Subgroups — C₂×C₅×#4689 #14411294

Order 1920.

1184 conjugacy classes of subgroups.

The subgroup lattice has 364 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
2	C₂²×C₅×D₃×C₈	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#872	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃×C₄×C₅×C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#815	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×C₈×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#803	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4689	C₂	1	8	yes	maximal, direct product factor
9	C₂×C₅×#405	—	3	1	no	maximal, Hall
10	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
14	C₂×C₅×(C₂×D₃)⋊C₄	C₄	1	2	yes	—
15	C₂×C₅×Dic₃⋊C₄	C₄	1	2	yes	—
16	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
17	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
18	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₅×ΓL(1,𝔽₂₅)	C₄	1	8	yes	complemented
20	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	4	yes	—
21	C₂×C₅×D₃×C₈	C₄	1	8	yes	complemented
22	C₂×C₅×D₃×C₈	C₂²	1	4	yes	—
23	C₅×#872	C₄	1	4	yes	—
24	C₅×#872	C₂²	1	4	yes	—
25	C₃×C₄×C₅×C₈	C₂²	1	4	yes	complemented
26	C₅×#815	C₂²	1	4	yes	complemented
27	C₅×C₈×Dic₃	C₂²	1	4	yes	complemented
28	C₅×#803	C₂²	1	4	yes	complemented
29	C₂×#4689	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
30	C₂²×C₅×M₁₆	—	3	1	no	—
31	C₂³×C₅×C₈	—	3	1	no	—
32	C₂×C₅×#117	—	3	1	no	—
33	C₅×#405	—	3	8	no	—
34	C₂×C₅×#97	—	3	1	no	—
35	C₂×C₅×#97	—	3	1	no	—
36	C₂×C₄×C₅×C₈	—	3	1	no	—
37	C₂×C₄×C₅×C₈	D₃	1	1	yes	characteristic, complemented
38	C₂³×C₅×D₃	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
40	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
41	C₂²×C₅×Dic₃	C₂×C₄	1	2	yes	—
42	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
44	C₂×C₄×C₅×D₃	C₂×C₄	1	4	yes	—
45	C₂×C₄×C₅×D₃	C₂×C₄	1	4	yes	—
46	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
47	C₂×C₃×C₅×C₈	C₂×C₄	1	4	yes	—
48	C₂×C₃×C₅×C₈	C₂×C₄	1	4	yes	—
49	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
50	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
51	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
52	C₃×C₄²×C₅	C₂³	1	2	yes	—
53	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	8	yes	—
54	C₅×Dic₃⋊C₄	C₂×C₄	1	8	yes	—
55	C₄×C₅×Dic₃	C₂×C₄	1	2	yes	—
56	C₄×C₅×Dic₃	C₂³	1	2	yes	—
57	C₂×C₅×C₃⋊C₈	C₂×C₄	1	4	yes	—
58	C₂×C₅×C₃⋊C₈	C₂×C₄	1	4	yes	—
59	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
60	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
61	C₅×ΓL(1,𝔽₂₅)	C₂×C₄	1	16	yes	complemented
62	C₅×D₃×C₈	C₂×C₄	1	16	yes	complemented
63	C₂²×ΓL(1,𝔽₂₅)	C₂×C₅	1	1	yes	characteristic
64	C₂²×D₃×C₈	C₂×C₅	1	1	yes	characteristic
65	C₂×#872	C₂×C₅	1	1	yes	characteristic
66	C₂×C₃×C₄×C₈	C₂×C₅	1	1	yes	characteristic, complemented
67	C₂×#815	C₂×C₅	1	1	yes	characteristic, complemented
68	C₂×C₈×Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
69	C₂×#803	C₂×C₅	1	1	yes	characteristic, complemented
70	#4689	C₂×C₅	1	8	yes	direct product factor
71	C₂³×C₄×C₅	—	3	1	no	—
72	C₂×C₅×M₁₆	—	3	8	no	—
73	C₂×C₅×M₁₆	—	3	4	no	—
74	C₂²×C₅×C₈	—	3	1	no	—
75	C₂²×C₅×C₈	—	3	1	no	—
76	C₂²×C₅×C₈	—	3	8	no	—
77	C₂²×C₅×C₈	—	3	4	no	—
78	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
