Subgroups — C₅×#78523 #14418969

Order 1920.

824 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅×#235	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5128	C₂	1	2	yes	maximal, complemented
4	C₅×#5127	C₂	1	2	yes	maximal, complemented
5	C₅×#4925	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4706	C₂	1	2	yes	maximal, complemented
7	C₅×#4701	C₂	1	2	yes	maximal, complemented
8	C₄×C₅×ΓL(1,𝔽₂₅)	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#4685	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4685	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₅×D₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#2965	—	3	1	no	maximal, Hall
13	C₂×C₅×#235	C₄	1	1	yes	characteristic
14	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
15	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
16	C₄×C₅×#67	C₄	1	1	yes	characteristic
17	C₄×C₅×#67	C₄	1	1	yes	characteristic
18	C₄×C₅×#67	C₂²	1	1	yes	characteristic
19	C₄×C₅×#67	C₂²	1	1	yes	characteristic
20	C₅×#926	C₄	1	1	yes	characteristic
21	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	—
22	C₂×C₅×D₃×C₈	C₂²	1	2	yes	—
23	C₄×C₅×D₁₂	C₄	1	1	yes	characteristic
24	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
25	C₅×#872	C₄	1	1	yes	characteristic
26	C₅×#872	C₄	1	1	yes	characteristic
27	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
28	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
29	C₄×C₅×Dic₆	C₄	1	1	yes	characteristic
30	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
31	C₃×C₅×#97	C₂²	1	2	yes	—
32	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
33	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
34	C₅×#830	C₂²	1	2	yes	—
35	C₅×(C₂×D₃)⋊C₈	C₂²	1	2	yes	—
36	C₅×(C₂×D₃)⋊C₈	C₂²	1	2	yes	—
37	C₅×#815	C₂²	1	2	yes	—
38	C₅×Dic₃⋊C₈	C₂²	1	2	yes	—
39	C₅×Dic₃⋊C₈	C₂²	1	2	yes	—
40	C₅×C₈×Dic₃	C₂²	1	2	yes	—
41	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	2	yes	—
42	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
43	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
44	#78523	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
45	C₄×C₅×#41	—	3	1	no	—
46	C₅×#446	—	3	2	no	—
47	C₅×#436	—	3	2	no	—
48	C₅×#435	—	3	2	no	—
49	C₅×#435	—	3	2	no	—
50	C₅×#431	—	3	1	no	—
51	C₅×#431	—	3	1	no	—
52	C₅×#431	—	3	1	no	—
53	C₄×C₅×M₁₆	—	3	1	no	—
54	C₄×C₅×M₁₆	D₃	1	1	yes	characteristic, complemented
55	C₂×C₄×C₅×C₈	—	3	1	no	—
56	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
57	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
58	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
59	C₂×C₅×#67	C₂×C₄	1	1	yes	characteristic
60	C₂×C₅×#67	C₂×C₄	1	1	yes	characteristic
61	C₅×#235	—	2	4	no	—
62	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
68	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
69	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
70	C₃×C₅×M₁₆	—	2	4	no	—
71	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
72	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
73	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
74	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
75	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
