Subgroups — C₅×#81821 #14439273

Order 1920.

1144 conjugacy classes of subgroups.

The subgroup lattice has 772 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	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#915	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#914	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#911	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×D₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5668	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#495	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#5190	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#5176	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#5167	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#5154	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#5059	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#5059	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#4696	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₅×ΓL(1,𝔽₂₅)	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3153	—	3	1	no	maximal, Hall
17	C₂×C₅×#239	C₂²	1	1	yes	characteristic
18	C₂×C₅×D₃×Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₅×#237	C₂²	1	1	yes	characteristic
20	C₂×C₅×D₃×D₄	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
25	C₃×C₅×#124	C₂²	1	1	yes	characteristic
26	C₃×C₅×#124	C₂²	1	1	yes	characteristic, complemented
27	C₅×#947	C₂²	1	1	yes	characteristic
28	C₅×#944	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₅×#216	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₅×#216	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₅×#215	C₂²	1	1	yes	characteristic
32	C₂×C₅×#215	C₂²	1	1	yes	characteristic, complemented
33	C₅×#940	C₂²	1	1	yes	characteristic, complemented
34	C₅×#936	C₂²	1	1	yes	characteristic
35	C₂×C₅×#214	C₂²	1	1	yes	characteristic
36	C₂×C₅×#214	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₅×#213	C₂²	1	1	yes	characteristic
38	C₂×C₅×#213	C₂²	1	1	yes	characteristic
39	C₅×#918	—	2	4	no	—
40	C₅×#915	—	2	4	no	—
41	C₅×#914	—	2	4	no	—
42	C₅×#911	—	2	4	no	—
43	C₂×C₅×Dic₁₂	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₅×D₂₄	C₂²	1	1	yes	characteristic
45	C₂×C₅×#204	C₂²	1	1	yes	characteristic
46	C₂×C₅×#204	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
48	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
49	C₅×#885	—	2	2	no	—
50	C₅×#884	—	2	2	no	—
51	C₅×#67⋊C₄	—	2	2	no	—
52	C₅×D₃×C₂²⋊C₄	—	2	2	no	—
53	C₅×#875	C₂²	1	1	yes	characteristic
54	C₅×#875	C₂²	1	1	yes	characteristic, complemented
55	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
56	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
57	C₅×#815	C₂²	1	1	yes	characteristic, complemented
58	C₅×#815	C₂²	1	1	yes	characteristic, complemented
59	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
60	#81821	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
61	C₂×C₅×#137	—	3	1	no	—
62	C₂×C₅×#137	—	3	1	no	—
63	C₂×C₅×AGL(1,ℤ/8)	—	3	1	no	—
64	C₂×C₅×AGL(1,ℤ/8)	—	3	1	no	—
65	C₅×#532	—	3	1	no	—
66	C₂×C₅×#124	—	3	1	no	—
67	C₅×#497	—	3	1	no	—
68	C₅×#497	—	3	1	no	—
69	C₅×#496	—	3	1	no	—
70	C₅×#496	—	3	1	no	—
71	C₅×#495	—	3	1	no	—
72	C₅×#495	—	3	1	no	—
73	C₅×#495	—	3	1	no	—
74	C₅×#495	D₃	1	1	yes	characteristic, complemented
75	C₄×C₅×M₁₆	—	3	1	no	—
76	C₂³×C₅×D₃	—	2	1	no	—
77	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
78	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