79	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
80	C₅×#117	—	3	4	no	—
81	C₅×#117	—	3	4	no	—
82	C₂×C₅×C₄⋊C₄	—	3	2	no	—
83	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
84	C₂×C₄²×C₅	—	3	1	no	—
85	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
86	C₅×#97	—	3	4	no	—
87	C₅×#97	—	3	4	no	—
88	C₄×C₅×C₈	—	3	4	no	—
89	C₄×C₅×C₈	C₂×D₃	1	4	yes	complemented
90	C₂×#405	—	3	1	no	Sylow
91	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₅×D₃	—	2	4	no	—
93	C₂²×C₅×D₃	C₄²	1	4	yes	—
94	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
95	C₂×C₃×C₄×C₅	—	2	4	no	—
96	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
97	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
99	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
100	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
101	C₂×C₅×Dic₃	—	2	4	no	—
102	C₂×C₅×Dic₃	C₄²	1	4	yes	—
103	C₂×C₅×Dic₃	C₂²×C₄	1	4	yes	—
104	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
105	C₄×C₅×D₃	C₄²	1	8	yes	—
106	C₄×C₅×D₃	C₂²×C₄	1	4	yes	—
107	C₄×C₅×D₃	C₂²×C₄	1	4	yes	—
108	C₃×C₅×C₈	C₂²×C₄	1	4	yes	—
109	C₃×C₅×C₈	C₂²×C₄	1	4	yes	—
110	C₅×C₃⋊C₈	C₂²×C₄	1	4	yes	—
111	C₅×C₃⋊C₈	C₂²×C₄	1	4	yes	—
112	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
113	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
114	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
115	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
116	C₂×(C₂×D₃)⋊C₄	C₄×C₅	1	2	yes	—
117	C₂×Dic₃⋊C₄	C₄×C₅	1	2	yes	—
118	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
119	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
120	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
121	C₂×ΓL(1,𝔽₂₅)	C₄×C₅	1	8	yes	complemented
122	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	4	yes	—
123	C₂×D₃×C₈	C₄×C₅	1	8	yes	complemented
124	C₂×D₃×C₈	C₂²×C₅	1	4	yes	—
125	#872	C₄×C₅	1	4	yes	—
126	#872	C₂²×C₅	1	4	yes	—
127	C₃×C₄×C₈	C₂²×C₅	1	4	yes	complemented
128	#815	C₂²×C₅	1	4	yes	complemented
129	C₈×Dic₃	C₂²×C₅	1	4	yes	complemented
130	#803	C₂²×C₅	1	4	yes	complemented
131	C₂⁴×C₅	—	3	1	no	—
132	C₂²×C₄×C₅	—	3	1	no	—
133	C₂²×C₄×C₅	—	3	2	no	—
134	C₂²×C₄×C₅	—	3	4	no	—
135	C₂²×C₄×C₅	—	3	4	no	—
136	C₂²×C₄×C₅	—	3	2	no	—
137	C₂²×C₄×C₅	—	3	2	no	—
138	C₂²×C₄×C₅	C₄×D₃	1	2	yes	—
139	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
140	C₅×M₁₆	—	3	16	no	—
141	C₂×C₅×C₈	—	3	4	no	—
142	C₂×C₅×C₈	—	3	4	no	—
143	C₂×C₅×C₈	—	3	2	no	—
144	C₂×C₅×C₈	—	3	2	no	—
145	C₂×C₅×C₈	—	3	16	no	—
146	C₂×C₅×C₈	C₄×D₃	1	4	yes	—
147	C₂×C₅×C₈	C₄×D₃	1	4	yes	—
148	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
149	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
150	C₅×C₄⋊C₄	—	3	8	no	—
151	C₅×C₂²⋊C₄	—	3	8	no	—
152	C₄²×C₅	—	3	2	no	—
153	C₄²×C₅	—	3	2	no	—
154	C₄²×C₅	C₄×D₃	1	2	yes	—
155	C₄²×C₅	C₂²×D₃	1	2	yes	—
156	C₂²×M₁₆	—	3	1	no	—
157	C₂³×C₈	—	3	1	no	—
158	C₂×#117	—	3	1	no	—
159	#405	—	3	8	no	—
160	C₂×#97	—	3	1	no	—
161	C₂×#97	—	3	1	no	—
162	C₂×C₄×C₈	—	3	1	no	—
163	C₂×C₄×C₈	C₅×D₃	1	1	yes	characteristic, complemented
164	C₂²×C₃×C₅	C₂×C₄²	1	2	yes	—
165	C₂²×C₃×C₅	#131	1	4	yes	—
166	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
167	C₂×C₅×D₃	—	2	4	no	—
168	C₂×C₅×D₃	—	2	8	no	—
169	C₂×C₅×D₃	C₂×C₄²	1	4	yes	—
170	C₃×C₄×C₅	—	2	4	no	—
171	C₃×C₄×C₅	C₂×C₄²	1	2	yes	—
172	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
