Subgroups — C₂×C₅×#4727 #14411677

Order 1920.

1584 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×#235	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₅×ΓL(1,𝔽₂₅)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₅×D₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×C₅×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#830	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×(C₂×D₃)⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×(C₂×D₃)⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4727	C₂	1	8	yes	maximal, direct product factor
9	C₂×C₅×#408	—	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×C₅×#67	C₄	1	1	yes	characteristic
13	C₂×C₅×#235	—	2	4	no	—
14	C₂×C₅×#235	—	2	4	no	—
15	C₂×C₅×#235	C₄	1	4	yes	—
16	C₂×C₅×#235	C₂²	1	4	yes	—
17	C₂²×C₅×D₁₂	C₄	1	1	yes	characteristic
18	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
19	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
20	C₂²×C₅×Dic₆	C₄	1	1	yes	characteristic
21	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
22	C₂²×C₃×C₅×C₈	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	C₂×C₅×D₃×C₈	—	2	4	no	—
28	C₂×C₅×D₃×C₈	C₂²	1	4	yes	complemented
29	C₃×C₅×C₂²⋊C₈	C₂²	1	4	yes	complemented
30	C₅×#830	C₂²	1	4	yes	complemented
31	C₅×(C₂×D₃)⋊C₈	C₂²	1	4	yes	complemented
32	C₅×(C₂×D₃)⋊C₈	C₂²	1	4	yes	complemented
33	C₂×#4727	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
34	C₂²×C₅×#41	—	3	1	no	—
35	C₂²×C₅×M₁₆	—	3	1	no	—
36	C₂³×C₅×C₈	—	3	1	no	—
37	C₅×#408	—	3	8	no	—
38	C₂×C₅×C₂²⋊C₈	—	3	1	no	—
39	C₂×C₅×C₂²⋊C₈	—	3	1	no	—
40	C₂×C₅×C₂²⋊C₈	—	3	1	no	—
41	C₂×C₅×C₂²⋊C₈	D₃	1	1	yes	characteristic, complemented
42	C₂⁴×C₃×C₅	C₂×C₄	1	1	yes	characteristic
43	C₂³×C₅×D₃	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₅×D₃	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₃×C₄×C₅	—	2	2	no	—
46	C₂²×C₃×C₄×C₅	—	2	2	no	—
47	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
49	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
50	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
51	C₂×C₅×#67	—	2	4	no	—
52	C₂×C₅×#67	—	2	4	no	—
53	C₂×C₅×#67	C₂×C₄	1	4	yes	—
54	C₂×C₅×#67	C₂×C₄	1	4	yes	—
55	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
56	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
57	C₅×#235	—	2	16	no	—
58	C₅×#235	—	2	8	no	—
59	C₅×#235	—	2	8	no	—
60	C₂×C₅×D₁₂	—	2	4	no	—
61	C₂×C₅×D₁₂	C₂×C₄	1	4	yes	—
62	C₂×C₄×C₅×D₃	—	2	2	no	—
63	C₂×C₄×C₅×D₃	—	2	2	no	—
64	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
65	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
66	C₂×C₄×C₅×D₃	D₄	1	4	yes	—
67	C₂×C₄×C₅×D₃	D₄	1	4	yes	—
68	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
69	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
70	C₂×C₅×Dic₆	—	2	4	no	—
71	C₂×C₅×Dic₆	C₂×C₄	1	4	yes	—
72	C₂×C₃×C₅×C₈	—	2	2	no	—
73	C₂×C₃×C₅×C₈	—	2	2	no	—
74	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
75	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
76	C₂×C₅×C₃⋊C₈	—	2	2	no	—
77	C₂×C₅×C₃⋊C₈	—	2	2	no	—