79	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
80	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
81	C₂×C₅×#67	—	2	1	no	—
82	C₂×C₅×#67	—	2	2	no	—
83	C₂×C₅×#67	—	2	1	no	—
84	C₂²×C₅×Dic₃	—	2	1	no	—
85	C₅×#239	—	2	2	no	—
86	C₅×#239	—	2	2	no	—
87	C₅×D₃×Q₈	—	2	2	no	—
88	C₅×D₃×Q₈	—	2	2	no	—
89	C₅×#237	—	2	2	no	—
90	C₅×#237	—	2	2	no	—
91	C₅×D₃×D₄	—	2	2	no	—
92	C₅×D₃×D₄	—	2	2	no	—
93	C₂×C₅×D₁₂	—	2	1	no	—
94	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
95	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
96	C₂×C₄×C₅×D₃	—	2	1	no	—
97	C₂×C₄×C₅×D₃	—	2	1	no	—
98	C₂×C₄×C₅×D₃	D₄	1	2	yes	—
99	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
100	C₂×C₅×Dic₆	—	2	1	no	—
101	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
102	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
103	C₃×C₅×Q₁₆	—	2	2	no	—
104	C₃×C₅×SD₁₆	—	2	2	no	—
105	C₃×C₅×SD₁₆	—	2	2	no	—
106	C₃×C₅×D₈	—	2	2	no	—
107	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
108	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
109	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
110	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
111	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
112	C₅×#217	—	2	2	no	—
113	C₅×#216	—	2	2	no	—
114	C₅×#216	—	2	2	no	—
115	C₅×#215	—	2	2	no	—
116	C₅×#215	—	2	2	no	—
117	C₅×#214	—	2	2	no	—
118	C₅×#214	—	2	2	no	—
119	C₅×#213	—	2	2	no	—
120	C₅×#213	—	2	2	no	—
121	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
122	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
123	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
124	C₅×Dic₃⋊C₄	—	2	2	no	—
125	C₄×C₅×Dic₃	D₄	1	2	yes	—
126	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
127	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
128	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
129	C₅×Dic₁₂	—	2	2	no	—
130	C₅×D₂₄	—	2	2	no	—
131	C₅×#204	—	2	2	no	—
132	C₅×#204	—	2	2	no	—
133	C₅×ΓL(1,𝔽₂₅)	D₄	1	4	yes	complemented
134	C₅×ΓL(1,𝔽₂₅)	D₄	1	4	yes	complemented
135	C₂×#918	C₂×C₅	1	1	yes	characteristic, complemented
136	C₂×#915	C₂×C₅	1	1	yes	characteristic, complemented
137	C₂×#914	C₂×C₅	1	1	yes	characteristic, complemented
138	C₂×#911	C₂×C₅	1	1	yes	characteristic, complemented
139	D₃×#124	C₂×C₅	1	1	yes	characteristic, complemented
140	#5668	C₂×C₅	1	1	yes	characteristic, complemented
141	C₃×#495	C₂×C₅	1	1	yes	characteristic, complemented
142	#5190	C₂×C₅	1	1	yes	characteristic, complemented
143	#5176	C₂×C₅	1	1	yes	characteristic, complemented
144	#5167	C₂×C₅	1	1	yes	characteristic, complemented
145	#5154	C₂×C₅	1	1	yes	characteristic, complemented
146	#5059	C₂×C₅	1	1	yes	characteristic, complemented
147	#5059	C₂×C₅	1	1	yes	characteristic, complemented
148	#4696	C₂×C₅	1	1	yes	characteristic, complemented
149	C₄×ΓL(1,𝔽₂₅)	C₂×C₅	1	1	yes	characteristic, complemented
150	C₂×C₅×#41	—	3	1	no	—
151	C₂×C₅×#41	—	3	1	no	—
152	C₂²×C₅×Q₈	—	3	1	no	—
153	C₂²×C₅×D₄	—	3	1	no	—
154	C₅×#137	—	6	4	no	—
155	C₅×#137	—	6	4	no	—
156	C₅×AGL(1,ℤ/8)	—	6	4	no	—
157	C₅×AGL(1,ℤ/8)	—	6	4	no	—
158	C₂×C₅×Q₁₆	—	3	1	no	—
159	C₂×C₅×Q₁₆	—	3	1	no	—
160	C₂×C₅×Q₁₆	—	3	1	no	—
161	C₂×C₅×Q₁₆	C₂×D₃	1	1	yes	characteristic, complemented
162	C₂×C₅×SD₁₆	—	3	1	no	—
163	C₂×C₅×SD₁₆	—	3	1	no	—
164	C₂×C₅×SD₁₆	—	3	1	no	—
165	C₂×C₅×SD₁₆	—	3	1	no	—
166	C₂×C₅×SD₁₆	—	3	1	no	—
167	C₂×C₅×SD₁₆	—	3	1	no	—
168	C₂×C₅×SD₁₆	C₂×D₃	1	1	yes	characteristic
