Subgroups — C₅×#78550 #14411522

Order 1920.

1112 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#907	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#901	C₂	1	1	yes	maximal, characteristic
3	C₅×#5522	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#405	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×Dic₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×#815	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4997	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4708	C₂	1	2	yes	maximal, complemented
9	C₅×D₃×#97	C₂	1	2	yes	maximal, complemented
10	C₅×#4689	C₂	1	2	yes	maximal, complemented
11	C₄×C₅×ΓL(1,𝔽₂₅)	C₂	1	2	yes	maximal, complemented
12	C₅×#2875	—	3	1	no	maximal, Hall
13	C₂×C₅×#235	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
16	C₃×C₅×#117	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
18	C₂×C₅×#208	C₂²	1	1	yes	characteristic
19	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
20	C₅×#907	C₄	1	8	yes	complemented
21	C₅×#901	C₄	1	8	yes	complemented
22	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	—
23	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	—
24	C₂×C₅×D₃×C₈	C₂²	1	2	yes	—
25	C₂×C₅×D₃×C₈	C₂²	1	2	yes	—
26	C₅×#893	C₄	1	2	yes	—
27	C₅×#887	C₄	1	2	yes	—
28	C₅×#67⋊C₄	C₄	1	4	yes	—
29	C₅×#872	C₂²	1	2	yes	—
30	C₄²×C₅×D₃	C₂²	1	2	yes	—
31	C₃×C₅×#97	C₂²	1	2	yes	—
32	C₃×C₄×C₅×C₈	C₂²	1	2	yes	—
33	C₅×#815	C₂²	1	1	yes	characteristic
34	C₅×#815	C₂²	1	2	yes	—
35	C₅×#815	C₂²	1	1	yes	characteristic
36	C₅×#815	C₂²	1	1	yes	characteristic
37	C₅×#815	C₂²	1	1	yes	characteristic
38	C₅×C₈×Dic₃	C₂²	1	2	yes	—
39	C₅×#803	C₂²	1	2	yes	—
40	C₄×C₅×C₃⋊C₈	C₂²	1	2	yes	—
41	#78550	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
42	C₂×C₅×#131	—	3	1	no	—
43	C₂×C₅×#131	—	3	1	no	—
44	C₄×C₅×#41	—	3	1	no	—
45	C₅×#405	—	3	2	no	—
46	C₅×#405	—	3	2	no	—
47	C₅×#405	—	3	1	no	—
48	C₅×#405	D₃	1	1	yes	characteristic, complemented
49	C₄×C₅×M₁₆	—	3	2	no	—
50	C₄×C₅×M₁₆	—	3	1	no	—
51	C₂×C₅×#97	—	3	2	no	—
52	C₂×C₅×#97	—	3	1	no	—
53	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
54	C₂×C₅×#67	C₂×C₄	1	2	yes	—
55	C₂²×C₅×Dic₃	C₂×C₄	1	2	yes	—
56	C₅×#235	C₂×C₄	1	4	yes	—
57	C₅×#235	C₂×C₄	1	4	yes	—
58	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄×C₅×D₃	C₂×C₄	1	4	yes	—
60	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
61	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
62	C₃×C₅×M₁₆	C₂×C₄	1	4	yes	complemented
63	C₂×C₃×C₅×C₈	C₂×C₄	1	4	yes	complemented
64	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
65	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
66	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
67	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
68	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
69	C₃×C₄²×C₅	C₂³	1	2	yes	—
70	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	4	yes	—
71	C₅×Dic₃⋊C₄	C₂×C₄	1	4	yes	—
72	C₄×C₅×Dic₃	C₂×C₄	1	4	yes	—
73	C₄×C₅×Dic₃	C₂×C₄	1	2	yes	—