173	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
174	C₅×Dic₃	—	2	4	no	—
175	C₅×Dic₃	C₂×C₄²	1	4	yes	—
176	C₂³×D₃	C₂×C₄×C₅	1	1	yes	characteristic
177	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
178	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
179	C₂²×Dic₃	C₂×C₄×C₅	1	2	yes	—
180	C₂²×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
181	C₂×C₄×D₃	C₂×C₄×C₅	1	2	yes	—
182	C₂×C₄×D₃	C₂×C₄×C₅	1	4	yes	—
183	C₂×C₄×D₃	C₂×C₄×C₅	1	4	yes	—
184	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
185	C₂×C₃×C₈	C₂×C₄×C₅	1	4	yes	—
186	C₂×C₃×C₈	C₂×C₄×C₅	1	4	yes	—
187	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
188	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
189	C₃×C₄²	C₂×C₄×C₅	1	2	yes	—
190	C₃×C₄²	C₂³×C₅	1	2	yes	—
191	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	8	yes	—
192	Dic₃⋊C₄	C₂×C₄×C₅	1	8	yes	—
193	C₄×Dic₃	C₂×C₄×C₅	1	2	yes	—
194	C₄×Dic₃	C₂³×C₅	1	2	yes	—
195	C₂×C₃⋊C₈	C₂×C₄×C₅	1	4	yes	—
196	C₂×C₃⋊C₈	C₂×C₄×C₅	1	4	yes	—
197	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
198	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
199	ΓL(1,𝔽₂₅)	C₂×C₄×C₅	1	16	yes	complemented
200	D₃×C₈	C₂×C₄×C₅	1	16	yes	complemented
201	C₂³×C₅	—	3	4	no	—
202	C₂³×C₅	—	3	2	no	—
203	C₂³×C₅	—	6	4	no	—
204	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
205	C₂×C₄×C₅	—	2	4	no	—
206	C₂×C₄×C₅	—	3	4	no	—
207	C₂×C₄×C₅	—	3	2	no	—
208	C₂×C₄×C₅	—	3	8	no	—
209	C₂×C₄×C₅	—	3	4	no	—
210	C₂×C₄×C₅	—	3	4	no	—
211	C₂×C₄×C₅	—	3	4	no	—
212	C₂×C₄×C₅	—	6	4	no	—
213	C₂×C₄×C₅	C₂×C₄×D₃	1	4	yes	—
214	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
215	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
216	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
217	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
218	C₅×C₈	—	3	4	no	—
219	C₅×C₈	—	3	4	no	—
220	C₅×C₈	C₂×C₄×D₃	1	4	yes	—
221	C₅×C₈	C₂×C₄×D₃	1	4	yes	—
222	C₂³×C₄	—	3	1	no	—
223	C₂×M₁₆	—	3	8	no	—
224	C₂×M₁₆	—	3	4	no	—
225	C₂²×C₈	—	3	1	no	—
226	C₂²×C₈	—	3	1	no	—
227	C₂²×C₈	—	3	8	no	—
228	C₂²×C₈	—	3	4	no	—
229	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
230	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
231	#117	—	3	4	no	—
232	#117	—	3	4	no	—
233	C₂×C₄⋊C₄	—	3	2	no	—
234	C₂×C₂²⋊C₄	—	3	2	no	—
235	C₂×C₄²	—	3	1	no	—
236	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
237	#97	—	3	4	no	—
238	#97	—	3	4	no	—
239	C₄×C₈	—	3	4	no	—
240	C₄×C₈	C₂×C₅×D₃	1	4	yes	complemented
241	C₂×C₃×C₅	#405	1	4	yes	complemented
242	C₂×C₃×C₅	C₂²×C₄²	1	1	yes	characteristic
243	C₂×C₃×C₅	C₂×#131	1	2	yes	—
244	C₅×D₃	—	2	4	no	—
245	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
246	C₂²×D₃	—	2	4	no	—
247	C₂²×D₃	C₄²×C₅	1	4	yes	—
248	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
249	C₂×C₃×C₄	—	2	4	no	—
250	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
251	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
252	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
253	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
254	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
255	C₂×Dic₃	—	2	4	no	—
256	C₂×Dic₃	C₄²×C₅	1	4	yes	—
257	C₂×Dic₃	C₂²×C₄×C₅	1	4	yes	—
258	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
259	C₄×D₃	C₄²×C₅	1	8	yes	—