169	C₂×C₅×SD₁₆	C₂×D₃	1	1	yes	characteristic, complemented
170	C₂×C₅×D₈	—	3	1	no	—
171	C₂×C₅×D₈	—	3	1	no	—
172	C₂×C₅×D₈	—	3	1	no	—
173	C₂×C₅×D₈	C₂×D₃	1	1	yes	characteristic
174	C₂×C₅×M₁₆	—	3	1	no	—
175	C₂×C₅×M₁₆	—	3	1	no	—
176	C₅×C₄⋊Q₈	—	3	1	no	—
177	C₅×#127	—	3	1	no	—
178	C₅×#124	—	3	1	no	—
179	C₅×#124	—	3	1	no	—
180	C₅×#124	—	3	1	no	—
181	C₅×#124	—	3	1	no	—
182	C₅×#124	—	6	2	no	—
183	C₅×#124	C₂×D₃	1	1	yes	characteristic
184	C₅×#124	C₂×D₃	1	1	yes	characteristic, complemented
185	C₅×#121	—	6	2	no	—
186	C₄×C₅×D₄	—	6	2	no	—
187	C₂×C₅×C₂²⋊C₄	—	6	2	no	—
188	C₂×C₄²×C₅	—	3	1	no	—
189	C₅×#97	—	3	1	no	—
190	C₅×#97	—	3	1	no	—
191	C₄×C₅×C₈	—	3	1	no	—
192	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic, complemented
193	#3153	—	3	1	no	Sylow
194	C₂³×C₃×C₅	—	2	1	no	—
195	C₂³×C₃×C₅	—	2	1	no	—
196	C₂²×C₅×D₃	—	2	1	no	—
197	C₂²×C₅×D₃	—	2	1	no	—
198	C₂²×C₅×D₃	—	4	4	no	—
199	C₂²×C₅×D₃	—	4	2	no	—
200	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
201	C₃×C₅×Q₈	—	2	1	no	—
202	C₃×C₅×Q₈	—	2	1	no	—
203	C₃×C₅×Q₈	—	2	1	no	—
204	C₃×C₅×Q₈	—	2	1	no	—
205	C₃×C₅×D₄	—	2	1	no	—
206	C₃×C₅×D₄	—	2	1	no	—
207	C₃×C₅×D₄	—	2	1	no	—
208	C₃×C₅×D₄	—	2	1	no	—
209	C₂×C₃×C₄×C₅	—	2	1	no	—
210	C₂×C₃×C₄×C₅	—	2	1	no	—
211	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
212	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
213	C₅×#67	—	4	4	no	—
214	C₅×#67	—	4	2	no	—
215	C₅×#67	—	4	2	no	—
216	C₂×C₅×Dic₃	—	2	1	no	—
217	C₂×C₅×Dic₃	—	2	1	no	—
218	C₂×C₅×Dic₃	—	4	2	no	—
219	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
220	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
221	C₅×D₁₂	—	2	1	no	—
222	C₅×D₁₂	—	2	1	no	—
223	C₅×D₁₂	—	2	1	no	—
224	C₅×D₁₂	—	2	1	no	—
225	C₅×D₁₂	—	4	2	no	—
226	C₄×C₅×D₃	—	4	2	no	—
227	C₄×C₅×D₃	—	4	2	no	—
228	C₄×C₅×D₃	—	4	2	no	—
229	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
230	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
231	C₅×Dic₆	—	2	1	no	—
232	C₅×Dic₆	—	2	1	no	—
233	C₅×Dic₆	—	2	1	no	—
234	C₅×Dic₆	—	2	1	no	—
235	C₅×Dic₆	—	4	2	no	—
236	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
237	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
238	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	—
239	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	—
240	C₂×#239	C₂²×C₅	1	1	yes	characteristic
241	C₂×D₃×Q₈	C₂²×C₅	1	1	yes	characteristic
242	C₂×#237	C₂²×C₅	1	1	yes	characteristic
243	C₂×D₃×D₄	C₂²×C₅	1	1	yes	characteristic
244	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
245	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
246	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
247	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
248	C₃×#124	C₂²×C₅	1	1	yes	characteristic
249	C₃×#124	C₂²×C₅	1	1	yes	characteristic, complemented
250	#947	C₂²×C₅	1	1	yes	characteristic
251	#944	C₂²×C₅	1	1	yes	characteristic, complemented
252	C₂×#216	C₂²×C₅	1	1	yes	characteristic, complemented
253	C₂×#216	C₂²×C₅	1	1	yes	characteristic, complemented
254	C₂×#215	C₂²×C₅	1	1	yes	characteristic
255	C₂×#215	C₂²×C₅	1	1	yes	characteristic, complemented
256	#940	C₂²×C₅	1	1	yes	characteristic, complemented
257	#936	C₂²×C₅	1	1	yes	characteristic
258	C₂×#214	C₂²×C₅	1	1	yes	characteristic
259	C₂×#214	C₂²×C₅	1	1	yes	characteristic, complemented
260	C₂×#213	C₂²×C₅	1	1	yes	characteristic
261	C₂×#213	C₂²×C₅	1	1	yes	characteristic
262	#918	—	2	4	no	—
263	#915	—	2	4	no	—
