Subgroups — C₂×C₅×#4706 #14414693

Order 1920.

1128 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×C₅×ΓL(1,𝔽₂₅)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×D₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₅×D₁₂	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃×C₅×#97	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×(C₂×D₃)⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×(C₂×D₃)⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×C₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4706	C₂	1	8	yes	maximal, direct product factor
9	C₂×C₅×#435	—	3	1	no	maximal, Hall
10	C₂²×C₅×D₁₂	C₄	1	1	yes	characteristic
11	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
12	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
16	C₂×C₅×(C₂×D₃)⋊C₄	C₄	1	1	yes	characteristic
17	C₂×C₅×(C₂×D₃)⋊C₄	C₄	1	1	yes	characteristic
18	C₂×C₅×C₄⋊Dic₃	C₄	1	1	yes	characteristic
19	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
20	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₅×ΓL(1,𝔽₂₅)	—	2	4	no	—
22	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	4	yes	complemented
23	C₂×C₅×D₃×C₈	—	2	4	no	—
24	C₂×C₅×D₃×C₈	C₂²	1	4	yes	complemented
25	C₄×C₅×D₁₂	C₄	1	4	yes	—
26	C₄×C₅×D₁₂	C₂²	1	4	yes	—
27	C₃×C₅×#97	C₂²	1	4	yes	complemented
28	C₅×(C₂×D₃)⋊C₈	C₂²	1	4	yes	complemented
29	C₅×(C₂×D₃)⋊C₈	C₂²	1	4	yes	complemented
30	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	4	yes	complemented
31	C₂×#4706	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
32	C₂²×C₅×M₁₆	—	3	1	no	—
33	C₂³×C₅×C₈	—	3	1	no	—
34	C₂×C₄×C₅×D₄	—	3	1	no	—
35	C₅×#435	—	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×C₅×#97	D₃	1	1	yes	characteristic, complemented
40	C₂³×C₅×D₃	C₂×C₄	1	1	yes	characteristic
41	C₂³×C₅×D₃	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
43	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
45	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
46	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
47	C₂×C₅×D₁₂	—	2	4	no	—
48	C₂×C₅×D₁₂	C₂×C₄	1	4	yes	—
49	C₂×C₄×C₅×D₃	—	2	2	no	—
50	C₂×C₄×C₅×D₃	—	2	2	no	—
51	C₂×C₄×C₅×D₃	—	2	2	no	—
52	C₂×C₄×C₅×D₃	—	2	2	no	—
53	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
54	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
55	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
56	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
57	C₂×C₃×C₅×C₈	—	2	2	no	—
58	C₂×C₃×C₅×C₈	D₄	1	4	yes	complemented
59	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
60	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
61	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
62	C₃×C₄²×C₅	C₂³	1	2	yes	—
63	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	4	yes	—
64	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	4	yes	—
65	C₅×C₄⋊Dic₃	C₂×C₄	1	4	yes	—
66	C₂×C₅×C₃⋊C₈	—	2	2	no	—
67	C₂×C₅×C₃⋊C₈	—	2	2	no	—
68	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