76	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
77	C₅×#217	C₂×C₄	1	1	yes	characteristic
78	C₅×#217	C₂×C₄	1	1	yes	characteristic
79	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
80	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
81	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
82	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
83	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
84	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
85	C₅×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
86	C₅×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
87	C₅×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
88	C₅×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
89	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
90	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
91	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
92	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
93	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
94	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
95	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
96	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
97	C₅×ΓL(1,𝔽₂₅)	—	2	4	no	—
98	C₅×D₃×C₈	—	2	4	no	—
99	C₄×#235	C₂×C₅	1	1	yes	characteristic
100	C₃×C₄×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
101	#5128	C₂×C₅	1	2	yes	complemented
102	#5127	C₂×C₅	1	2	yes	complemented
103	#4925	C₂×C₅	1	1	yes	characteristic, complemented
104	#4706	C₂×C₅	1	2	yes	complemented
105	#4701	C₂×C₅	1	2	yes	complemented
106	C₄×ΓL(1,𝔽₂₅)	C₂×C₅	1	1	yes	characteristic, complemented
107	#4685	C₂×C₅	1	1	yes	characteristic, complemented
108	#4685	C₂×C₅	1	1	yes	characteristic, complemented
109	C₄×D₃×C₈	C₂×C₅	1	1	yes	characteristic, complemented
110	C₂×C₅×#41	—	3	1	no	—
111	C₂×C₅×M₁₆	—	3	2	no	—
112	C₂×C₅×M₁₆	C₂×D₃	1	2	yes	—
113	C₂²×C₅×C₈	—	3	2	no	—
114	C₄×C₅×Q₈	—	3	1	no	—
115	C₄×C₅×Q₈	—	3	1	no	—
116	C₄×C₅×D₄	—	3	1	no	—
117	C₄×C₅×D₄	—	3	1	no	—
118	C₄×C₅×D₄	—	3	1	no	—
119	C₄×C₅×D₄	—	3	1	no	—
120	C₄×C₅×D₄	—	3	1	no	—
121	C₄×C₅×D₄	—	3	1	no	—
122	C₅×#117	—	3	1	no	—
123	C₅×#117	—	3	1	no	—
124	C₅×#117	—	3	1	no	—
125	C₂×C₄²×C₅	—	3	1	no	—
126	C₂×C₄²×C₅	—	3	1	no	—
127	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
128	C₅×C₄⋊C₈	—	3	2	no	—
129	C₅×C₄⋊C₈	—	3	2	no	—
130	C₅×C₄⋊C₈	—	3	2	no	—
131	C₅×C₂²⋊C₈	—	3	2	no	—
132	C₅×C₂²⋊C₈	—	3	2	no	—
133	C₅×C₂²⋊C₈	—	3	2	no	—
134	C₅×#97	—	3	2	no	—
135	C₅×#97	C₂×D₃	1	2	yes	—
136	C₄×C₅×C₈	—	3	2	no	—
137	C₄×C₅×C₈	—	3	1	no	—
138	C₄×C₅×C₈	—	3	1	no	—
139	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
140	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
141	#2965	—	3	1	no	Sylow
142	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
143	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
145	C₂×C₃×C₄×C₅	—	2	2	no	—
146	C₂×C₃×C₄×C₅	—	2	2	no	—
147	C₂×C₃×C₄×C₅	—	2	2	no	—
148	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
154	C₅×#67	—	2	2	no	—
155	C₅×#67	—	2	2	no	—
156	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
157	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
158	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