264	#914	—	2	4	no	—
265	#911	—	2	4	no	—
266	C₂×Dic₁₂	C₂²×C₅	1	1	yes	characteristic, complemented
267	C₂×D₂₄	C₂²×C₅	1	1	yes	characteristic
268	C₂×#204	C₂²×C₅	1	1	yes	characteristic
269	C₂×#204	C₂²×C₅	1	1	yes	characteristic, complemented
270	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	1	yes	characteristic
271	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	1	yes	characteristic
272	#885	—	2	2	no	—
273	#884	—	2	2	no	—
274	#67⋊C₄	—	2	2	no	—
275	D₃×C₂²⋊C₄	—	2	2	no	—
276	#875	C₂²×C₅	1	1	yes	characteristic
277	#875	C₂²×C₅	1	1	yes	characteristic, complemented
278	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
279	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
280	#815	C₂²×C₅	1	1	yes	characteristic, complemented
281	#815	C₂²×C₅	1	1	yes	characteristic, complemented
282	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
283	C₂⁴×C₅	—	6	1	no	—
284	C₅×#41	—	6	2	no	—
285	C₅×#41	—	6	2	no	—
286	C₅×#41	—	6	2	no	—
287	C₅×#41	—	6	2	no	—
288	C₂×C₅×Q₈	—	3	1	no	—
289	C₂×C₅×Q₈	—	3	1	no	—
290	C₂×C₅×Q₈	—	6	1	no	—
291	C₂×C₅×Q₈	—	6	2	no	—
292	C₂×C₅×Q₈	—	6	2	no	—
293	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
294	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
295	C₂×C₅×D₄	—	3	1	no	—
296	C₂×C₅×D₄	—	3	1	no	—
297	C₂×C₅×D₄	—	6	1	no	—
298	C₂×C₅×D₄	—	6	2	no	—
299	C₂×C₅×D₄	—	6	2	no	—
300	C₂×C₅×D₄	—	6	2	no	—
301	C₂×C₅×D₄	—	6	1	no	—
302	C₂×C₅×D₄	—	6	1	no	—
303	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
304	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
305	C₂²×C₄×C₅	—	3	1	no	—
306	C₂²×C₄×C₅	—	3	2	no	—
307	C₂²×C₄×C₅	—	6	1	no	—
308	C₂²×C₄×C₅	—	6	1	no	—
309	C₂²×C₄×C₅	—	6	1	no	—
310	C₅×Q₁₆	—	2	2	no	—
311	C₅×Q₁₆	—	6	2	no	—
312	C₅×Q₁₆	—	6	2	no	—
313	C₅×Q₁₆	—	6	2	no	—
314	C₅×SD₁₆	—	2	2	no	—
315	C₅×SD₁₆	—	2	2	no	—
316	C₅×SD₁₆	—	6	2	no	—
317	C₅×SD₁₆	—	6	2	no	—
318	C₅×SD₁₆	—	6	2	no	—
319	C₅×SD₁₆	—	6	2	no	—
320	C₅×SD₁₆	—	6	2	no	—
321	C₅×SD₁₆	—	6	2	no	—
322	C₅×D₈	—	2	2	no	—
323	C₅×D₈	—	6	2	no	—
324	C₅×D₈	—	6	2	no	—
325	C₅×D₈	—	6	2	no	—
326	C₅×M₁₆	—	3	4	no	—
327	C₅×M₁₆	—	3	4	no	—
328	C₂×C₅×C₈	—	3	1	no	—
329	C₂×C₅×C₈	—	3	1	no	—
330	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
331	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
332	C₅×C₄⋊C₄	—	6	2	no	—
333	C₅×C₂²⋊C₄	—	2	2	no	—
334	C₅×C₂²⋊C₄	—	2	2	no	—
335	C₅×C₂²⋊C₄	—	6	2	no	—
336	C₅×C₂²⋊C₄	—	6	2	no	—
337	C₅×C₂²⋊C₄	—	6	2	no	—
338	C₅×C₂²⋊C₄	—	6	2	no	—
339	C₄²×C₅	—	3	2	no	—
340	C₄²×C₅	—	3	1	no	—
341	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
342	C₂×#137	—	3	1	no	—
343	C₂×#137	—	3	1	no	—
344	C₂×AGL(1,ℤ/8)	—	3	1	no	—
345	C₂×AGL(1,ℤ/8)	—	3	1	no	—
346	#532	—	3	1	no	—
347	C₂×#124	—	3	1	no	—
348	#497	—	3	1	no	—
349	#497	—	3	1	no	—
350	#496	—	3	1	no	—
351	#496	—	3	1	no	—
352	#495	—	3	1	no	—
353	#495	—	3	1	no	—
354	#495	—	3	1	no	—
355	#495	C₅×D₃	1	1	yes	characteristic, complemented
356	C₄×M₁₆	—	3	1	no	—
357	C₂²×C₃×C₅	—	4	1	no	—
358	C₂²×C₃×C₅	—	4	1	no	—
359	C₂²×C₃×C₅	—	4	2	no	—
360	C₂²×C₃×C₅	—	4	2	no	—
361	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
362	C₂×C₅×D₃	—	2	2	no	—
363	C₂×C₅×D₃	—	4	1	no	—
364	C₂×C₅×D₃	—	4	1	no	—
365	C₂×C₅×D₃	—	4	2	no	—
366	C₂×C₅×D₃	—	4	2	no	—
367	C₂×C₅×D₃	—	8	4	no	—
368	C₂×C₅×D₃	#127	1	2	yes	—
369	C₃×C₄×C₅	—	2	2	no	—
370	C₃×C₄×C₅	—	4	1	no	—
371	C₃×C₄×C₅	—	4	1	no	—
372	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
373	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