69	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
70	C₅×ΓL(1,𝔽₂₅)	—	2	8	no	—
71	C₅×D₃×C₈	—	2	8	no	—
72	C₂²×ΓL(1,𝔽₂₅)	C₂×C₅	1	1	yes	characteristic, complemented
73	C₂²×D₃×C₈	C₂×C₅	1	1	yes	characteristic, complemented
74	C₂×C₄×D₁₂	C₂×C₅	1	1	yes	characteristic
75	C₂×C₃×#97	C₂×C₅	1	1	yes	characteristic, complemented
76	C₂×(C₂×D₃)⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
77	C₂×(C₂×D₃)⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
78	C₂×C₄⋊(C₃⋊C₈)	C₂×C₅	1	1	yes	characteristic, complemented
79	#4706	C₂×C₅	1	8	yes	direct product factor
80	C₂²×C₅×D₄	—	3	1	no	—
81	C₂³×C₄×C₅	—	3	1	no	—
82	C₂³×C₄×C₅	—	3	1	no	—
83	C₂×C₅×M₁₆	—	3	4	no	—
84	C₂×C₅×M₁₆	—	6	4	no	—
85	C₂²×C₅×C₈	—	3	1	no	—
86	C₂²×C₅×C₈	—	3	1	no	—
87	C₂²×C₅×C₈	—	3	4	no	—
88	C₂²×C₅×C₈	—	6	4	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	C₂×D₃	1	1	yes	characteristic
97	C₅×C₄⋊C₈	—	3	4	no	—
98	C₅×C₂²⋊C₈	—	3	4	no	—
99	C₅×C₂²⋊C₈	—	3	4	no	—
100	C₅×#97	C₂×D₃	1	4	yes	complemented
101	C₂×#435	—	3	1	no	Sylow
102	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₅×D₃	—	2	2	no	—
104	C₂²×C₅×D₃	—	2	2	no	—
105	C₂²×C₅×D₃	—	2	2	no	—
106	C₂²×C₅×D₃	—	2	2	no	—
107	C₂²×C₅×D₃	—	2	2	no	—
108	C₂²×C₅×D₃	M₁₆	1	4	yes	complemented
109	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
110	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
111	C₂×C₃×C₄×C₅	—	2	2	no	—
112	C₂×C₃×C₄×C₅	—	2	2	no	—
113	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
114	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
115	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
117	C₂×C₃×C₄×C₅	#41	1	2	yes	—
118	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
119	C₂×C₅×Dic₃	—	2	2	no	—
120	C₂×C₅×Dic₃	—	2	2	no	—
121	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
122	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
123	C₅×D₁₂	—	2	8	no	—
124	C₄×C₅×D₃	—	2	4	no	—
125	C₄×C₅×D₃	—	2	4	no	—
126	C₄×C₅×D₃	—	2	2	no	—
127	C₄×C₅×D₃	—	2	2	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	C₂²×D₁₂	C₄×C₅	1	1	yes	characteristic
135	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
136	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
137	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
138	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
139	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
140	C₂×(C₂×D₃)⋊C₄	C₄×C₅	1	1	yes	characteristic
141	C₂×(C₂×D₃)⋊C₄	C₄×C₅	1	1	yes	characteristic
142	C₂×C₄⋊Dic₃	C₄×C₅	1	1	yes	characteristic
143	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
144	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
145	C₂×ΓL(1,𝔽₂₅)	—	2	4	no	—
146	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	4	yes	complemented
147	C₂×D₃×C₈	—	2	4	no	—
148	C₂×D₃×C₈	C₂²×C₅	1	4	yes	complemented
149	C₄×D₁₂	C₄×C₅	1	4	yes	—
150	C₄×D₁₂	C₂²×C₅	1	4	yes	—
151	C₃×#97	C₂²×C₅	1	4	yes	complemented
152	(C₂×D₃)⋊C₈	C₂²×C₅	1	4	yes	complemented