74	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
75	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
76	C₅×#208	C₂×C₄	1	4	yes	complemented
77	C₂×C₅×C₃⋊C₈	C₂×C₄	1	4	yes	complemented
78	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
79	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
80	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
81	C₅×ΓL(1,𝔽₂₅)	C₂×C₄	1	8	yes	complemented
82	C₅×ΓL(1,𝔽₂₅)	C₂×C₄	1	8	yes	complemented
83	C₅×D₃×C₈	C₂×C₄	1	8	yes	complemented
84	C₅×D₃×C₈	C₂×C₄	1	8	yes	complemented
85	C₂×#907	C₂×C₅	1	1	yes	characteristic
86	C₂×#901	C₂×C₅	1	1	yes	characteristic
87	#5522	C₂×C₅	1	1	yes	characteristic
88	C₃×#405	C₂×C₅	1	1	yes	characteristic, complemented
89	Dic₃×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
90	C₂×#815	C₂×C₅	1	1	yes	characteristic, complemented
91	#4997	C₂×C₅	1	1	yes	characteristic, complemented
92	#4708	C₂×C₅	1	2	yes	complemented
93	D₃×#97	C₂×C₅	1	2	yes	complemented
94	#4689	C₂×C₅	1	2	yes	complemented
95	C₄×ΓL(1,𝔽₂₅)	C₂×C₅	1	2	yes	complemented
96	C₂×C₅×#41	—	3	1	no	—
97	C₅×#131	—	3	8	no	—
98	C₅×#131	—	3	8	no	—
99	C₂×C₅×M₁₆	—	3	1	no	—
100	C₂×C₅×M₁₆	—	3	2	no	—
101	C₂×C₅×M₁₆	—	3	2	no	—
102	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
103	C₂²×C₅×C₈	—	3	1	no	—
104	C₂²×C₅×C₈	—	3	2	no	—
105	C₂²×C₅×C₈	—	3	2	no	—
106	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
107	C₄×C₅×Q₈	—	3	2	no	—
108	C₄×C₅×D₄	—	3	2	no	—
109	C₄×C₅×D₄	—	3	4	no	—
110	C₅×#117	—	3	2	no	—
111	C₅×#117	C₂×D₃	1	1	yes	characteristic
112	C₂×C₄²×C₅	—	3	1	no	—
113	C₂×C₄²×C₅	—	3	2	no	—
114	C₅×#97	—	3	1	no	—
115	C₅×#97	—	3	2	no	—
116	C₅×#97	—	3	1	no	—
117	C₅×#97	—	3	1	no	—
118	C₅×#97	—	3	1	no	—
119	C₅×#97	—	3	2	no	—
120	C₅×#97	C₂×D₃	1	2	yes	—
121	C₄×C₅×C₈	—	3	2	no	—
122	C₄×C₅×C₈	—	3	2	no	—
123	C₄×C₅×C₈	C₂×D₃	1	2	yes	—
124	#2875	—	3	1	no	Sylow
125	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
127	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
128	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
130	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
131	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
132	C₅×#67	C₄²	1	8	yes	—
133	C₂×C₅×Dic₃	—	4	2	no	—
134	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
135	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
136	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
137	C₅×D₁₂	C₄²	1	4	yes	—
138	C₄×C₅×D₃	—	4	4	no	—
139	C₄×C₅×D₃	C₂²×C₄	1	4	yes	—
140	C₄×C₅×D₃	C₂²×C₄	1	4	yes	—
141	C₅×Dic₆	C₄²	1	4	yes	—
142	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
143	C₃×C₅×C₈	C₂²×C₄	1	4	yes	—
144	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
145	C₅×C₃⋊C₈	C₂²×C₄	1	2	yes	—
146	C₅×C₃⋊C₈	C₂²×C₄	1	4	yes	—
147	C₅×C₃⋊C₈	C₂²×C₄	1	2	yes	—
148	C₂×#235	C₂²×C₅	1	1	yes	characteristic
149	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
150	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
151	C₃×#117	C₂²×C₅	1	1	yes	characteristic
152	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
