³×C₅	—	3	1	no	—
322	C₂³×C₅	—	6	2	no	—
323	C₅×Q₈	—	3	2	no	—
324	C₅×Q₈	—	6	2	no	—
325	C₅×Q₈	C₂×C₄×D₃	1	2	yes	—
326	C₅×D₄	—	2	2	no	—
327	C₅×D₄	—	3	2	no	—
328	C₅×D₄	—	6	2	no	—
329	C₅×D₄	—	6	2	no	—
330	C₅×D₄	—	6	2	no	—
331	C₅×D₄	—	6	2	no	—
332	C₅×D₄	C₂×C₄×D₃	1	2	yes	—
333	C₂×C₄×C₅	—	2	1	no	—
334	C₂×C₄×C₅	—	2	2	no	—
335	C₂×C₄×C₅	—	3	1	no	—
336	C₂×C₄×C₅	—	3	2	no	—
337	C₂×C₄×C₅	—	3	2	no	—
338	C₂×C₄×C₅	—	6	2	no	—
339	C₂×C₄×C₅	—	6	2	no	—
340	C₂×C₄×C₅	—	6	2	no	—
341	C₂×C₄×C₅	—	6	2	no	—
342	C₂×C₄×C₅	—	6	1	no	—
343	C₂×C₄×C₅	—	12	2	no	—
344	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
345	C₅×C₈	—	2	2	no	—
346	C₅×C₈	—	3	2	no	—
347	C₅×C₈	—	3	2	no	—
348	C₅×C₈	—	6	2	no	—
349	C₅×C₈	C₂×C₄×D₃	1	1	yes	characteristic
350	C₅×C₈	C₂×C₄×D₃	1	1	yes	characteristic
351	C₅×C₈	D₃×D₄	1	1	yes	characteristic
352	C₅×C₈	D₃×D₄	1	1	yes	characteristic
353	C₂×#41	—	3	2	no	—
354	#137	—	3	2	no	—
355	#137	—	3	2	no	—
356	AGL(1,ℤ/8)	—	3	2	no	—
357	AGL(1,ℤ/8)	—	3	2	no	—
358	#135	—	3	2	no	—
359	#135	—	3	1	no	—
360	#135	C₂×C₅×D₃	1	1	yes	characteristic
361	#131	—	3	2	no	—
362	#131	—	3	2	no	—
363	#131	—	3	2	no	—
364	#131	—	6	2	no	—
365	#131	—	6	2	no	—
366	#131	C₂×C₅×D₃	1	2	yes	complemented
367	C₂×M₁₆	—	3	1	no	—
368	C₂×M₁₆	—	3	1	no	—
369	C₂×M₁₆	—	3	2	no	—
370	C₂×M₁₆	—	6	2	no	—
371	C₂×M₁₆	—	6	2	no	—
372	C₂×C₄²	—	3	1	no	—
373	#108	—	3	2	no	—
374	#108	—	3	1	no	—
375	#108	C₂×C₅×D₃	1	1	yes	characteristic, complemented
376	#104	—	3	2	no	—
377	#104	—	3	2	no	—
378	#104	—	3	2	no	—
379	#104	C₂×C₅×D₃	1	2	yes	complemented
380	#97	—	3	1	no	—
381	#97	—	3	1	no	—
382	C₄×C₈	—	3	1	no	—
383	C₄×C₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
384	C₂×C₃×C₅	—	2	1	no	—
385	C₂×C₃×C₅	—	4	2	no	—
386	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
387	C₅×D₃	—	2	2	no	—
388	C₅×D₃	—	4	2	no	—
389	C₂²×D₃	—	2	2	no	—
390	C₂²×D₃	C₅×#41	1	1	yes	characteristic
391	C₃×Q₈	C₂²×C₄×C₅	1	2	yes	—
392	C₃×D₄	—	2	2	no	—
393	C₃×D₄	C₂²×C₄×C₅	1	2	yes	—
394	C₂×C₃×C₄	—	2	1	no	—
395	C₂×C₃×C₄	—	2	2	no	—
396	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
397	#67	—	2	2	no	—
398	#67	—	2	2	no	—
399	#67	—	2	2	no	—
400	C₂×Dic₃	—	2	2	no	—
401	C₂×Dic₃	—	2	1	no	—
402	C₂×Dic₃	C₅×#41	1	1	yes	characteristic
403	D₁₂	—	2	2	no	—
404	D₁₂	C₂²×C₄×C₅	1	2	yes	—
405	C₄×D₃	—	2	2	no	—
406	C₄×D₃	—	2	2	no	—
407	C₄×D₃	—	2	2	no	—
408	C₄×D₃	—	4	2	no	—
409	C₄×D₃	C₂²×C₄×C₅	1	2	yes	—
410	C₄×D₃	C₂×C₅×D₄	1	2	yes	—
411	Dic₆	—	2	2	no	—
412	Dic₆	C₂²×C₄×C₅	1	2	yes	—
413	C₃×C₈	—	2	2	no	—