153	(C₂×D₃)⋊C₈	C₂²×C₅	1	4	yes	complemented
154	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	4	yes	complemented
155	C₂⁴×C₅	—	3	1	no	—
156	C₂⁴×C₅	—	3	1	no	—
157	C₂×C₅×D₄	—	3	4	no	—
158	C₂×C₅×D₄	—	6	4	no	—
159	C₂²×C₄×C₅	—	3	1	no	—
160	C₂²×C₄×C₅	—	3	1	no	—
161	C₂²×C₄×C₅	—	3	2	no	—
162	C₂²×C₄×C₅	—	3	2	no	—
163	C₂²×C₄×C₅	—	3	2	no	—
164	C₂²×C₄×C₅	—	3	2	no	—
165	C₂²×C₄×C₅	—	6	2	no	—
166	C₂²×C₄×C₅	—	6	2	no	—
167	C₂²×C₄×C₅	—	6	2	no	—
168	C₂²×C₄×C₅	—	6	2	no	—
169	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
170	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
171	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
172	C₅×M₁₆	—	6	8	no	—
173	C₂×C₅×C₈	—	2	2	no	—
174	C₂×C₅×C₈	—	3	2	no	—
175	C₂×C₅×C₈	—	3	2	no	—
176	C₂×C₅×C₈	—	6	2	no	—
177	C₂×C₅×C₈	—	6	2	no	—
178	C₂×C₅×C₈	—	6	8	no	—
179	C₂×C₅×C₈	D₁₂	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	C₄×D₃	1	2	yes	—
186	C₄²×C₅	C₂²×D₃	1	2	yes	—
187	C₂²×M₁₆	—	3	1	no	—
188	C₂³×C₈	—	3	1	no	—
189	C₂×C₄×D₄	—	3	1	no	—
190	#435	—	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×#97	C₅×D₃	1	1	yes	characteristic, complemented
195	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
196	C₂²×C₃×C₅	C₂×M₁₆	1	2	yes	—
197	C₂²×C₃×C₅	#131	1	2	yes	—
198	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
199	C₂×C₅×D₃	—	2	2	no	—
200	C₂×C₅×D₃	—	2	2	no	—
201	C₂×C₅×D₃	—	2	8	no	—
202	C₂×C₅×D₃	—	2	2	no	—
203	C₂×C₅×D₃	—	2	2	no	—
204	C₂×C₅×D₃	—	2	2	no	—
205	C₂×C₅×D₃	—	4	4	no	—
206	C₂×C₅×D₃	C₂×M₁₆	1	4	yes	complemented
207	C₃×C₄×C₅	—	2	2	no	—
208	C₃×C₄×C₅	—	2	2	no	—
209	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
210	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
211	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
212	C₅×Dic₃	—	2	2	no	—
213	C₅×Dic₃	—	2	2	no	—
214	C₂³×D₃	C₂×C₄×C₅	1	1	yes	characteristic
215	C₂³×D₃	C₂×C₄×C₅	1	1	yes	characteristic
216	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
217	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
218	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
219	C₂²×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
220	C₂²×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
221	C₂×D₁₂	—	2	4	no	—
222	C₂×D₁₂	C₂×C₄×C₅	1	4	yes	—
223	C₂×C₄×D₃	—	2	2	no	—
224	C₂×C₄×D₃	—	2	2	no	—
225	C₂×C₄×D₃	—	2	2	no	—
226	C₂×C₄×D₃	—	2	2	no	—
227	C₂×C₄×D₃	C₂×C₄×C₅	1	2	yes	—
228	C₂×C₄×D₃	C₂×C₄×C₅	1	2	yes	—
229	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
230	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
231	C₂×C₃×C₈	—	2	2	no	—
232	C₂×C₃×C₈	C₅×D₄	1	4	yes	complemented
233	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
234	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
235	C₃×C₄²	C₂×C₄×C₅	1	2	yes	—
236	C₃×C₄²	C₂³×C₅	1	2	yes	—
237	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	4	yes	—
238	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	4	yes	—