159	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
160	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
161	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
162	C₅×D₁₂	—	2	2	no	—
163	C₄×C₅×D₃	—	2	2	no	—
164	C₄×C₅×D₃	—	2	2	no	—
165	C₄×C₅×D₃	—	2	2	no	—
166	C₄×C₅×D₃	—	2	2	no	—
167	C₄×C₅×D₃	—	2	2	no	—
168	C₄×C₅×D₃	M₁₆	1	4	yes	complemented
169	C₅×Dic₆	—	2	2	no	—
170	C₃×C₅×C₈	—	2	2	no	—
171	C₃×C₅×C₈	#41	1	4	yes	complemented
172	C₅×C₃⋊C₈	—	2	2	no	—
173	C₅×C₃⋊C₈	—	2	2	no	—
174	C₂×#235	C₄×C₅	1	1	yes	characteristic
175	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	—
176	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
177	C₄×#67	C₄×C₅	1	1	yes	characteristic
178	C₄×#67	C₄×C₅	1	1	yes	characteristic
179	C₄×#67	C₂²×C₅	1	1	yes	characteristic
180	C₄×#67	C₂²×C₅	1	1	yes	characteristic
181	#926	C₄×C₅	1	1	yes	characteristic
182	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	2	yes	—
183	C₂×D₃×C₈	C₂²×C₅	1	2	yes	—
184	C₄×D₁₂	C₄×C₅	1	1	yes	characteristic
185	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
186	#872	C₄×C₅	1	1	yes	characteristic
187	#872	C₄×C₅	1	1	yes	characteristic
188	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
189	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
190	C₄×Dic₆	C₄×C₅	1	1	yes	characteristic
191	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic
192	C₃×#97	C₂²×C₅	1	2	yes	—
193	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
194	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
195	#830	C₂²×C₅	1	2	yes	—
196	(C₂×D₃)⋊C₈	C₂²×C₅	1	2	yes	—
197	(C₂×D₃)⋊C₈	C₂²×C₅	1	2	yes	—
198	#815	C₂²×C₅	1	2	yes	—
199	Dic₃⋊C₈	C₂²×C₅	1	2	yes	—
200	Dic₃⋊C₈	C₂²×C₅	1	2	yes	—
201	C₈×Dic₃	C₂²×C₅	1	2	yes	—
202	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	2	yes	—
203	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
204	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
205	C₅×#41	—	6	4	no	—
206	C₂×C₅×Q₈	—	3	1	no	—
207	C₂×C₅×D₄	—	3	1	no	—
208	C₂×C₅×D₄	—	3	1	no	—
209	C₂×C₅×D₄	—	3	1	no	—
210	C₂²×C₄×C₅	—	3	1	no	—
211	C₂²×C₄×C₅	—	3	1	no	—
212	C₂²×C₄×C₅	—	3	1	no	—
213	C₂²×C₄×C₅	—	3	1	no	—
214	C₂²×C₄×C₅	—	3	1	no	—
215	C₂²×C₄×C₅	—	3	1	no	—
216	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
217	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
218	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
219	C₅×M₁₆	—	2	4	no	—
220	C₅×M₁₆	—	6	4	no	—
221	C₂×C₅×C₈	—	3	2	no	—
222	C₂×C₅×C₈	—	3	2	no	—
223	C₂×C₅×C₈	—	6	4	no	—
224	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
225	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
226	C₅×C₄⋊C₄	—	3	1	no	—
227	C₅×C₄⋊C₄	—	3	1	no	—
228	C₅×C₄⋊C₄	—	3	1	no	—
229	C₅×C₄⋊C₄	—	3	1	no	—
230	C₅×C₄⋊C₄	—	3	1	no	—
231	C₅×C₄⋊C₄	—	3	1	no	—
232	C₅×C₂²⋊C₄	—	3	1	no	—
233	C₅×C₂²⋊C₄	—	3	1	no	—
234	C₅×C₂²⋊C₄	—	3	1	no	—
235	C₅×C₂²⋊C₄	—	3	1	no	—
236	C₅×C₂²⋊C₄	—	3	1	no	—
237	C₅×C₂²⋊C₄	—	3	1	no	—
238	C₄²×C₅	—	3	1	no	—
239	C₄²×C₅	—	3	1	no	—
240	C₄²×C₅	—	3	1	no	—
241	C₄²×C₅	—	3	1	no	—
242	C₄²×C₅	—	3	1	no	—
243	C₄²×C₅	—	3	1	no	—
244	C₄²×C₅	C₄×D₃	1	1	yes	characteristic
245	C₄²×C₅	C₄×D₃	1	1	yes	characteristic
246	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