260	C₄×D₃	C₂²×C₄×C₅	1	4	yes	—
261	C₄×D₃	C₂²×C₄×C₅	1	4	yes	—
262	C₃×C₈	C₂²×C₄×C₅	1	4	yes	—
263	C₃×C₈	C₂²×C₄×C₅	1	4	yes	—
264	C₃⋊C₈	C₂²×C₄×C₅	1	4	yes	—
265	C₃⋊C₈	C₂²×C₄×C₅	1	4	yes	—
266	C₂²×C₅	—	3	4	no	—
267	C₂²×C₅	—	6	8	no	—
268	C₂²×C₅	—	6	4	no	—
269	C₂²×C₅	C₄²×D₃	1	2	yes	—
270	C₂²×C₅	#901	1	4	yes	—
271	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
272	C₄×C₅	—	2	4	no	—
273	C₄×C₅	—	3	4	no	—
274	C₄×C₅	—	6	4	no	—
275	C₄×C₅	C₄²×D₃	1	2	yes	—
276	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
277	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
278	C₂⁴	—	3	1	no	—
279	C₂²×C₄	—	3	1	no	—
280	C₂²×C₄	—	3	2	no	—
281	C₂²×C₄	—	3	4	no	—
282	C₂²×C₄	—	3	4	no	—
283	C₂²×C₄	—	3	2	no	—
284	C₂²×C₄	—	3	2	no	—
285	C₂²×C₄	C₄×C₅×D₃	1	2	yes	—
286	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
287	M₁₆	—	3	16	no	—
288	C₂×C₈	—	3	4	no	—
289	C₂×C₈	—	3	4	no	—
290	C₂×C₈	—	3	2	no	—
291	C₂×C₈	—	3	2	no	—
292	C₂×C₈	—	3	16	no	—
293	C₂×C₈	C₄×C₅×D₃	1	4	yes	—
294	C₂×C₈	C₄×C₅×D₃	1	4	yes	—
295	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
296	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
297	C₄⋊C₄	—	3	8	no	—
298	C₂²⋊C₄	—	3	8	no	—
299	C₄²	—	3	2	no	—
300	C₄²	—	3	2	no	—
301	C₄²	C₄×C₅×D₃	1	2	yes	—
302	C₄²	C₂²×C₅×D₃	1	2	yes	—
303	C₃×C₅	C₂×#405	1	1	yes	characteristic, complemented, Hall
304	C₂²×C₃	C₂×C₄²×C₅	1	2	yes	—
305	C₂²×C₃	C₅×#131	1	4	yes	—
306	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
307	C₂×D₃	—	2	8	no	—
308	C₂×D₃	—	2	4	no	—
309	C₂×D₃	C₂×C₄²×C₅	1	4	yes	—
310	C₃×C₄	—	2	4	no	—
311	C₃×C₄	C₂×C₄²×C₅	1	2	yes	—
312	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
313	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
314	Dic₃	—	2	4	no	—
315	Dic₃	C₂×C₄²×C₅	1	4	yes	—
316	C₂×C₅	—	6	4	no	—
317	C₂×C₅	#4689	1	4	yes	direct product factor
318	C₂×C₅	C₂×C₄²×D₃	1	1	yes	characteristic
319	C₂×C₅	C₂×#901	1	2	yes	—
320	C₂³	—	3	4	no	—
321	C₂³	—	3	2	no	—
322	C₂³	—	6	4	no	—
323	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	3	4	no	—
326	C₂×C₄	—	3	2	no	—
327	C₂×C₄	—	3	8	no	—
328	C₂×C₄	—	3	4	no	—
329	C₂×C₄	—	3	4	no	—
330	C₂×C₄	—	3	4	no	—
331	C₂×C₄	—	6	4	no	—
332	C₂×C₄	C₂×C₄×C₅×D₃	1	4	yes	—
333	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
334	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
335	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
336	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
337	C₈	—	3	4	no	—
338	C₈	—	3	4	no	—
339	C₈	C₂×C₄×C₅×D₃	1	4	yes	—
340	C₈	C₂×C₄×C₅×D₃	1	4	yes	—
341	C₂×C₃	C₅×#405	1	4	yes	complemented
342	C₂×C₃	C₂²×C₄²×C₅	1	1	yes	characteristic
343	C₂×C₃	C₂×C₅×#131	1	2	yes	—
344	D₃	—	2	4	no	—
345	C₅	C₂×#4689	1	1	yes	characteristic, direct product factor, Sylow
346	C₂²	—	3	4	no	—
347	C₂²	—	6	8	no	—
348	C₂²	—	6	4	no	—
349	C₂²	C₄²×C₅×D₃	1	2	yes	—
350	C₂²	C₅×#901	1	4	yes	—
351	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
352	C₄	—	2	4	no	—
353	C₄	—	3	4	no	—
354	C₄	—	6	4	no	—
355	C₄	C₄²×C₅×D₃	1	2	yes	—
356	C₄	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
357	C₄	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
358	C₃	C₂×C₅×#405	1	1	yes	characteristic, complemented, Sylow
359	C₂	—	6	4	no	—
360	C₂	C₅×#4689	1	4	yes	direct product factor
361	C₂	C₂×C₄²×C₅×D₃	1	1	yes	characteristic
362	C₂	C₂×C₅×#901	1	2	yes	—