153	C₂×#208	C₂²×C₅	1	1	yes	characteristic
154	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
155	#907	C₄×C₅	1	8	yes	complemented
156	#901	C₄×C₅	1	8	yes	complemented
157	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	2	yes	—
158	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	2	yes	—
159	C₂×D₃×C₈	C₂²×C₅	1	2	yes	—
160	C₂×D₃×C₈	C₂²×C₅	1	2	yes	—
161	#893	C₄×C₅	1	2	yes	—
162	#887	C₄×C₅	1	2	yes	—
163	#67⋊C₄	C₄×C₅	1	4	yes	—
164	#872	C₂²×C₅	1	2	yes	—
165	C₄²×D₃	C₂²×C₅	1	2	yes	—
166	C₃×#97	C₂²×C₅	1	2	yes	—
167	C₃×C₄×C₈	C₂²×C₅	1	2	yes	—
168	#815	C₂²×C₅	1	1	yes	characteristic
169	#815	C₂²×C₅	1	2	yes	—
170	#815	C₂²×C₅	1	1	yes	characteristic
171	#815	C₂²×C₅	1	1	yes	characteristic
172	#815	C₂²×C₅	1	1	yes	characteristic
173	C₈×Dic₃	C₂²×C₅	1	2	yes	—
174	#803	C₂²×C₅	1	2	yes	—
175	C₄×C₃⋊C₈	C₂²×C₅	1	2	yes	—
176	C₅×#41	—	3	4	no	—
177	C₅×#41	—	3	4	no	—
178	C₂×C₅×Q₈	—	3	1	no	—
179	C₂×C₅×D₄	—	3	2	no	—
180	C₂×C₅×D₄	—	3	1	no	—
181	C₂²×C₄×C₅	—	3	2	no	—
182	C₂²×C₄×C₅	—	3	2	no	—
183	C₂²×C₄×C₅	—	3	4	no	—
184	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
185	C₅×M₁₆	—	3	4	no	—
186	C₅×M₁₆	—	3	8	no	—
187	C₅×M₁₆	—	3	8	no	—
188	C₅×M₁₆	C₄×D₃	1	4	yes	complemented
189	C₂×C₅×C₈	—	3	4	no	—
190	C₂×C₅×C₈	—	3	1	no	—
191	C₂×C₅×C₈	—	3	1	no	—
192	C₂×C₅×C₈	—	3	2	no	—
193	C₂×C₅×C₈	—	3	8	no	—
194	C₂×C₅×C₈	—	3	8	no	—
195	C₂×C₅×C₈	C₄×D₃	1	4	yes	complemented
196	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
197	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
198	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
199	C₅×C₄⋊C₄	—	3	4	no	—
200	C₅×C₄⋊C₄	C₄×D₃	1	2	yes	—
201	C₅×C₂²⋊C₄	—	3	4	no	—
202	C₅×C₂²⋊C₄	C₄×D₃	1	2	yes	—
203	C₄²×C₅	—	3	4	no	—
204	C₄²×C₅	—	3	2	no	—
205	C₄²×C₅	—	3	1	no	—
206	C₄²×C₅	—	3	1	no	—
207	C₄²×C₅	C₂²×D₃	1	2	yes	—
208	C₂×#131	—	3	1	no	—
209	C₂×#131	—	3	1	no	—
210	C₄×#41	—	3	1	no	—
211	#405	—	3	1	no	—
212	#405	—	3	2	no	—
213	#405	—	3	2	no	—
214	#405	C₅×D₃	1	1	yes	characteristic, complemented
215	C₄×M₁₆	—	3	1	no	—
216	C₄×M₁₆	—	3	2	no	—
217	C₂×#97	—	3	1	no	—
218	C₂×#97	—	3	2	no	—
219	C₂²×C₃×C₅	—	2	2	no	—
220	C₂²×C₃×C₅	C₂×C₄²	1	2	yes	—
221	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
222	C₂×C₅×D₃	—	2	4	no	—
223	C₂×C₅×D₃	C₂×C₄²	1	4	yes	—
224	C₃×C₄×C₅	—	2	4	no	—
225	C₃×C₄×C₅	C₂×C₄²	1	2	yes	—
226	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
227	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
228	C₅×Dic₃	—	2	2	no	—
229	C₅×Dic₃	—	2	2	no	—
230	C₅×Dic₃	C₂×C₄²	1	4	yes	—
231	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
232	C₂×#67	C₂×C₄×C₅	1	2	yes	—
233	C₂²×Dic₃	C₂×C₄×C₅	1	2	yes	—
234	#235	C₂×C₄×C₅	1	4	yes	—
235	#235	C₂×C₄×C₅	1	4	yes	—
236	C₂×D₁₂	C₂×C₄×C₅	1	1	yes	characteristic
237	C₂×C₄×D₃	C₂×C₄×C₅	1	4	yes	—
238	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
239	C₂×Dic₆	C₂×C₄×C₅	1	1	yes	characteristic
240	C₃×M₁₆	C₂×C₄×C₅	1	4	yes	complemented
241	C₂×C₃×C₈	C₂×C₄×C₅	1	4	yes	complemented
242	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