374	C₅×Dic₃	—	2	2	no	—
375	C₅×Dic₃	—	4	1	no	—
376	C₅×Dic₃	—	4	1	no	—
377	C₅×Dic₃	#127	1	2	yes	—
378	C₂³×D₃	—	2	1	no	—
379	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
380	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
381	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
382	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
383	C₂×#67	—	2	1	no	—
384	C₂×#67	—	2	2	no	—
385	C₂×#67	—	2	1	no	—
386	C₂²×Dic₃	—	2	1	no	—
387	#239	—	2	2	no	—
388	#239	—	2	2	no	—
389	D₃×Q₈	—	2	2	no	—
390	D₃×Q₈	—	2	2	no	—
391	#237	—	2	2	no	—
392	#237	—	2	2	no	—
393	D₃×D₄	—	2	2	no	—
394	D₃×D₄	—	2	2	no	—
395	C₂×D₁₂	—	2	1	no	—
396	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
397	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
398	C₂×C₄×D₃	—	2	1	no	—
399	C₂×C₄×D₃	—	2	1	no	—
400	C₂×C₄×D₃	C₅×D₄	1	2	yes	—
401	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
402	C₂×Dic₆	—	2	1	no	—
403	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
404	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
405	C₃×Q₁₆	—	2	2	no	—
406	C₃×SD₁₆	—	2	2	no	—
407	C₃×SD₁₆	—	2	2	no	—
408	C₃×D₈	—	2	2	no	—
409	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
410	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
411	C₃×C₂²⋊C₄	—	2	2	no	—
412	C₃×C₂²⋊C₄	—	2	2	no	—
413	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
414	#217	—	2	2	no	—
415	#216	—	2	2	no	—
416	#216	—	2	2	no	—
417	#215	—	2	2	no	—
418	#215	—	2	2	no	—
419	#214	—	2	2	no	—
420	#214	—	2	2	no	—
421	#213	—	2	2	no	—
422	#213	—	2	2	no	—
423	(C₂×D₃)⋊C₄	—	2	2	no	—
424	(C₂×D₃)⋊C₄	—	2	2	no	—
425	(C₂×D₃)⋊C₄	—	2	2	no	—
426	Dic₃⋊C₄	—	2	2	no	—
427	C₄×Dic₃	C₅×D₄	1	2	yes	—
428	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
429	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
430	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
431	Dic₁₂	—	2	2	no	—
432	D₂₄	—	2	2	no	—
433	#204	—	2	2	no	—
434	#204	—	2	2	no	—
435	ΓL(1,𝔽₂₅)	C₅×D₄	1	4	yes	complemented
436	ΓL(1,𝔽₂₅)	C₅×D₄	1	4	yes	complemented
437	C₂³×C₅	—	2	1	no	—
438	C₂³×C₅	—	2	1	no	—
439	C₂³×C₅	—	3	1	no	—
440	C₂³×C₅	—	6	1	no	—
441	C₂³×C₅	—	6	1	no	—
442	C₂³×C₅	—	12	2	no	—
443	C₂³×C₅	—	12	4	no	—
444	C₅×Q₈	—	2	1	no	—
445	C₅×Q₈	—	2	1	no	—
446	C₅×Q₈	—	2	1	no	—
447	C₅×Q₈	—	2	1	no	—
448	C₅×Q₈	—	6	1	no	—
449	C₅×Q₈	—	6	1	no	—
450	C₅×Q₈	—	6	1	no	—
451	C₅×Q₈	—	6	1	no	—
452	C₅×Q₈	—	12	2	no	—
453	C₅×D₄	—	2	1	no	—
454	C₅×D₄	—	2	1	no	—
455	C₅×D₄	—	2	1	no	—
456	C₅×D₄	—	2	1	no	—
457	C₅×D₄	—	6	1	no	—
458	C₅×D₄	—	6	1	no	—
459	C₅×D₄	—	6	1	no	—
460	C₅×D₄	—	6	1	no	—
461	C₅×D₄	—	12	2	no	—
462	C₅×D₄	—	12	2	no	—
463	C₅×D₄	—	12	4	no	—
464	C₅×D₄	—	12	2	no	—
465	C₂×C₄×C₅	—	2	1	no	—
466	C₂×C₄×C₅	—	2	1	no	—
467	C₂×C₄×C₅	—	3	1	no	—
468	C₂×C₄×C₅	—	3	2	no	—
469	C₂×C₄×C₅	—	3	2	no	—
470	C₂×C₄×C₅	—	3	2	no	—
471	C₂×C₄×C₅	—	6	1	no	—
472	C₂×C₄×C₅	—	6	1	no	—
473	C₂×C₄×C₅	—	12	2	no	—
474	C₂×C₄×C₅	—	12	2	no	—
475	C₂×C₄×C₅	—	12	2	no	—
476	C₂×C₄×C₅	—	12	2	no	—
477	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
478	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
479	C₅×C₈	—	3	2	no	—
480	C₅×C₈	—	3	2	no	—
481	C₅×C₈	D₃×D₄	1	2	yes	—
482	C₅×C₈	D₃×D₄	1	2	yes	—
483	C₂×#41	—	3	1	no	—
484	C₂×#41	—	3	1	no	—
485	C₂²×Q₈	—	3	1	no	—
486	C₂²×D₄	—	3	1	no	—
487	#137	—	6	4	no	—
488	#137	—	6	4	no	—
489	AGL(1,ℤ/8)	—	6	4	no	—
490	AGL(1,ℤ/8)	—	6	4	no	—
491	C₂×Q₁₆	—	3	1	no	—
492	C₂×Q₁₆	—	3	1	no	—
493	C₂×Q₁₆	—	3	1	no	—