247	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
248	C₄×#41	—	3	1	no	—
249	#446	—	3	2	no	—
250	#436	—	3	2	no	—
251	#435	—	3	2	no	—
252	#435	—	3	2	no	—
253	#431	—	3	1	no	—
254	#431	—	3	1	no	—
255	#431	—	3	1	no	—
256	C₄×M₁₆	—	3	1	no	—
257	C₄×M₁₆	C₅×D₃	1	1	yes	characteristic, complemented
258	C₂×C₄×C₈	—	3	1	no	—
259	C₂²×C₃×C₅	—	2	1	no	—
260	C₂²×C₃×C₅	—	2	1	no	—
261	C₂²×C₃×C₅	—	2	1	no	—
262	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
263	C₂×C₅×D₃	—	2	1	no	—
264	C₂×C₅×D₃	—	2	1	no	—
265	C₂×C₅×D₃	—	2	1	no	—
266	C₂×C₅×D₃	—	2	1	no	—
267	C₂×C₅×D₃	—	2	1	no	—
268	C₂×C₅×D₃	C₂×M₁₆	1	2	yes	—
269	C₃×C₄×C₅	—	2	1	no	—
270	C₃×C₄×C₅	—	2	1	no	—
271	C₃×C₄×C₅	—	2	1	no	—
272	C₃×C₄×C₅	C₂×M₁₆	1	2	yes	—
273	C₃×C₄×C₅	#131	1	2	yes	—
274	C₃×C₄×C₅	C₂×#41	1	2	yes	—
275	C₅×Dic₃	—	2	1	no	—
276	C₅×Dic₃	—	2	1	no	—
277	C₅×Dic₃	—	2	1	no	—
278	C₅×Dic₃	—	2	1	no	—
279	C₅×Dic₃	—	2	1	no	—
280	C₅×Dic₃	C₂×M₁₆	1	2	yes	—
281	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
282	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
283	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
284	C₂×#67	C₂×C₄×C₅	1	1	yes	characteristic
285	C₂×#67	C₂×C₄×C₅	1	1	yes	characteristic
286	#235	—	2	4	no	—
287	C₂×D₁₂	C₂×C₄×C₅	1	1	yes	characteristic
288	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
289	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
290	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
291	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
292	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
293	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
294	C₂×Dic₆	C₂×C₄×C₅	1	1	yes	characteristic
295	C₃×M₁₆	—	2	4	no	—
296	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
297	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
298	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
299	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
300	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
301	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
302	#217	C₂×C₄×C₅	1	1	yes	characteristic
303	#217	C₂×C₄×C₅	1	1	yes	characteristic
304	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
305	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
306	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
307	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
308	C₄⋊Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
309	C₄⋊Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
310	Dic₃⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
311	Dic₃⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
312	Dic₃⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
313	Dic₃⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
314	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
315	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
316	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
317	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
318	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
319	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
320	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