243	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
244	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
245	C₃×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
246	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
247	C₃×C₄²	C₂³×C₅	1	2	yes	—
248	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	4	yes	—
249	Dic₃⋊C₄	C₂×C₄×C₅	1	4	yes	—
250	C₄×Dic₃	C₂×C₄×C₅	1	4	yes	—
251	C₄×Dic₃	C₂×C₄×C₅	1	2	yes	—
252	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
253	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
254	#208	C₂×C₄×C₅	1	4	yes	complemented
255	C₂×C₃⋊C₈	C₂×C₄×C₅	1	4	yes	complemented
256	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
257	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
258	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
259	ΓL(1,𝔽₂₅)	C₂×C₄×C₅	1	8	yes	complemented
260	ΓL(1,𝔽₂₅)	C₂×C₄×C₅	1	8	yes	complemented
261	D₃×C₈	C₂×C₄×C₅	1	8	yes	complemented
262	D₃×C₈	C₂×C₄×C₅	1	8	yes	complemented
263	C₂³×C₅	—	3	2	no	—
264	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
265	C₅×Q₈	—	3	4	no	—
266	C₅×D₄	—	3	8	no	—
267	C₅×D₄	—	3	4	no	—
268	C₂×C₄×C₅	—	3	2	no	—
269	C₂×C₄×C₅	—	3	4	no	—
270	C₂×C₄×C₅	—	3	4	no	—
271	C₂×C₄×C₅	—	3	2	no	—
272	C₂×C₄×C₅	—	3	2	no	—
273	C₂×C₄×C₅	—	12	4	no	—
274	C₂×C₄×C₅	—	12	2	no	—
275	C₂×C₄×C₅	C₂×C₄×D₃	1	4	yes	—
276	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
277	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
278	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
279	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
280	C₅×C₈	—	3	2	no	—
281	C₅×C₈	—	3	4	no	—
282	C₅×C₈	—	3	2	no	—
283	C₅×C₈	C₂×C₄×D₃	1	2	yes	—
284	C₅×C₈	C₂×C₄×D₃	1	4	yes	—
285	C₅×C₈	C₂×C₄×D₃	1	2	yes	—
286	C₂×#41	—	3	1	no	—
287	#131	—	3	8	no	—
288	#131	—	3	8	no	—
289	C₂×M₁₆	—	3	1	no	—
290	C₂×M₁₆	—	3	2	no	—
291	C₂×M₁₆	—	3	2	no	—
292	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
293	C₂²×C₈	—	3	1	no	—
294	C₂²×C₈	—	3	2	no	—
295	C₂²×C₈	—	3	2	no	—
296	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
297	C₄×Q₈	—	3	2	no	—
298	C₄×D₄	—	3	2	no	—
299	C₄×D₄	—	3	4	no	—
300	#117	—	3	2	no	—
301	#117	C₂×C₅×D₃	1	1	yes	characteristic
302	C₂×C₄²	—	3	1	no	—
303	C₂×C₄²	—	3	2	no	—
304	#97	—	3	1	no	—
305	#97	—	3	2	no	—
306	#97	—	3	1	no	—
307	#97	—	3	1	no	—
308	#97	—	3	1	no	—
309	#97	—	3	2	no	—
310	#97	C₂×C₅×D₃	1	2	yes	—
311	C₄×C₈	—	3	2	no	—
312	C₄×C₈	—	3	2	no	—
313	C₄×C₈	C₂×C₅×D₃	1	2	yes	—
314	C₂×C₃×C₅	—	2	2	no	—
315	C₂×C₃×C₅	C₂²×C₄²	1	1	yes	characteristic
316	C₂×C₃×C₅	#568	1	2	yes	—
317	C₅×D₃	—	2	4	no	—
318	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
319	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
320	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
321	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
322	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
323	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
324	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