239	C₄⋊Dic₃	C₂×C₄×C₅	1	4	yes	—
240	C₂×C₃⋊C₈	—	2	2	no	—
241	C₂×C₃⋊C₈	—	2	2	no	—
242	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
243	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
244	ΓL(1,𝔽₂₅)	—	2	8	no	—
245	D₃×C₈	—	2	8	no	—
246	C₂³×C₅	—	3	4	no	—
247	C₂³×C₅	—	3	2	no	—
248	C₂³×C₅	—	3	2	no	—
249	C₂³×C₅	—	6	2	no	—
250	C₂³×C₅	—	6	2	no	—
251	C₂³×C₅	—	6	2	no	—
252	C₂³×C₅	—	6	2	no	—
253	C₂³×C₅	—	6	2	no	—
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	2	no	—
258	C₂×C₄×C₅	—	3	2	no	—
259	C₂×C₄×C₅	—	3	2	no	—
260	C₂×C₄×C₅	—	6	2	no	—
261	C₂×C₄×C₅	—	6	2	no	—
262	C₂×C₄×C₅	—	6	4	no	—
263	C₂×C₄×C₅	—	6	4	no	—
264	C₂×C₄×C₅	—	6	2	no	—
265	C₂×C₄×C₅	—	6	2	no	—
266	C₂×C₄×C₅	—	6	2	no	—
267	C₂×C₄×C₅	—	6	2	no	—
268	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
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	C₂×D₁₂	1	2	yes	—
272	C₂×C₄×C₅	#235	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×D₁₂	1	4	yes	complemented
278	C₂²×D₄	—	3	1	no	—
279	C₂³×C₄	—	3	1	no	—
280	C₂³×C₄	—	3	1	no	—
281	C₂×M₁₆	—	3	4	no	—
282	C₂×M₁₆	—	6	4	no	—
283	C₂²×C₈	—	3	1	no	—
284	C₂²×C₈	—	3	1	no	—
285	C₂²×C₈	—	3	4	no	—
286	C₂²×C₈	—	6	4	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	C₂×C₅×D₃	1	1	yes	characteristic
295	C₄⋊C₈	—	3	4	no	—
296	C₂²⋊C₈	—	3	4	no	—
297	C₂²⋊C₈	—	3	4	no	—
298	#97	C₂×C₅×D₃	1	4	yes	complemented
299	C₂×C₃×C₅	#435	1	4	yes	complemented
300	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
301	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
302	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
303	C₅×D₃	—	2	4	no	—
304	C₅×D₃	—	4	2	no	—
305	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
306	C₂²×D₃	—	2	2	no	—
307	C₂²×D₃	—	2	2	no	—
308	C₂²×D₃	—	2	2	no	—
309	C₂²×D₃	—	2	2	no	—
310	C₂²×D₃	—	2	2	no	—
311	C₂²×D₃	C₅×M₁₆	1	4	yes	complemented
312	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
313	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
314	C₂×C₃×C₄	—	2	2	no	—
315	C₂×C₃×C₄	—	2	2	no	—
316	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
317	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
318	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
319	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
320	C₂×C₃×C₄	C₅×#41	1	2	yes	—
321	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
322	C₂×Dic₃	—	2	2	no	—
323	C₂×Dic₃	—	2	2	no	—
324	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
325	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
326	D₁₂	—	2	8	no	—
327	C₄×D₃	—	2	4	no	—
328	C₄×D₃	—	2	4	no	—
329	C₄×D₃	—	2	2	no	—
330	C₄×D₃	—	2	2	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	—	3	4	no	—
338	C₂²×C₅	—	6	2	no	—
339	C₂²×C₅	—	6	8	no	—
340	C₂²×C₅	—	6	2	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	C₄×D₁₂	1	2	yes	—
346	C₂²×C₅	D₃×M₁₆	1	2	yes	—
347	C₂²×C₅	#907	1	2	yes	—
348	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
349	C₄×C₅	—	2	2	no	—
350	C₄×C₅	—	2	2	no	—