321	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
322	ΓL(1,𝔽₂₅)	—	2	4	no	—
323	D₃×C₈	—	2	4	no	—
324	C₂³×C₅	—	3	1	no	—
325	C₂³×C₅	—	3	1	no	—
326	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
327	C₅×Q₈	—	6	2	no	—
328	C₅×D₄	—	6	2	no	—
329	C₅×D₄	—	6	2	no	—
330	C₅×D₄	—	6	2	no	—
331	C₂×C₄×C₅	—	2	2	no	—
332	C₂×C₄×C₅	—	2	2	no	—
333	C₂×C₄×C₅	—	2	2	no	—
334	C₂×C₄×C₅	—	3	1	no	—
335	C₂×C₄×C₅	—	3	4	no	—
336	C₂×C₄×C₅	—	3	1	no	—
337	C₂×C₄×C₅	—	3	1	no	—
338	C₂×C₄×C₅	—	3	1	no	—
339	C₂×C₄×C₅	—	3	1	no	—
340	C₂×C₄×C₅	—	3	1	no	—
341	C₂×C₄×C₅	—	6	2	no	—
342	C₂×C₄×C₅	—	6	2	no	—
343	C₂×C₄×C₅	—	6	2	no	—
344	C₂×C₄×C₅	—	6	2	no	—
345	C₂×C₄×C₅	—	6	2	no	—
346	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
347	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
348	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
349	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
350	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
351	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
352	C₅×C₈	—	2	2	no	—
353	C₅×C₈	—	6	2	no	—
354	C₅×C₈	—	6	2	no	—
355	C₅×C₈	#235	1	4	yes	complemented
356	C₂×#41	—	3	1	no	—
357	C₂×M₁₆	—	3	2	no	—
358	C₂×M₁₆	C₂×C₅×D₃	1	2	yes	—
359	C₂²×C₈	—	3	2	no	—
360	C₄×Q₈	—	3	1	no	—
361	C₄×Q₈	—	3	1	no	—
362	C₄×D₄	—	3	1	no	—
363	C₄×D₄	—	3	1	no	—
364	C₄×D₄	—	3	1	no	—
365	C₄×D₄	—	3	1	no	—
366	C₄×D₄	—	3	1	no	—
367	C₄×D₄	—	3	1	no	—
368	#117	—	3	1	no	—
369	#117	—	3	1	no	—
370	#117	—	3	1	no	—
371	C₂×C₄²	—	3	1	no	—
372	C₂×C₄²	—	3	1	no	—
373	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
374	C₄⋊C₈	—	3	2	no	—
375	C₄⋊C₈	—	3	2	no	—
376	C₄⋊C₈	—	3	2	no	—
377	C₂²⋊C₈	—	3	2	no	—
378	C₂²⋊C₈	—	3	2	no	—
379	C₂²⋊C₈	—	3	2	no	—
380	#97	—	3	2	no	—
381	#97	C₂×C₅×D₃	1	2	yes	—
382	C₄×C₈	—	3	2	no	—
383	C₄×C₈	—	3	1	no	—
384	C₄×C₈	—	3	1	no	—
385	C₄×C₈	C₂×C₅×D₃	1	1	yes	characteristic
386	C₄×C₈	C₂×C₅×D₃	1	1	yes	characteristic
387	C₂×C₃×C₅	—	4	1	no	—
388	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
389	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
390	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
391	C₅×D₃	—	2	2	no	—
392	C₅×D₃	—	4	1	no	—
393	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
394	C₂²×D₃	C₂²×C₄×C₅	1	1	yes	characteristic
395	C₂²×D₃	C₂²×C₄×C₅	1	1	yes	characteristic
396	C₂×C₃×C₄	—	2	2	no	—
397	C₂×C₃×C₄	—	2	2	no	—
398	C₂×C₃×C₄	—	2	2	no	—
399	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
400	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
401	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
402	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
403	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
404	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
405	#67	—	2	2	no	—
406	#67	—	2	2	no	—
407	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
408	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
409	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
410	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
411	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
412	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
413	D₁₂	—	2	2	no	—
414	C₄×D₃	—	2	2	no	—
415	C₄×D₃	—	2	2	no	—