494	C₂×Q₁₆	C₂×C₅×D₃	1	1	yes	characteristic, complemented
495	C₂×SD₁₆	—	3	1	no	—
496	C₂×SD₁₆	—	3	1	no	—
497	C₂×SD₁₆	—	3	1	no	—
498	C₂×SD₁₆	—	3	1	no	—
499	C₂×SD₁₆	—	3	1	no	—
500	C₂×SD₁₆	—	3	1	no	—
501	C₂×SD₁₆	C₂×C₅×D₃	1	1	yes	characteristic
502	C₂×SD₁₆	C₂×C₅×D₃	1	1	yes	characteristic, complemented
503	C₂×D₈	—	3	1	no	—
504	C₂×D₈	—	3	1	no	—
505	C₂×D₈	—	3	1	no	—
506	C₂×D₈	C₂×C₅×D₃	1	1	yes	characteristic
507	C₂×M₁₆	—	3	1	no	—
508	C₂×M₁₆	—	3	1	no	—
509	C₄⋊Q₈	—	3	1	no	—
510	#127	—	3	1	no	—
511	#124	—	3	1	no	—
512	#124	—	3	1	no	—
513	#124	—	3	1	no	—
514	#124	—	3	1	no	—
515	#124	—	6	2	no	—
516	#124	C₂×C₅×D₃	1	1	yes	characteristic
517	#124	C₂×C₅×D₃	1	1	yes	characteristic, complemented
518	#121	—	6	2	no	—
519	C₄×D₄	—	6	2	no	—
520	C₂×C₂²⋊C₄	—	6	2	no	—
521	C₂×C₄²	—	3	1	no	—
522	#97	—	3	1	no	—
523	#97	—	3	1	no	—
524	C₄×C₈	—	3	1	no	—
525	C₄×C₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
526	C₂×C₃×C₅	—	8	1	no	—
527	C₂×C₃×C₅	—	8	1	no	—
528	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
529	C₂×C₃×C₅	#575	1	2	yes	—
530	C₅×D₃	—	2	2	no	—
531	C₅×D₃	—	8	1	no	—
532	C₅×D₃	—	8	1	no	—
533	C₂³×C₃	—	2	1	no	—
534	C₂³×C₃	—	2	1	no	—
535	C₂²×D₃	—	2	1	no	—
536	C₂²×D₃	—	2	1	no	—
537	C₂²×D₃	—	4	4	no	—
538	C₂²×D₃	—	4	2	no	—
539	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
540	C₃×Q₈	—	2	1	no	—
541	C₃×Q₈	—	2	1	no	—
542	C₃×Q₈	—	2	1	no	—
543	C₃×Q₈	—	2	1	no	—
544	C₃×D₄	—	2	1	no	—
545	C₃×D₄	—	2	1	no	—
546	C₃×D₄	—	2	1	no	—
547	C₃×D₄	—	2	1	no	—
548	C₂×C₃×C₄	—	2	1	no	—
549	C₂×C₃×C₄	—	2	1	no	—
550	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
551	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
552	#67	—	4	4	no	—
553	#67	—	4	2	no	—
554	#67	—	4	2	no	—
555	C₂×Dic₃	—	2	1	no	—
556	C₂×Dic₃	—	2	1	no	—
557	C₂×Dic₃	—	4	2	no	—
558	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
559	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
560	D₁₂	—	2	1	no	—
561	D₁₂	—	2	1	no	—
562	D₁₂	—	2	1	no	—
563	D₁₂	—	2	1	no	—
564	D₁₂	—	4	2	no	—
565	C₄×D₃	—	4	2	no	—
566	C₄×D₃	—	4	2	no	—
567	C₄×D₃	—	4	2	no	—
568	C₄×D₃	C₂×C₅×D₄	1	2	yes	—
569	C₄×D₃	C₂×C₅×D₄	1	2	yes	—
570	Dic₆	—	2	1	no	—
571	Dic₆	—	2	1	no	—
572	Dic₆	—	2	1	no	—
573	Dic₆	—	2	1	no	—
574	Dic₆	—	4	2	no	—
575	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
576	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
577	C₃⋊C₈	C₂×C₅×D₄	1	2	yes	—
578	C₃⋊C₈	C₂×C₅×D₄	1	2	yes	—
579	C₂²×C₅	—	3	2	no	—
580	C₂²×C₅	—	4	1	no	—
581	C₂²×C₅	—	4	1	no	—
582	C₂²×C₅	—	4	2	no	—
583	C₂²×C₅	—	4	2	no	—
584	C₂²×C₅	—	6	2	no	—
585	C₂²×C₅	—	12	1	no	—
586	C₂²×C₅	—	12	1	no	—
587	C₂²×C₅	—	12	2	no	—
588	C₂²×C₅	—	12	2	no	—
589	C₂²×C₅	—	24	4	no	—
590	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
591	C₄×C₅	—	2	2	no	—
592	C₄×C₅	—	3	2	no	—
593	C₄×C₅	—	4	1	no	—
594	C₄×C₅	—	4	1	no	—
595	C₄×C₅	—	6	2	no	—
596	C₄×C₅	—	12	1	no	—
597	C₄×C₅	—	12	1	no	—
598	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
599	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
600	C₂⁴	—	6	1	no	—
601	#41	—	6	2	no	—
602	#41	—	6	2	no	—
603	#41	—	6	2	no	—
604	#41	—	6	2	no	—
605	C₂×Q₈	—	3	1	no	—
606	C₂×Q₈	—	3	1	no	—
607	C₂×Q₈	—	6	1	no	—
608	C₂×Q₈	—	6	2	no	—
609	C₂×Q₈	—	6	2	no	—
610	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
611	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
612	C₂×D₄	—	3	1	no	—
613	C₂×D₄	—	3	1	no	—
614	C₂×D₄	—	6	1	no	—
615	C₂×D₄	—	6	2	no	—
616	C₂×D₄	—	6	2	no	—
617	C₂×D₄	—	6	2	no	—
618	C₂×D₄	—	6	1	no	—