414	C₃×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
415	C₃×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
416	C₃×C₈	C₂×C₅×D₄	1	1	yes	characteristic
417	C₃×C₈	C₂×C₅×D₄	1	1	yes	characteristic
418	C₃⋊C₈	—	2	2	no	—
419	C₃⋊C₈	C₂²×C₄×C₅	1	2	yes	—
420	C₃⋊C₈	C₂×C₅×D₄	1	2	yes	—
421	C₂²×C₅	—	2	2	no	—
422	C₂²×C₅	—	3	2	no	—
423	C₂²×C₅	—	6	2	no	—
424	C₂²×C₅	—	12	1	no	—
425	C₂²×C₅	—	24	2	no	—
426	C₂²×C₅	D₃×#41	1	1	yes	characteristic
427	C₄×C₅	—	2	2	no	—
428	C₄×C₅	—	2	2	no	—
429	C₄×C₅	—	3	2	no	—
430	C₄×C₅	—	6	2	no	—
431	C₄×C₅	—	12	1	no	—
432	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
433	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
434	#41	—	3	2	no	—
435	#41	—	3	2	no	—
436	#41	—	3	2	no	—
437	#41	—	6	2	no	—
438	#41	—	6	2	no	—
439	#41	C₂²×C₅×D₃	1	2	yes	—
440	C₂×Q₈	—	3	2	no	—
441	C₂×D₄	—	3	2	no	—
442	C₂×D₄	—	6	2	no	—
443	C₂²×C₄	—	3	1	no	—
444	C₂²×C₄	—	6	2	no	—
445	C₂²×C₄	—	6	1	no	—
446	Q₁₆	—	3	2	no	—
447	Q₁₆	—	3	1	no	—
448	Q₁₆	C₄×C₅×D₃	1	1	yes	characteristic, complemented
449	SD₁₆	—	3	2	no	—
450	SD₁₆	—	3	2	no	—
451	SD₁₆	—	3	2	no	—
452	SD₁₆	C₄×C₅×D₃	1	2	yes	complemented
453	D₈	—	3	2	no	—
454	D₈	—	3	1	no	—
455	D₈	C₄×C₅×D₃	1	1	yes	characteristic, complemented
456	M₁₆	—	2	2	no	—
457	M₁₆	—	3	2	no	—
458	M₁₆	—	3	2	no	—
459	M₁₆	—	3	2	no	—
460	M₁₆	—	3	2	no	—
461	M₁₆	—	3	2	no	—
462	M₁₆	—	6	2	no	—
463	M₁₆	—	6	2	no	—
464	M₁₆	—	6	2	no	—
465	M₁₆	—	6	2	no	—
466	M₁₆	C₂²×C₅×D₃	1	2	yes	—
467	C₂×C₈	—	2	2	no	—
468	C₂×C₈	—	3	1	no	—
469	C₂×C₈	—	3	1	no	—
470	C₂×C₈	—	6	2	no	—
471	C₂×C₈	—	6	2	no	—
472	C₂×C₈	—	6	2	no	—
473	C₂×C₈	—	6	2	no	—
474	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
475	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
476	C₄²	—	3	1	no	—
477	C₄²	—	6	1	no	—
478	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
479	C₃×C₅	#2956	1	1	yes	characteristic, complemented, Hall
480	C₂²×C₃	—	2	2	no	—
481	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
482	C₂×D₃	—	2	2	no	—
483	C₂×D₃	—	4	1	no	—
484	C₂×D₃	—	8	2	no	—
485	C₂×D₃	C₄×C₅×D₄	1	2	yes	—
486	C₃×C₄	—	2	2	no	—
487	C₃×C₄	—	2	2	no	—
488	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
489	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
490	Dic₃	—	2	2	no	—
491	Dic₃	—	4	1	no	—
492	Dic₃	C₄×C₅×D₄	1	2	yes	—
493	C₂×C₅	—	2	1	no	—
494	C₂×C₅	—	4	2	no	—
495	C₂×C₅	—	6	2	no	—
496	C₂×C₅	—	12	2	no	—
497	C₂×C₅	C₄×D₃×D₄	1	1	yes	characteristic
498	C₂³	—	3	1	no	—
499	C₂³	—	6	2	no	—
500	Q₈	—	3	2	no	—
501	Q₈	—	6	2	no	—
502	Q₈	C₂×C₄×C₅×D₃	1	2	yes	—
503	D₄	—	2	2	no	—