416	C₄×D₃	—	2	2	no	—
417	C₄×D₃	—	2	2	no	—
418	C₄×D₃	—	2	2	no	—
419	C₄×D₃	C₅×M₁₆	1	4	yes	complemented
420	Dic₆	—	2	2	no	—
421	C₃×C₈	—	2	2	no	—
422	C₃×C₈	C₅×#41	1	4	yes	complemented
423	C₃⋊C₈	—	2	2	no	—
424	C₃⋊C₈	—	2	2	no	—
425	C₂²×C₅	—	2	1	no	—
426	C₂²×C₅	—	2	1	no	—
427	C₂²×C₅	—	2	1	no	—
428	C₂²×C₅	—	3	2	no	—
429	C₂²×C₅	—	6	1	no	—
430	C₂²×C₅	—	6	1	no	—
431	C₂²×C₅	—	6	1	no	—
432	C₂²×C₅	—	6	1	no	—
433	C₂²×C₅	—	6	1	no	—
434	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
435	C₄×C₅	—	2	1	no	—
436	C₄×C₅	—	2	1	no	—
437	C₄×C₅	—	2	1	no	—
438	C₄×C₅	—	3	2	no	—
439	C₄×C₅	—	6	1	no	—
440	C₄×C₅	—	6	1	no	—
441	C₄×C₅	—	6	1	no	—
442	C₄×C₅	—	6	1	no	—
443	C₄×C₅	—	6	1	no	—
444	C₄×C₅	D₃×M₁₆	1	2	yes	—
445	C₄×C₅	#907	1	2	yes	—
446	C₄×C₅	C₂×#235	1	2	yes	—
447	#41	—	6	4	no	—
448	C₂×Q₈	—	3	1	no	—
449	C₂×D₄	—	3	1	no	—
450	C₂×D₄	—	3	1	no	—
451	C₂×D₄	—	3	1	no	—
452	C₂²×C₄	—	3	1	no	—
453	C₂²×C₄	—	3	1	no	—
454	C₂²×C₄	—	3	1	no	—
455	C₂²×C₄	—	3	1	no	—
456	C₂²×C₄	—	3	1	no	—
457	C₂²×C₄	—	3	1	no	—
458	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
459	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
460	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
461	M₁₆	—	2	4	no	—
462	M₁₆	—	6	4	no	—
463	C₂×C₈	—	3	2	no	—
464	C₂×C₈	—	3	2	no	—
465	C₂×C₈	—	6	4	no	—
466	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
467	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
468	C₄⋊C₄	—	3	1	no	—
469	C₄⋊C₄	—	3	1	no	—
470	C₄⋊C₄	—	3	1	no	—
471	C₄⋊C₄	—	3	1	no	—
472	C₄⋊C₄	—	3	1	no	—
473	C₄⋊C₄	—	3	1	no	—
474	C₂²⋊C₄	—	3	1	no	—
475	C₂²⋊C₄	—	3	1	no	—
476	C₂²⋊C₄	—	3	1	no	—
477	C₂²⋊C₄	—	3	1	no	—
478	C₂²⋊C₄	—	3	1	no	—
479	C₂²⋊C₄	—	3	1	no	—
480	C₄²	—	3	1	no	—
481	C₄²	—	3	1	no	—
482	C₄²	—	3	1	no	—
483	C₄²	—	3	1	no	—
484	C₄²	—	3	1	no	—
485	C₄²	—	3	1	no	—
486	C₄²	C₄×C₅×D₃	1	1	yes	characteristic
487	C₄²	C₄×C₅×D₃	1	1	yes	characteristic
488	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
489	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
490	C₃×C₅	#2965	1	1	yes	characteristic, complemented, Hall
491	C₂²×C₃	—	2	1	no	—
492	C₂²×C₃	—	2	1	no	—
493	C₂²×C₃	—	2	1	no	—
494	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
495	C₂×D₃	—	2	1	no	—
496	C₂×D₃	—	2	1	no	—
497	C₂×D₃	—	2	1	no	—
498	C₂×D₃	—	2	1	no	—
499	C₂×D₃	—	2	1	no	—
500	C₂×D₃	C₂×C₅×M₁₆	1	2	yes	—
501	C₃×C₄	—	2	1	no	—
502	C₃×C₄	—	2	1	no	—
503	C₃×C₄	—	2	1	no	—
504	C₃×C₄	C₂×C₅×M₁₆	1	2	yes	—
505	C₃×C₄	C₅×#131	1	2	yes	—
506	C₃×C₄	C₂×C₅×#41	1	2	yes	—
507	Dic₃	—	2	1	no	—
508	Dic₃	—	2	1	no	—
509	Dic₃	—	2	1	no	—
510	Dic₃	—	2	1	no	—
511	Dic₃	—	2	1	no	—
512	Dic₃	C₂×C₅×M₁₆	1	2	yes	—
513	C₂×C₅	—	4	1	no	—
514	C₂×C₅	—	6	2	no	—
515	C₂×C₅	—	12	1	no	—
516	C₂×C₅	C₄×#235	1	1	yes	characteristic
517	C₂×C₅	C₂×D₃×M₁₆	1	1	yes	characteristic
518	C₂×C₅	C₂×#907	1	1	yes	characteristic
519	C₂³	—	3	1	no	—
520	C₂³	—	3	1	no	—
521	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
522	Q₈	—	6	2	no	—
523	D₄	—	6	2	no	—
524	D₄	—	6	2	no	—
525	D₄	—	6	2	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	3	1	no	—
530	C₂×C₄	—	3	4	no	—
531	C₂×C₄	—	3	1	no	—
532	C₂×C₄	—	3	1	no	—
533	C₂×C₄	—	3	1	no	—
534	C₂×C₄	—	3	1	no	—
535	C₂×C₄	—	3	1	no	—
536	C₂×C₄	—	6	2	no	—