325	#67	C₄²×C₅	1	8	yes	—
326	C₂×Dic₃	—	4	2	no	—
327	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
328	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
329	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
330	D₁₂	C₄²×C₅	1	4	yes	—
331	C₄×D₃	—	4	4	no	—
332	C₄×D₃	C₂²×C₄×C₅	1	4	yes	—
333	C₄×D₃	C₂²×C₄×C₅	1	4	yes	—
334	Dic₆	C₄²×C₅	1	4	yes	—
335	C₃×C₈	C₂²×C₄×C₅	1	2	yes	—
336	C₃×C₈	C₂²×C₄×C₅	1	4	yes	—
337	C₃×C₈	C₂²×C₄×C₅	1	2	yes	—
338	C₃⋊C₈	C₂²×C₄×C₅	1	2	yes	—
339	C₃⋊C₈	C₂²×C₄×C₅	1	4	yes	—
340	C₃⋊C₈	C₂²×C₄×C₅	1	2	yes	—
341	C₂²×C₅	—	2	2	no	—
342	C₂²×C₅	—	3	4	no	—
343	C₂²×C₅	—	6	4	no	—
344	C₂²×C₅	C₄²×D₃	1	2	yes	—
345	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
346	C₄×C₅	—	2	4	no	—
347	C₄×C₅	—	3	4	no	—
348	C₄×C₅	—	6	2	no	—
349	C₄×C₅	—	6	2	no	—
350	C₄×C₅	C₄²×D₃	1	2	yes	—
351	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
352	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
353	#41	—	3	4	no	—
354	#41	—	3	4	no	—
355	C₂×Q₈	—	3	1	no	—
356	C₂×D₄	—	3	2	no	—
357	C₂×D₄	—	3	1	no	—
358	C₂²×C₄	—	3	2	no	—
359	C₂²×C₄	—	3	2	no	—
360	C₂²×C₄	—	3	4	no	—
361	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
362	M₁₆	—	3	4	no	—
363	M₁₆	—	3	8	no	—
364	M₁₆	—	3	8	no	—
365	M₁₆	C₄×C₅×D₃	1	4	yes	complemented
366	C₂×C₈	—	3	4	no	—
367	C₂×C₈	—	3	2	no	—
368	C₂×C₈	—	3	1	no	—
369	C₂×C₈	—	3	1	no	—
370	C₂×C₈	—	3	8	no	—
371	C₂×C₈	—	3	8	no	—
372	C₂×C₈	C₄×C₅×D₃	1	4	yes	complemented
373	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
374	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
375	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
376	C₄⋊C₄	—	3	4	no	—
377	C₄⋊C₄	C₄×C₅×D₃	1	2	yes	—
378	C₂²⋊C₄	—	3	4	no	—
379	C₂²⋊C₄	C₄×C₅×D₃	1	2	yes	—
380	C₄²	—	3	4	no	—
381	C₄²	—	3	2	no	—
382	C₄²	—	3	1	no	—
383	C₄²	—	3	1	no	—
384	C₄²	C₂²×C₅×D₃	1	2	yes	—
385	C₃×C₅	#2875	1	1	yes	characteristic, complemented, Hall
386	C₂²×C₃	—	2	2	no	—
387	C₂²×C₃	C₂×C₄²×C₅	1	2	yes	—
388	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
389	C₂×D₃	—	2	4	no	—
390	C₂×D₃	C₂×C₄²×C₅	1	4	yes	—
391	C₃×C₄	—	2	4	no	—
392	C₃×C₄	C₂×C₄²×C₅	1	2	yes	—
393	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
394	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
395	Dic₃	—	2	2	no	—
396	Dic₃	—	2	2	no	—
397	Dic₃	C₂×C₄²×C₅	1	4	yes	—
398	C₂×C₅	—	2	2	no	—
399	C₂×C₅	—	6	4	no	—
400	C₂×C₅	C₂×C₄²×D₃	1	1	yes	characteristic
401	C₂×C₅	#5750	1	2	yes	—
402	C₂³	—	3	2	no	—
403	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
404	Q₈	—	3	4	no	—
405	D₄	—	3	8	no	—
406	D₄	—	3	4	no	—
407	C₂×C₄	—	3	2	no	—
408	C₂×C₄	—	3	4	no	—
409	C₂×C₄	—	3	4	no	—
410	C₂×C₄	—	3	2	no	—
411	C₂×C₄	—	3	2	no	—
412	C₂×C₄	—	12	4	no	—
413	C₂×C₄	—	12	2	no	—
414	C₂×C₄	C₂×C₄×C₅×D₃	1	4	yes	—
415	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
416	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
417	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
418	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
419	C₈	—	3	2	no	—