504	D₄	—	3	2	no	—
505	D₄	—	6	2	no	—
506	D₄	—	6	2	no	—
507	D₄	—	6	2	no	—
508	D₄	—	6	2	no	—
509	D₄	C₂×C₄×C₅×D₃	1	2	yes	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	3	1	no	—
513	C₂×C₄	—	3	2	no	—
514	C₂×C₄	—	3	2	no	—
515	C₂×C₄	—	6	2	no	—
516	C₂×C₄	—	6	2	no	—
517	C₂×C₄	—	6	2	no	—
518	C₂×C₄	—	6	2	no	—
519	C₂×C₄	—	6	1	no	—
520	C₂×C₄	—	12	2	no	—
521	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
522	C₈	—	2	2	no	—
523	C₈	—	3	2	no	—
524	C₈	—	3	2	no	—
525	C₈	—	6	2	no	—
526	C₈	C₂×C₄×C₅×D₃	1	1	yes	characteristic
527	C₈	C₂×C₄×C₅×D₃	1	1	yes	characteristic
528	C₈	C₅×D₃×D₄	1	1	yes	characteristic
529	C₈	C₅×D₃×D₄	1	1	yes	characteristic
530	C₂×C₃	—	2	1	no	—
531	C₂×C₃	—	4	2	no	—
532	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
533	D₃	—	2	2	no	—
534	D₃	—	4	2	no	—
535	C₅	#79889	1	1	yes	characteristic, direct product factor, Sylow
536	C₂²	—	2	2	no	—
537	C₂²	—	3	2	no	—
538	C₂²	—	6	2	no	—
539	C₂²	—	12	1	no	—
540	C₂²	—	24	2	no	—
541	C₂²	C₅×D₃×#41	1	1	yes	characteristic
542	C₄	—	2	2	no	—
543	C₄	—	2	2	no	—
544	C₄	—	3	2	no	—
545	C₄	—	6	2	no	—
546	C₄	—	12	1	no	—
547	C₄	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
548	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
549	C₃	C₅×#2956	1	1	yes	characteristic, complemented, Sylow
550	C₂	—	2	1	no	—
551	C₂	—	4	2	no	—
552	C₂	—	6	2	no	—
553	C₂	—	12	2	no	—
554	C₂	C₄×C₅×D₃×D₄	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₅	C₂×D₃×D₄
commutator	C₃×C₄	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#443	C₂
socle	C₂×C₃×C₅	C₂×C₄×D₄
prime radical	C₅×#5768	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₅×#443	D₃
hypocenter	C₃	C₅×#2956
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄×C₅ ◁ C₂×C₅×C₈ ◁ C₅×#443

Complements

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

N	H ≅ G/N	type
2. C₅×#5750	C₂	semidirect
3. C₃×C₅×#443	C₂	semidirect
4. C₅×#5197	C₂	semidirect
5. C₅×#5145	C₂	semidirect
6. C₅×#4894	C₂	semidirect
7. C₅×#4893	C₂	semidirect
8. C₅×#4824	C₂	semidirect
9. C₅×D₃×#104	C₂	semidirect
10. C₅×#4700	C₂	semidirect
11. C₄×C₅×ΓL(1,𝔽₂₅)	C₂	semidirect
15. C₃×C₅×#131	C₂²	semidirect
17. C₅×#948	C₂²	semidirect
18. C₅×#918	C₄	semidirect
19. C₅×#915	C₄	semidirect
20. C₅×#914	C₄	semidirect
21. C₅×#911	C₄	semidirect
23. C₅×#907	C₂²	semidirect
28. C₅×#901	C₂²	semidirect
33. C₃×C₅×#108	C₂²	semidirect
34. C₃×C₅×#104	C₂²	semidirect
35. C₃×C₄×C₅×C₈	C₂²	semidirect
36. C₅×#837	C₂²	semidirect
37. C₅×#825	C₂²	semidirect
38. C₅×#822	C₂²	semidirect