78	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
79	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
80	C₅×ΓL(1,𝔽₂₅)	—	2	8	no	—
81	C₅×D₃×C₈	—	2	8	no	—
82	C₂²×#235	C₂×C₅	1	1	yes	characteristic
83	C₂²×ΓL(1,𝔽₂₅)	C₂×C₅	1	1	yes	characteristic, complemented
84	C₂²×D₃×C₈	C₂×C₅	1	1	yes	characteristic, complemented
85	C₂×C₃×C₂²⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
86	C₂×#830	C₂×C₅	1	1	yes	characteristic, complemented
87	C₂×(C₂×D₃)⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
88	C₂×(C₂×D₃)⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
89	#4727	C₂×C₅	1	8	yes	direct product factor
90	C₂×C₅×#41	—	3	4	no	—
91	C₂×C₅×#41	—	3	4	no	—
92	C₂×C₅×#41	—	6	4	no	—
93	C₂×C₅×#41	—	6	4	no	—
94	C₂²×C₅×Q₈	—	3	1	no	—
95	C₂²×C₅×D₄	—	3	1	no	—
96	C₂²×C₅×D₄	—	3	1	no	—
97	C₂²×C₅×D₄	—	3	1	no	—
98	C₂³×C₄×C₅	—	3	1	no	—
99	C₂³×C₄×C₅	—	3	1	no	—
100	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
101	C₂×C₅×M₁₆	—	3	4	no	—
102	C₂×C₅×M₁₆	—	6	4	no	—
103	C₂²×C₅×C₈	—	3	1	no	—
104	C₂²×C₅×C₈	—	3	1	no	—
105	C₂²×C₅×C₈	—	3	4	no	—
106	C₂²×C₅×C₈	—	6	4	no	—
107	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
108	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
109	C₅×C₂²⋊C₈	—	3	4	no	—
110	C₅×C₂²⋊C₈	—	3	4	no	—
111	C₅×C₂²⋊C₈	—	3	4	no	—
112	C₅×C₂²⋊C₈	C₂×D₃	1	4	yes	complemented
113	C₂×#408	—	3	1	no	Sylow
114	C₂³×C₃×C₅	—	2	2	no	—
115	C₂³×C₃×C₅	—	2	2	no	—
116	C₂³×C₃×C₅	—	2	2	no	—
117	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
118	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₅×D₃	—	2	2	no	—
120	C₂²×C₅×D₃	—	2	2	no	—
121	C₂²×C₅×D₃	—	2	2	no	—
122	C₂²×C₅×D₃	—	2	2	no	—
123	C₂²×C₅×D₃	—	2	2	no	—
124	C₂²×C₅×D₃	C₂²⋊C₄	1	4	yes	—
125	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
126	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
127	C₂×C₃×C₄×C₅	—	2	2	no	—
128	C₂×C₃×C₄×C₅	—	2	4	no	—
129	C₂×C₃×C₄×C₅	—	2	2	no	—
130	C₂×C₃×C₄×C₅	—	2	2	no	—
131	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
132	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
134	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
135	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
136	C₅×#67	—	2	8	no	—
137	C₅×#67	—	2	8	no	—
138	C₂×C₅×Dic₃	—	2	2	no	—
139	C₂×C₅×Dic₃	C₂²⋊C₄	1	4	yes	—
140	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
141	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
142	C₅×D₁₂	—	2	8	no	—
143	C₄×C₅×D₃	—	2	4	no	—
144	C₄×C₅×D₃	—	2	2	no	—
145	C₄×C₅×D₃	—	2	2	no	—
146	C₄×C₅×D₃	C₂²⋊C₄	1	8	yes	—
147	C₄×C₅×D₃	C₂×D₄	1	4	yes	—
148	C₄×C₅×D₃	C₂×D₄	1	4	yes	—
149	C₅×Dic₆	—	2	8	no	—
150	C₃×C₅×C₈	—	2	2	no	—
151	C₃×C₅×C₈	—	2	2	no	—
152	C₅×C₃⋊C₈	—	2	2	no	—
153	C₅×C₃⋊C₈	—	2	2	no	—
154	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
155	C₂²×#67	C₄×C₅	1	1	yes	characteristic
156	C₂²×#67	C₄×C₅	1	1	yes	characteristic
157	C₂×#235	—	2	4	no	—
158	C₂×#235	—	2	4	no	—
159	C₂×#235	C₄×C₅	1	4	yes	—
160	C₂×#235	C₂²×C₅	1	4	yes	—
161	C₂²×D₁₂	C₄×C₅	1	1	yes	characteristic
162	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