420	C₈	—	3	2	no	—
421	C₈	—	3	4	no	—
422	C₈	C₂×C₄×C₅×D₃	1	2	yes	—
423	C₈	C₂×C₄×C₅×D₃	1	4	yes	—
424	C₈	C₂×C₄×C₅×D₃	1	2	yes	—
425	C₂×C₃	—	2	2	no	—
426	C₂×C₃	C₂²×C₄²×C₅	1	1	yes	characteristic
427	C₂×C₃	C₅×#568	1	2	yes	—
428	D₃	—	2	4	no	—
429	C₅	#78550	1	1	yes	characteristic, direct product factor, Sylow
430	C₂²	—	2	2	no	—
431	C₂²	—	3	4	no	—
432	C₂²	—	6	4	no	—
433	C₂²	C₄²×C₅×D₃	1	2	yes	—
434	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
435	C₄	—	2	4	no	—
436	C₄	—	3	4	no	—
437	C₄	—	6	2	no	—
438	C₄	—	6	2	no	—
439	C₄	C₄²×C₅×D₃	1	2	yes	—
440	C₄	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
441	C₄	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
442	C₃	C₅×#2875	1	1	yes	characteristic, complemented, Sylow
443	C₂	—	2	2	no	—
444	C₂	—	6	4	no	—
445	C₂	C₂×C₄²×C₅×D₃	1	1	yes	characteristic
446	C₂	C₅×#5750	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₅	C₂³×D₃
commutator	C₂×C₃	C₂²×C₄²×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#405	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂×C₅×#235	C₂²
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₅×#405	D₃
hypocenter	C₃	C₅×#2875
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₅×#405

Complements

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

N	H ≅ G/N	type
4. C₃×C₅×#405	C₂	semidirect
5. C₅×Dic₃×M₁₆	C₂	semidirect
6. C₂×C₅×#815	C₂	semidirect
7. C₅×#4997	C₂	semidirect
8. C₅×#4708	C₂	semidirect
9. C₅×D₃×#97	C₂	semidirect
10. C₅×#4689	C₂	semidirect
11. C₄×C₅×ΓL(1,𝔽₂₅)	C₂	semidirect
20. C₅×#907	C₄	semidirect
21. C₅×#901	C₄	semidirect
41. #78550	C₅	direct (N × H)
48. C₅×#405	D₃	semidirect
62. C₃×C₅×M₁₆	C₂×C₄	semidirect
63. C₂×C₃×C₅×C₈	C₂×C₄	semidirect
76. C₅×#208	C₂×C₄	semidirect
77. C₂×C₅×C₃⋊C₈	C₂×C₄	semidirect
81. C₅×ΓL(1,𝔽₂₅)	C₂×C₄	semidirect
82. C₅×ΓL(1,𝔽₂₅)	C₂×C₄	semidirect
83. C₅×D₃×C₈	C₂×C₄	semidirect
84. C₅×D₃×C₈	C₂×C₄	semidirect
88. C₃×#405	C₂×C₅	semidirect
89. Dic₃×M₁₆	C₂×C₅	semidirect
90. C₂×#815	C₂×C₅	semidirect
91. #4997	C₂×C₅	semidirect
92. #4708	C₂×C₅	semidirect
93. D₃×#97	C₂×C₅	semidirect
94. #4689	C₂×C₅	semidirect
95. C₄×ΓL(1,𝔽₂₅)	C₂×C₅	semidirect
155. #907	C₄×C₅	semidirect
156. #901	C₄×C₅	semidirect
188. C₅×M₁₆	C₄×D₃	semidirect
195. C₂×C₅×C₈	C₄×D₃	semidirect
214. #405	C₅×D₃	semidirect
240. C₃×M₁₆	C₂×C₄×C₅	semidirect
241. C₂×C₃×C₈	C₂×C₄×C₅	semidirect
254. #208	C₂×C₄×C₅	semidirect
255. C₂×C₃⋊C₈	C₂×C₄×C₅	semidirect
259. ΓL(1,𝔽₂₅)	C₂×C₄×C₅	semidirect
260. ΓL(1,𝔽₂₅)	C₂×C₄×C₅	semidirect
261. D₃×C₈	C₂×C₄×C₅	semidirect
262. D₃×C₈	C₂×C₄×C₅	semidirect
365. M₁₆	C₄×C₅×D₃	semidirect
372. C₂×C₈	C₄×C₅×D₃	semidirect
385. C₃×C₅	#2875	semidirect
429. C₅	#78550	direct (N × H)
442. C₃	C₅×#2875	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#907	2
C₂×C₅×#901	2
C₅×#5522	2
C₃×C₅×#405	2
C₅×Dic₃×M₁₆	2
C₂×C₅×#815	2
C₅×#4997	2
C₅×#4708	2
C₅×D₃×#97	2
C₅×#4689	2
C₄×C₅×ΓL(1,𝔽₂₅)	2
C₅×#2875	3
#78550	5

Subgroups — C5×#78550 #14411522

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#78550 #14411522