619	C₂×D₄	—	6	1	no	—
620	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
621	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
622	C₂²×C₄	—	3	1	no	—
623	C₂²×C₄	—	3	2	no	—
624	C₂²×C₄	—	6	1	no	—
625	C₂²×C₄	—	6	1	no	—
626	C₂²×C₄	—	6	1	no	—
627	Q₁₆	—	2	2	no	—
628	Q₁₆	—	6	2	no	—
629	Q₁₆	—	6	2	no	—
630	Q₁₆	—	6	2	no	—
631	SD₁₆	—	2	2	no	—
632	SD₁₆	—	2	2	no	—
633	SD₁₆	—	6	2	no	—
634	SD₁₆	—	6	2	no	—
635	SD₁₆	—	6	2	no	—
636	SD₁₆	—	6	2	no	—
637	SD₁₆	—	6	2	no	—
638	SD₁₆	—	6	2	no	—
639	D₈	—	2	2	no	—
640	D₈	—	6	2	no	—
641	D₈	—	6	2	no	—
642	D₈	—	6	2	no	—
643	M₁₆	—	3	4	no	—
644	M₁₆	—	3	4	no	—
645	C₂×C₈	—	3	1	no	—
646	C₂×C₈	—	3	1	no	—
647	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
648	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
649	C₄⋊C₄	—	6	2	no	—
650	C₂²⋊C₄	—	2	2	no	—
651	C₂²⋊C₄	—	2	2	no	—
652	C₂²⋊C₄	—	6	2	no	—
653	C₂²⋊C₄	—	6	2	no	—
654	C₂²⋊C₄	—	6	2	no	—
655	C₂²⋊C₄	—	6	2	no	—
656	C₄²	—	3	2	no	—
657	C₄²	—	3	1	no	—
658	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
659	C₃×C₅	#3153	1	1	yes	characteristic, complemented, Hall
660	C₂²×C₃	—	4	1	no	—
661	C₂²×C₃	—	4	1	no	—
662	C₂²×C₃	—	4	2	no	—
663	C₂²×C₃	—	4	2	no	—
664	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
665	C₂×D₃	—	2	2	no	—
666	C₂×D₃	—	4	1	no	—
667	C₂×D₃	—	4	1	no	—
668	C₂×D₃	—	4	2	no	—
669	C₂×D₃	—	4	2	no	—
670	C₂×D₃	—	8	4	no	—
671	C₂×D₃	C₅×#127	1	2	yes	—
672	C₃×C₄	—	2	2	no	—
673	C₃×C₄	—	4	1	no	—
674	C₃×C₄	—	4	1	no	—
675	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
676	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
677	Dic₃	—	2	2	no	—
678	Dic₃	—	4	1	no	—
679	Dic₃	—	4	1	no	—
680	Dic₃	C₅×#127	1	2	yes	—
681	C₂×C₅	—	6	2	no	—
682	C₂×C₅	—	8	1	no	—
683	C₂×C₅	—	8	1	no	—
684	C₂×C₅	—	24	1	no	—
685	C₂×C₅	—	24	1	no	—
686	C₂×C₅	D₃×#127	1	1	yes	characteristic
687	C₂×C₅	#5768	1	2	yes	—
688	C₂³	—	2	1	no	—
689	C₂³	—	2	1	no	—
690	C₂³	—	3	1	no	—
691	C₂³	—	6	1	no	—
692	C₂³	—	6	1	no	—
693	C₂³	—	12	2	no	—
694	C₂³	—	12	4	no	—
695	Q₈	—	2	1	no	—
696	Q₈	—	2	1	no	—
697	Q₈	—	2	1	no	—
698	Q₈	—	2	1	no	—
699	Q₈	—	6	1	no	—
700	Q₈	—	6	1	no	—
701	Q₈	—	6	1	no	—
702	Q₈	—	6	1	no	—
703	Q₈	—	12	2	no	—
704	D₄	—	2	1	no	—
705	D₄	—	2	1	no	—
706	D₄	—	2	1	no	—
707	D₄	—	2	1	no	—
708	D₄	—	6	1	no	—
709	D₄	—	6	1	no	—
710	D₄	—	6	1	no	—
711	D₄	—	6	1	no	—
712	D₄	—	12	2	no	—
713	D₄	—	12	2	no	—
714	D₄	—	12	4	no	—
715	D₄	—	12	2	no	—
716	C₂×C₄	—	2	1	no	—
717	C₂×C₄	—	2	1	no	—
718	C₂×C₄	—	3	1	no	—
719	C₂×C₄	—	3	2	no	—
720	C₂×C₄	—	3	2	no	—
721	C₂×C₄	—	3	2	no	—
722	C₂×C₄	—	6	1	no	—
723	C₂×C₄	—	6	1	no	—
724	C₂×C₄	—	12	2	no	—
725	C₂×C₄	—	12	2	no	—
726	C₂×C₄	—	12	2	no	—
727	C₂×C₄	—	12	2	no	—
728	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
729	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
730	C₈	—	3	2	no	—
731	C₈	—	3	2	no	—
732	C₈	C₅×D₃×D₄	1	2	yes	—
733	C₈	C₅×D₃×D₄	1	2	yes	—
734	C₂×C₃	—	8	1	no	—
735	C₂×C₃	—	8	1	no	—
736	C₂×C₃	C₂×C₅×#127	1	1	yes	characteristic
737	C₂×C₃	C₅×#575	1	2	yes	—
738	D₃	—	2	2	no	—
739	D₃	—	8	1	no	—
740	D₃	—	8	1	no	—
741	C₅	#81821	1	1	yes	characteristic, direct product factor, Sylow
742	C₂²	—	3	2	no	—
743	C₂²	—	4	1	no	—
744	C₂²	—	4	1	no	—
745	C₂²	—	4	2	no	—
746	C₂²	—	4	2	no	—
747	C₂²	—	6	2	no	—
748	C₂²	—	12	1	no	—
749	C₂²	—	12	1	no	—
750	C₂²	—	12	2	no	—
751	C₂²	—	12	2	no	—
752	C₂²	—	24	4	no	—
753	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
754	C₄	—	2	2	no	—
755	C₄	—	3	2	no	—
756	C₄	—	4	1	no	—