39. C₅×#819	C₂²	semidirect
40. C₅×#815	C₂²	semidirect
41. C₅×#815	C₂²	semidirect
42. C₅×#805	C₂²	semidirect
43. C₄×C₅×C₃⋊C₈	C₂²	semidirect
44. #79889	C₅	direct (N × H)
52. C₅×#443	D₃	semidirect
68. C₃×C₅×Q₁₆	C₂×C₄	semidirect
69. C₃×C₅×SD₁₆	C₂×C₄	semidirect
70. C₃×C₅×D₈	C₂×C₄	semidirect
77. C₅×#216	C₂×C₄	semidirect
78. C₅×#215	C₂×C₄	semidirect
79. C₅×#214	C₂×C₄	semidirect
80. C₅×#213	C₂×C₄	semidirect
88. C₅×Dic₁₂	C₂×C₄	semidirect
89. C₅×D₂₄	C₂×C₄	semidirect
90. C₅×#204	C₂×C₄	semidirect
102. #5750	C₂×C₅	semidirect
103. C₃×#443	C₂×C₅	semidirect
104. #5197	C₂×C₅	semidirect
105. #5145	C₂×C₅	semidirect
106. #4894	C₂×C₅	semidirect
107. #4893	C₂×C₅	semidirect
108. #4824	C₂×C₅	semidirect
109. D₃×#104	C₂×C₅	semidirect
110. #4700	C₂×C₅	semidirect
111. C₄×ΓL(1,𝔽₂₅)	C₂×C₅	semidirect
125. C₅×#131	C₂×D₃	semidirect
134. C₅×#108	C₂×D₃	semidirect
138. C₅×#104	C₂×D₃	semidirect
142. C₄×C₅×C₈	C₂×D₃	semidirect
178. C₃×#131	C₂²×C₅	semidirect
180. #948	C₂²×C₅	semidirect
181. #918	C₄×C₅	semidirect
182. #915	C₄×C₅	semidirect
183. #914	C₄×C₅	semidirect
184. #911	C₄×C₅	semidirect
186. #907	C₂²×C₅	semidirect
191. #901	C₂²×C₅	semidirect
196. C₃×#108	C₂²×C₅	semidirect
197. C₃×#104	C₂²×C₅	semidirect
198. C₃×C₄×C₈	C₂²×C₅	semidirect
199. #837	C₂²×C₅	semidirect
200. #825	C₂²×C₅	semidirect
201. #822	C₂²×C₅	semidirect
202. #819	C₂²×C₅	semidirect
203. #815	C₂²×C₅	semidirect
204. #815	C₂²×C₅	semidirect
205. #805	C₂²×C₅	semidirect
206. C₄×C₃⋊C₈	C₂²×C₅	semidirect
221. C₅×Q₁₆	C₄×D₃	semidirect
225. C₅×SD₁₆	C₄×D₃	semidirect
228. C₅×D₈	C₄×D₃	semidirect
259. #443	C₅×D₃	semidirect
288. C₃×Q₁₆	C₂×C₄×C₅	semidirect
289. C₃×SD₁₆	C₂×C₄×C₅	semidirect
290. C₃×D₈	C₂×C₄×C₅	semidirect
297. #216	C₂×C₄×C₅	semidirect
298. #215	C₂×C₄×C₅	semidirect
299. #214	C₂×C₄×C₅	semidirect
300. #213	C₂×C₄×C₅	semidirect
308. Dic₁₂	C₂×C₄×C₅	semidirect
309. D₂₄	C₂×C₄×C₅	semidirect
310. #204	C₂×C₄×C₅	semidirect
366. #131	C₂×C₅×D₃	semidirect
375. #108	C₂×C₅×D₃	semidirect
379. #104	C₂×C₅×D₃	semidirect
383. C₄×C₈	C₂×C₅×D₃	semidirect
448. Q₁₆	C₄×C₅×D₃	semidirect
452. SD₁₆	C₄×C₅×D₃	semidirect
455. D₈	C₄×C₅×D₃	semidirect
479. C₃×C₅	#2956	semidirect
535. C₅	#79889	direct (N × H)
549. C₃	C₅×#2956	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5768	2
C₅×#5750	2
C₃×C₅×#443	2
C₅×#5197	2
C₅×#5145	2
C₅×#4894	2
C₅×#4893	2
C₅×#4824	2
C₅×D₃×#104	2
C₅×#4700	2
C₄×C₅×ΓL(1,𝔽₂₅)	2
C₅×#2956	3
#79889	5

Subgroups — C5×#79889 #14418104

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#79889 #14418104