	subgroup	G/H
center	C₂²×C₅×C₈	C₂×D₃
commutator	C₂×C₃	C₂²×C₄²×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂×C₃×C₄×C₅×C₈	C₂
socle	C₂³×C₃×C₅	C₂²×C₄
prime radical	C₂³×C₅×D₃	C₂×C₄
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₂×C₄×C₅×C₈	D₃
hypocenter	C₃	C₂×C₅×#405
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅×C₈ ◁ C₂×C₄×C₅×C₈

Complements

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

N	H ≅ G/N	type
4. C₂×C₃×C₄×C₅×C₈	C₂	semidirect
5. C₂×C₅×#815	C₂	semidirect
6. C₂×C₅×C₈×Dic₃	C₂	semidirect
7. C₂×C₅×#803	C₂	semidirect
8. C₅×#4689	C₂	direct (N × H)
19. C₂×C₅×ΓL(1,𝔽₂₅)	C₄	semidirect
21. C₂×C₅×D₃×C₈	C₄	semidirect
25. C₃×C₄×C₅×C₈	C₂²	semidirect
26. C₅×#815	C₂²	semidirect
27. C₅×C₈×Dic₃	C₂²	semidirect
28. C₅×#803	C₂²	semidirect
29. C₂×#4689	C₅	direct (N × H)
37. C₂×C₄×C₅×C₈	D₃	semidirect
61. C₅×ΓL(1,𝔽₂₅)	C₂×C₄	semidirect
62. C₅×D₃×C₈	C₂×C₄	semidirect
66. C₂×C₃×C₄×C₈	C₂×C₅	semidirect
67. C₂×#815	C₂×C₅	semidirect
68. C₂×C₈×Dic₃	C₂×C₅	semidirect
69. C₂×#803	C₂×C₅	semidirect
70. #4689	C₂×C₅	direct (N × H)
89. C₄×C₅×C₈	C₂×D₃	semidirect
121. C₂×ΓL(1,𝔽₂₅)	C₄×C₅	semidirect
123. C₂×D₃×C₈	C₄×C₅	semidirect
127. C₃×C₄×C₈	C₂²×C₅	semidirect
128. #815	C₂²×C₅	semidirect
129. C₈×Dic₃	C₂²×C₅	semidirect
130. #803	C₂²×C₅	semidirect
163. C₂×C₄×C₈	C₅×D₃	semidirect
199. ΓL(1,𝔽₂₅)	C₂×C₄×C₅	semidirect
200. D₃×C₈	C₂×C₄×C₅	semidirect
240. C₄×C₈	C₂×C₅×D₃	semidirect
241. C₂×C₃×C₅	#405	semidirect
303. C₃×C₅	C₂×#405	semidirect
317. C₂×C₅	#4689	direct (N × H)
341. C₂×C₃	C₅×#405	semidirect
345. C₅	C₂×#4689	direct (N × H)
358. C₃	C₂×C₅×#405	semidirect
360. C₂	C₅×#4689	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×C₅×#872	2
C₂×C₃×C₄×C₅×C₈	2
C₂×C₅×#815	2
C₂×C₅×C₈×Dic₃	2
C₂×C₅×#803	2
C₅×#4689	2
C₂×C₅×#405	3
C₂×#4689	5

Subgroups — C2×C5×#4689 #14411294

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#4689 #14411294