351	C₄×C₅	—	6	2	no	—
352	C₄×C₅	—	6	2	no	—
353	C₄×C₅	C₄×D₁₂	1	2	yes	—
354	C₄×C₅	C₂²×D₁₂	1	1	yes	characteristic
355	C₄×C₅	C₂×#235	1	1	yes	characteristic
356	C₂⁴	—	3	1	no	—
357	C₂⁴	—	3	1	no	—
358	C₂×D₄	—	3	4	no	—
359	C₂×D₄	—	6	4	no	—
360	C₂²×C₄	—	3	1	no	—
361	C₂²×C₄	—	3	1	no	—
362	C₂²×C₄	—	3	2	no	—
363	C₂²×C₄	—	3	2	no	—
364	C₂²×C₄	—	3	2	no	—
365	C₂²×C₄	—	3	2	no	—
366	C₂²×C₄	—	6	2	no	—
367	C₂²×C₄	—	6	2	no	—
368	C₂²×C₄	—	6	2	no	—
369	C₂²×C₄	—	6	2	no	—
370	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
371	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
372	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
373	M₁₆	—	6	8	no	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	3	2	no	—
376	C₂×C₈	—	3	2	no	—
377	C₂×C₈	—	6	2	no	—
378	C₂×C₈	—	6	2	no	—
379	C₂×C₈	—	6	8	no	—
380	C₂×C₈	C₅×D₁₂	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	C₄×C₅×D₃	1	2	yes	—
387	C₄²	C₂²×C₅×D₃	1	2	yes	—
388	C₃×C₅	C₂×#435	1	1	yes	characteristic, complemented, Hall
389	C₂²×C₃	C₄×C₅×D₄	1	2	yes	—
390	C₂²×C₃	C₂×C₅×M₁₆	1	2	yes	—
391	C₂²×C₃	C₅×#131	1	2	yes	—
392	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
393	C₂×D₃	—	2	8	no	—
394	C₂×D₃	—	2	2	no	—
395	C₂×D₃	—	2	2	no	—
396	C₂×D₃	—	2	2	no	—
397	C₂×D₃	—	2	2	no	—
398	C₂×D₃	—	2	2	no	—
399	C₂×D₃	—	4	4	no	—
400	C₂×D₃	C₂×C₅×M₁₆	1	4	yes	complemented
401	C₃×C₄	—	2	2	no	—
402	C₃×C₄	—	2	2	no	—
403	C₃×C₄	C₄×C₅×D₄	1	2	yes	—
404	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
405	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
406	Dic₃	—	2	2	no	—
407	Dic₃	—	2	2	no	—
408	C₂×C₅	—	6	4	no	—
409	C₂×C₅	—	12	2	no	—
410	C₂×C₅	#4706	1	4	yes	direct product factor
411	C₂×C₅	C₂×C₄×D₁₂	1	1	yes	characteristic
412	C₂×C₅	C₂×D₃×M₁₆	1	1	yes	characteristic
413	C₂×C₅	C₂×#907	1	1	yes	characteristic
414	C₂³	—	3	4	no	—
415	C₂³	—	3	2	no	—
416	C₂³	—	3	2	no	—
417	C₂³	—	6	2	no	—
418	C₂³	—	6	2	no	—
419	C₂³	—	6	2	no	—
420	C₂³	—	6	2	no	—
421	C₂³	—	6	2	no	—
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	2	no	—
426	C₂×C₄	—	3	2	no	—
427	C₂×C₄	—	3	2	no	—
428	C₂×C₄	—	6	2	no	—
429	C₂×C₄	—	6	2	no	—
430	C₂×C₄	—	6	4	no	—
431	C₂×C₄	—	6	4	no	—
432	C₂×C₄	—	6	2	no	—
433	C₂×C₄	—	6	2	no	—
434	C₂×C₄	—	6	2	no	—
435	C₂×C₄	—	6	2	no	—
436	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
437	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
438	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
439	C₂×C₄	C₂×C₅×D₁₂	1	2	yes	—
440	C₂×C₄	C₅×#235	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×D₁₂	1	4	yes	complemented
446	C₂×C₃	C₅×#435	1	4	yes	complemented
447	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
448	C₂×C₃	C₂²×C₅×M₁₆	1	1	yes	characteristic
449	C₂×C₃	C₂×C₅×#131	1	1	yes	characteristic
450	D₃	—	2	4	no	—
451	D₃	—	4	2	no	—
452	C₅	C₂×#4706	1	1	yes	characteristic, direct product factor, Sylow
453	C₂²	—	3	4	no	—
454	C₂²	—	6	8	no	—
455	C₂²	—	6	2	no	—
456	C₂²	—	6	2	no	—
457	C₂²	—	6	2	no	—