757	C₄	—	4	1	no	—
758	C₄	—	6	2	no	—
759	C₄	—	12	1	no	—
760	C₄	—	12	1	no	—
761	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
762	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
763	C₃	C₅×#3153	1	1	yes	characteristic, complemented, Sylow
764	C₂	—	6	2	no	—
765	C₂	—	8	1	no	—
766	C₂	—	8	1	no	—
767	C₂	—	24	1	no	—
768	C₂	—	24	1	no	—
769	C₂	C₅×D₃×#127	1	1	yes	characteristic
770	C₂	C₅×#5768	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×#495	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₅×#495	D₃
hypocenter	C₃	C₅×#3153
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#495

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. C₂×C₅×#914	C₂	semidirect
4. C₂×C₅×#911	C₂	semidirect
5. C₅×D₃×#124	C₂	semidirect
6. C₅×#5668	C₂	semidirect
7. C₃×C₅×#495	C₂	semidirect
8. C₅×#5190	C₂	semidirect
9. C₅×#5176	C₂	semidirect
10. C₅×#5167	C₂	semidirect
11. C₅×#5154	C₂	semidirect
12. C₅×#5059	C₂	semidirect
13. C₅×#5059	C₂	semidirect
14. C₅×#4696	C₂	semidirect
15. C₄×C₅×ΓL(1,𝔽₂₅)	C₂	semidirect
21. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
23. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
26. C₃×C₅×#124	C₂²	semidirect
28. C₅×#944	C₂²	semidirect
29. C₂×C₅×#216	C₂²	semidirect
30. C₂×C₅×#216	C₂²	semidirect
32. C₂×C₅×#215	C₂²	semidirect
33. C₅×#940	C₂²	semidirect
36. C₂×C₅×#214	C₂²	semidirect
43. C₂×C₅×Dic₁₂	C₂²	semidirect
46. C₂×C₅×#204	C₂²	semidirect
54. C₅×#875	C₂²	semidirect
56. C₃×C₄×C₅×C₈	C₂²	semidirect
57. C₅×#815	C₂²	semidirect
58. C₅×#815	C₂²	semidirect
59. C₄×C₅×C₃⋊C₈	C₂²	semidirect
60. #81821	C₅	direct (N × H)
74. C₅×#495	D₃	semidirect
133. C₅×ΓL(1,𝔽₂₅)	D₄	semidirect
134. C₅×ΓL(1,𝔽₂₅)	D₄	semidirect
135. C₂×#918	C₂×C₅	semidirect
136. C₂×#915	C₂×C₅	semidirect
137. C₂×#914	C₂×C₅	semidirect
138. C₂×#911	C₂×C₅	semidirect
139. D₃×#124	C₂×C₅	semidirect
140. #5668	C₂×C₅	semidirect
141. C₃×#495	C₂×C₅	semidirect
142. #5190	C₂×C₅	semidirect
143. #5176	C₂×C₅	semidirect
144. #5167	C₂×C₅	semidirect
145. #5154	C₂×C₅	semidirect
146. #5059	C₂×C₅	semidirect
147. #5059	C₂×C₅	semidirect
148. #4696	C₂×C₅	semidirect
149. C₄×ΓL(1,𝔽₂₅)	C₂×C₅	semidirect
161. C₂×C₅×Q₁₆	C₂×D₃	semidirect
169. C₂×C₅×SD₁₆	C₂×D₃	semidirect
184. C₅×#124	C₂×D₃	semidirect
192. C₄×C₅×C₈	C₂×D₃	semidirect
244. C₂×C₃×Q₁₆	C₂²×C₅	semidirect
246. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
249. C₃×#124	C₂²×C₅	semidirect
251. #944	C₂²×C₅	semidirect
252. C₂×#216	C₂²×C₅	semidirect
253. C₂×#216	C₂²×C₅	semidirect
255. C₂×#215	C₂²×C₅	semidirect
256. #940	C₂²×C₅	semidirect
259. C₂×#214	C₂²×C₅	semidirect
266. C₂×Dic₁₂	C₂²×C₅	semidirect
269. C₂×#204	C₂²×C₅	semidirect
277. #875	C₂²×C₅	semidirect
279. C₃×C₄×C₈	C₂²×C₅	semidirect
280. #815	C₂²×C₅	semidirect
281. #815	C₂²×C₅	semidirect
282. C₄×C₃⋊C₈	C₂²×C₅	semidirect
355. #495	C₅×D₃	semidirect
435. ΓL(1,𝔽₂₅)	C₅×D₄	semidirect
436. ΓL(1,𝔽₂₅)	C₅×D₄	semidirect
494. C₂×Q₁₆	C₂×C₅×D₃	semidirect
502. C₂×SD₁₆	C₂×C₅×D₃	semidirect
517. #124	C₂×C₅×D₃	semidirect
525. C₄×C₈	C₂×C₅×D₃	semidirect
659. C₃×C₅	#3153	semidirect
741. C₅	#81821	direct (N × H)
763. C₃	C₅×#3153	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
C₂×C₅×#914	2
C₂×C₅×#911	2
C₅×D₃×#124	2
C₅×#5668	2
C₃×C₅×#495	2
C₅×#5190	2
C₅×#5176	2
C₅×#5167	2
C₅×#5154	2
C₅×#5059	2
C₅×#4696	2
C₄×C₅×ΓL(1,𝔽₂₅)	2
C₅×#3153	3
#81821	5

Subgroups — C5×#81821 #14439273

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#81821 #14439273