163	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
164	C₂²×Dic₆	C₄×C₅	1	1	yes	characteristic
165	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
166	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
167	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
168	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
169	C₂×ΓL(1,𝔽₂₅)	—	2	4	no	—
170	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	4	yes	complemented
171	C₂×D₃×C₈	—	2	4	no	—
172	C₂×D₃×C₈	C₂²×C₅	1	4	yes	complemented
173	C₃×C₂²⋊C₈	C₂²×C₅	1	4	yes	complemented
174	#830	C₂²×C₅	1	4	yes	complemented
175	(C₂×D₃)⋊C₈	C₂²×C₅	1	4	yes	complemented
176	(C₂×D₃)⋊C₈	C₂²×C₅	1	4	yes	complemented
177	C₂⁴×C₅	—	3	1	no	—
178	C₂⁴×C₅	—	3	1	no	—
179	C₂⁴×C₅	C₄×D₃	1	1	yes	characteristic
180	C₅×#41	—	6	16	no	—
181	C₅×#41	—	6	8	no	—
182	C₅×#41	—	6	8	no	—
183	C₂×C₅×Q₈	—	3	4	no	—
184	C₂×C₅×Q₈	—	6	4	no	—
185	C₂×C₅×D₄	—	3	4	no	—
186	C₂×C₅×D₄	—	3	4	no	—
187	C₂×C₅×D₄	—	3	4	no	—
188	C₂×C₅×D₄	—	6	4	no	—
189	C₂×C₅×D₄	—	6	4	no	—
190	C₂×C₅×D₄	—	6	4	no	—
191	C₂²×C₄×C₅	—	2	2	no	—
192	C₂²×C₄×C₅	—	2	2	no	—
193	C₂²×C₄×C₅	—	3	1	no	—
194	C₂²×C₄×C₅	—	3	2	no	—
195	C₂²×C₄×C₅	—	3	4	no	—
196	C₂²×C₄×C₅	—	3	4	no	—
197	C₂²×C₄×C₅	—	3	2	no	—
198	C₂²×C₄×C₅	—	3	1	no	—
199	C₂²×C₄×C₅	—	3	2	no	—
200	C₂²×C₄×C₅	—	3	2	no	—
201	C₂²×C₄×C₅	—	6	2	no	—
202	C₂²×C₄×C₅	—	6	2	no	—
203	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
204	C₂²×C₄×C₅	C₄×D₃	1	2	yes	—
205	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
206	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
207	C₅×M₁₆	—	6	8	no	—
208	C₂×C₅×C₈	—	2	2	no	—
209	C₂×C₅×C₈	—	2	2	no	—
210	C₂×C₅×C₈	—	3	2	no	—
211	C₂×C₅×C₈	—	3	2	no	—
212	C₂×C₅×C₈	—	6	8	no	—
213	C₂×C₅×C₈	—	6	2	no	—
214	C₂×C₅×C₈	—	6	2	no	—
215	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
216	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
217	C₂²×#41	—	3	1	no	—
218	C₂²×M₁₆	—	3	1	no	—
219	C₂³×C₈	—	3	1	no	—
220	#408	—	3	8	no	—
221	C₂×C₂²⋊C₈	—	3	1	no	—
222	C₂×C₂²⋊C₈	—	3	1	no	—
223	C₂×C₂²⋊C₈	—	3	1	no	—
224	C₂×C₂²⋊C₈	C₅×D₃	1	1	yes	characteristic, complemented
225	C₂²×C₃×C₅	—	2	2	no	—
226	C₂²×C₃×C₅	—	2	2	no	—
227	C₂²×C₃×C₅	—	2	2	no	—
228	C₂²×C₃×C₅	—	4	4	no	—
229	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	2	yes	—
230	C₂²×C₃×C₅	#131	1	2	yes	—
231	C₂²×C₃×C₅	#131	1	2	yes	—
232	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
233	C₂×C₅×D₃	—	2	2	no	—
234	C₂×C₅×D₃	—	2	2	no	—
235	C₂×C₅×D₃	—	2	8	no	—
236	C₂×C₅×D₃	—	2	2	no	—
237	C₂×C₅×D₃	—	2	2	no	—
238	C₂×C₅×D₃	—	2	2	no	—
239	C₂×C₅×D₃	—	4	4	no	—
240	C₂×C₅×D₃	C₂×C₂²⋊C₄	1	4	yes	—
241	C₃×C₄×C₅	—	2	2	no	—
242	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
243	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
244	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
245	C₅×Dic₃	—	2	2	no	—
246	C₅×Dic₃	C₂×C₂²⋊C₄	1	4	yes	—
247	C₂⁴×C₃	C₂×C₄×C₅	1	1	yes	characteristic
248	C₂³×D₃	C₂×C₄×C₅	1	1	yes	characteristic
249	C₂³×D₃	C₂×C₄×C₅	1	1	yes	characteristic
250	C₂²×C₃×C₄	—	2	2	no	—
251	C₂²×C₃×C₄	—	2	2	no	—
