Subgroups — C₂×C₅×#5128 #14414816

Order 1920.

1104 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₂²×C₄×C₅	C₂²×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂²×C₃×C₅×M₁₆	C₂
socle	C₂³×C₃×C₅	C₂²×C₄
prime radical	C₂²×C₅×#67	C₄
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₂²×C₅×M₁₆	D₃
hypocenter	C₃	C₂×C₅×#436
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ C₂²×C₅×M₁₆

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₅×M₁₆	C₂	semidirect
3. C₂²×C₅×ΓL(1,𝔽₂₅)	C₂	semidirect
4. C₂×C₅×#830	C₂	semidirect
5. C₅×#5128	C₂	direct (N × H)
6. C₂×C₅×(C₂×D₃)⋊C₈	C₂	semidirect
7. C₂×C₅×Dic₃⋊C₈	C₂	semidirect
8. C₂×C₅×C₈×Dic₃	C₂	semidirect
14. C₂×C₃×C₅×M₁₆	C₂²	semidirect
26. C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	semidirect
27. C₅×#830	C₂²	semidirect
28. C₅×(C₂×D₃)⋊C₈	C₂²	semidirect
29. C₅×Dic₃⋊C₈	C₂²	semidirect
30. C₅×C₈×Dic₃	C₂²	semidirect
31. C₂×#5128	C₅	direct (N × H)
33. C₂²×C₅×M₁₆	D₃	semidirect
59. C₂×C₃×C₅×C₈	D₄	semidirect
72. C₂²×C₃×M₁₆	C₂×C₅	semidirect
74. C₂²×ΓL(1,𝔽₂₅)	C₂×C₅	semidirect
75. C₂×#830	C₂×C₅	semidirect
76. #5128	C₂×C₅	direct (N × H)
77. C₂×(C₂×D₃)⋊C₈	C₂×C₅	semidirect
78. C₂×Dic₃⋊C₈	C₂×C₅	semidirect
79. C₂×C₈×Dic₃	C₂×C₅	semidirect
86. C₂×C₅×M₁₆	C₂×D₃	semidirect
123. C₂×C₅×Dic₃	M₁₆	semidirect
131. C₃×C₅×C₈	C₂×D₄	semidirect
138. C₂×C₃×M₁₆	C₂²×C₅	semidirect
150. C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	semidirect
151. #830	C₂²×C₅	semidirect
152. (C₂×D₃)⋊C₈	C₂²×C₅	semidirect
153. Dic₃⋊C₈	C₂²×C₅	semidirect
154. C₈×Dic₃	C₂²×C₅	semidirect
179. C₂×C₅×C₈	#67	semidirect
188. C₂²×M₁₆	C₅×D₃	semidirect
213. C₅×Dic₃	C₂×M₁₆	semidirect
233. C₂×C₃×C₈	C₅×D₄	semidirect
277. C₅×C₈	C₂×#67	semidirect
284. C₂×M₁₆	C₂×C₅×D₃	semidirect
300. C₂×C₃×C₅	#436	semidirect
326. C₂×Dic₃	C₅×M₁₆	semidirect
334. C₃×C₈	C₂×C₅×D₄	semidirect
380. C₂×C₈	C₅×#67	semidirect
388. C₃×C₅	C₂×#436	semidirect
407. Dic₃	C₂×C₅×M₁₆	semidirect
410. C₂×C₅	#5128	direct (N × H)
445. C₈	C₂×C₅×#67	semidirect
447. C₂×C₃	C₅×#436	semidirect
452. C₅	C₂×#5128	direct (N × H)
472. C₃	C₂×C₅×#436	semidirect
475. C₂	C₅×#5128	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₅×M₁₆	2
C₂×C₄×C₅×#67	2
C₂²×C₅×ΓL(1,𝔽₂₅)	2
C₂×C₅×#830	2
C₅×#5128	2
C₂×C₅×(C₂×D₃)⋊C₈	2
C₂×C₅×Dic₃⋊C₈	2
C₂×C₅×C₈×Dic₃	2
C₂×C₅×#436	3
C₂×#5128	5

Subgroups — C2×C5×#5128 #14414816

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5128 #14414816