537	C₂×C₄	—	6	2	no	—
538	C₂×C₄	—	6	2	no	—
539	C₂×C₄	—	6	2	no	—
540	C₂×C₄	—	6	2	no	—
541	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
542	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
543	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
544	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
545	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
546	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
547	C₈	—	2	2	no	—
548	C₈	—	6	2	no	—
549	C₈	—	6	2	no	—
550	C₈	C₅×#235	1	4	yes	complemented
551	C₂×C₃	—	4	1	no	—
552	C₂×C₃	C₄×C₅×#41	1	1	yes	characteristic
553	C₂×C₃	C₂²×C₅×M₁₆	1	1	yes	characteristic
554	C₂×C₃	C₂×C₅×#131	1	1	yes	characteristic
555	D₃	—	2	2	no	—
556	D₃	—	4	1	no	—
557	C₅	#78523	1	1	yes	characteristic, direct product factor, Sylow
558	C₂²	—	2	1	no	—
559	C₂²	—	2	1	no	—
560	C₂²	—	2	1	no	—
561	C₂²	—	3	2	no	—
562	C₂²	—	6	1	no	—
563	C₂²	—	6	1	no	—
564	C₂²	—	6	1	no	—
565	C₂²	—	6	1	no	—
566	C₂²	—	6	1	no	—
567	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
568	C₄	—	2	1	no	—
569	C₄	—	2	1	no	—
570	C₄	—	2	1	no	—
571	C₄	—	3	2	no	—
572	C₄	—	6	1	no	—
573	C₄	—	6	1	no	—
574	C₄	—	6	1	no	—
575	C₄	—	6	1	no	—
576	C₄	—	6	1	no	—
577	C₄	C₅×D₃×M₁₆	1	2	yes	—
578	C₄	C₅×#907	1	2	yes	—
579	C₄	C₂×C₅×#235	1	2	yes	—
580	C₃	C₅×#2965	1	1	yes	characteristic, complemented, Sylow
581	C₂	—	4	1	no	—
582	C₂	—	6	2	no	—
583	C₂	—	12	1	no	—
584	C₂	C₄×C₅×#235	1	1	yes	characteristic
585	C₂	C₂×C₅×D₃×M₁₆	1	1	yes	characteristic
586	C₂	C₂×C₅×#907	1	1	yes	characteristic

	subgroup	G/H
center	C₄²×C₅	C₂²×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₄×C₅×M₁₆	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂×C₅×#235	C₄
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₄×C₅×M₁₆	D₃
hypocenter	C₃	C₅×#2965
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₄²×C₅ ◁ C₄×C₅×M₁₆

Complements

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

N	H ≅ G/N	type
2. C₃×C₄×C₅×M₁₆	C₂	semidirect
3. C₅×#5128	C₂	semidirect
4. C₅×#5127	C₂	semidirect
5. C₅×#4925	C₂	semidirect
6. C₅×#4706	C₂	semidirect
7. C₅×#4701	C₂	semidirect
8. C₄×C₅×ΓL(1,𝔽₂₅)	C₂	semidirect
9. C₅×#4685	C₂	semidirect
10. C₅×#4685	C₂	semidirect
11. C₄×C₅×D₃×C₈	C₂	semidirect
44. #78523	C₅	direct (N × H)
54. C₄×C₅×M₁₆	D₃	semidirect
100. C₃×C₄×M₁₆	C₂×C₅	semidirect
101. #5128	C₂×C₅	semidirect
102. #5127	C₂×C₅	semidirect
103. #4925	C₂×C₅	semidirect
104. #4706	C₂×C₅	semidirect
105. #4701	C₂×C₅	semidirect
106. C₄×ΓL(1,𝔽₂₅)	C₂×C₅	semidirect
107. #4685	C₂×C₅	semidirect
108. #4685	C₂×C₅	semidirect
109. C₄×D₃×C₈	C₂×C₅	semidirect
168. C₄×C₅×D₃	M₁₆	semidirect
171. C₃×C₅×C₈	#41	semidirect
257. C₄×M₁₆	C₅×D₃	semidirect
355. C₅×C₈	#235	semidirect
419. C₄×D₃	C₅×M₁₆	semidirect
422. C₃×C₈	C₅×#41	semidirect
490. C₃×C₅	#2965	semidirect
550. C₈	C₅×#235	semidirect
557. C₅	#78523	direct (N × H)
580. C₃	C₅×#2965	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₅×#235	2
C₃×C₄×C₅×M₁₆	2
C₅×#5128	2
C₅×#5127	2
C₅×#4925	2
C₅×#4706	2
C₅×#4701	2
C₄×C₅×ΓL(1,𝔽₂₅)	2
C₅×#4685	2
C₄×C₅×D₃×C₈	2
C₅×#2965	3
#78523	5

Subgroups — C5×#78523 #14418969

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#78523 #14418969