458	C₂²	—	6	2	no	—
459	C₂²	—	6	2	no	—
460	C₂²	—	12	4	no	—
461	C₂²	C₄×C₅×D₁₂	1	2	yes	—
462	C₂²	C₅×D₃×M₁₆	1	2	yes	—
463	C₂²	C₅×#907	1	2	yes	—
464	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
465	C₄	—	2	2	no	—
466	C₄	—	2	2	no	—
467	C₄	—	6	2	no	—
468	C₄	—	6	2	no	—
469	C₄	C₄×C₅×D₁₂	1	2	yes	—
470	C₄	C₂²×C₅×D₁₂	1	1	yes	characteristic
471	C₄	C₂×C₅×#235	1	1	yes	characteristic
472	C₃	C₂×C₅×#435	1	1	yes	characteristic, complemented, Sylow
473	C₂	—	6	4	no	—
474	C₂	—	12	2	no	—
475	C₂	C₅×#4706	1	4	yes	direct product factor
476	C₂	C₂×C₄×C₅×D₁₂	1	1	yes	characteristic
477	C₂	C₂×C₅×D₃×M₁₆	1	1	yes	characteristic
478	C₂	C₂×C₅×#907	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	C₂×C₃×C₅×#97	C₂
socle	C₂³×C₃×C₅	C₂²×C₄
prime radical	C₂²×C₅×D₁₂	C₄
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₂×C₅×#97	D₃
hypocenter	C₃	C₂×C₅×#435
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×#97

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×ΓL(1,𝔽₂₅)	C₂	semidirect
2. C₂²×C₅×D₃×C₈	C₂	semidirect
4. C₂×C₃×C₅×#97	C₂	semidirect
5. C₂×C₅×(C₂×D₃)⋊C₈	C₂	semidirect
6. C₂×C₅×(C₂×D₃)⋊C₈	C₂	semidirect
7. C₂×C₅×C₄⋊(C₃⋊C₈)	C₂	semidirect
8. C₅×#4706	C₂	direct (N × H)
22. C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	semidirect
24. C₂×C₅×D₃×C₈	C₂²	semidirect
27. C₃×C₅×#97	C₂²	semidirect
28. C₅×(C₂×D₃)⋊C₈	C₂²	semidirect
29. C₅×(C₂×D₃)⋊C₈	C₂²	semidirect
30. C₅×C₄⋊(C₃⋊C₈)	C₂²	semidirect
31. C₂×#4706	C₅	direct (N × H)
39. C₂×C₅×#97	D₃	semidirect
58. C₂×C₃×C₅×C₈	D₄	semidirect
72. C₂²×ΓL(1,𝔽₂₅)	C₂×C₅	semidirect
73. C₂²×D₃×C₈	C₂×C₅	semidirect
75. C₂×C₃×#97	C₂×C₅	semidirect
76. C₂×(C₂×D₃)⋊C₈	C₂×C₅	semidirect
77. C₂×(C₂×D₃)⋊C₈	C₂×C₅	semidirect
78. C₂×C₄⋊(C₃⋊C₈)	C₂×C₅	semidirect
79. #4706	C₂×C₅	direct (N × H)
100. C₅×#97	C₂×D₃	semidirect
108. C₂²×C₅×D₃	M₁₆	semidirect
131. C₃×C₅×C₈	C₂×D₄	semidirect
146. C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	semidirect
148. C₂×D₃×C₈	C₂²×C₅	semidirect
151. C₃×#97	C₂²×C₅	semidirect
152. (C₂×D₃)⋊C₈	C₂²×C₅	semidirect
153. (C₂×D₃)⋊C₈	C₂²×C₅	semidirect
154. C₄⋊(C₃⋊C₈)	C₂²×C₅	semidirect
179. C₂×C₅×C₈	D₁₂	semidirect
194. C₂×#97	C₅×D₃	semidirect
206. C₂×C₅×D₃	C₂×M₁₆	semidirect
232. C₂×C₃×C₈	C₅×D₄	semidirect
277. C₅×C₈	C₂×D₁₂	semidirect
298. #97	C₂×C₅×D₃	semidirect
299. C₂×C₃×C₅	#435	semidirect
311. C₂²×D₃	C₅×M₁₆	semidirect
334. C₃×C₈	C₂×C₅×D₄	semidirect
380. C₂×C₈	C₅×D₁₂	semidirect
388. C₃×C₅	C₂×#435	semidirect
400. C₂×D₃	C₂×C₅×M₁₆	semidirect
410. C₂×C₅	#4706	direct (N × H)
445. C₈	C₂×C₅×D₁₂	semidirect
446. C₂×C₃	C₅×#435	semidirect
452. C₅	C₂×#4706	direct (N × H)
472. C₃	C₂×C₅×#435	semidirect
475. C₂	C₅×#4706	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×C₅×ΓL(1,𝔽₂₅)	2
C₂²×C₅×D₃×C₈	2
C₂×C₄×C₅×D₁₂	2
C₂×C₃×C₅×#97	2
C₂×C₅×(C₂×D₃)⋊C₈	2
C₂×C₅×C₄⋊(C₃⋊C₈)	2
C₅×#4706	2
C₂×C₅×#435	3
C₂×#4706	5

Subgroups — C2×C5×#4706 #14414693

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#4706 #14414693