252	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
253	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
254	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
255	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
256	C₂×#67	—	2	4	no	—
257	C₂×#67	—	2	4	no	—
258	C₂×#67	C₂×C₄×C₅	1	4	yes	—
259	C₂×#67	C₂×C₄×C₅	1	4	yes	—
260	C₂²×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
261	C₂²×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
262	#235	—	2	16	no	—
263	#235	—	2	8	no	—
264	#235	—	2	8	no	—
265	C₂×D₁₂	—	2	4	no	—
266	C₂×D₁₂	C₂×C₄×C₅	1	4	yes	—
267	C₂×C₄×D₃	—	2	2	no	—
268	C₂×C₄×D₃	—	2	2	no	—
269	C₂×C₄×D₃	C₂×C₄×C₅	1	2	yes	—
270	C₂×C₄×D₃	C₂×C₄×C₅	1	2	yes	—
271	C₂×C₄×D₃	C₅×D₄	1	4	yes	—
272	C₂×C₄×D₃	C₅×D₄	1	4	yes	—
273	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
274	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
275	C₂×Dic₆	—	2	4	no	—
276	C₂×Dic₆	C₂×C₄×C₅	1	4	yes	—
277	C₂×C₃×C₈	—	2	2	no	—
278	C₂×C₃×C₈	—	2	2	no	—
279	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
280	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
281	C₂×C₃⋊C₈	—	2	2	no	—
282	C₂×C₃⋊C₈	—	2	2	no	—
283	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
284	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
285	ΓL(1,𝔽₂₅)	—	2	8	no	—
286	D₃×C₈	—	2	8	no	—
287	C₂³×C₅	—	2	2	no	—
288	C₂³×C₅	—	2	2	no	—
289	C₂³×C₅	—	2	2	no	—
290	C₂³×C₅	—	3	4	no	—
291	C₂³×C₅	—	3	2	no	—
292	C₂³×C₅	—	3	2	no	—
293	C₂³×C₅	—	6	2	no	—
294	C₂³×C₅	—	6	2	no	—
295	C₂³×C₅	—	6	2	no	—
296	C₂³×C₅	—	6	2	no	—
297	C₂³×C₅	—	6	2	no	—
298	C₂³×C₅	C₂×C₄×D₃	1	2	yes	—
299	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
300	C₅×Q₈	—	6	8	no	—
301	C₅×D₄	—	6	8	no	—
302	C₅×D₄	—	6	8	no	—
303	C₅×D₄	—	6	8	no	—
304	C₂×C₄×C₅	—	2	2	no	—
305	C₂×C₄×C₅	—	2	4	no	—
306	C₂×C₄×C₅	—	2	2	no	—
307	C₂×C₄×C₅	—	2	2	no	—
308	C₂×C₄×C₅	—	3	4	no	—
309	C₂×C₄×C₅	—	3	2	no	—
310	C₂×C₄×C₅	—	3	8	no	—
311	C₂×C₄×C₅	—	3	4	no	—
312	C₂×C₄×C₅	—	3	4	no	—
313	C₂×C₄×C₅	—	3	2	no	—
314	C₂×C₄×C₅	—	6	2	no	—
315	C₂×C₄×C₅	—	6	4	no	—
316	C₂×C₄×C₅	—	6	2	no	—
317	C₂×C₄×C₅	—	6	2	no	—
318	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
319	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
320	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
321	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
322	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
323	C₅×C₈	—	2	2	no	—
324	C₅×C₈	—	2	2	no	—
325	C₅×C₈	—	6	2	no	—
326	C₅×C₈	—	6	2	no	—
327	C₂×#41	—	3	4	no	—
328	C₂×#41	—	3	4	no	—
329	C₂×#41	—	6	4	no	—
330	C₂×#41	—	6	4	no	—
331	C₂²×Q₈	—	3	1	no	—
332	C₂²×D₄	—	3	1	no	—
333	C₂²×D₄	—	3	1	no	—
334	C₂²×D₄	—	3	1	no	—
335	C₂³×C₄	—	3	1	no	—
336	C₂³×C₄	—	3	1	no	—
337	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
338	C₂×M₁₆	—	3	4	no	—
339	C₂×M₁₆	—	6	4	no	—
340	C₂²×C₈	—	3	1	no	—
341	C₂²×C₈	—	3	1	no	—
342	C₂²×C₈	—	3	4	no	—
343	C₂²×C₈	—	6	4	no	—
344	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
345	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
346	C₂²⋊C₈	—	3	4	no	—
347	C₂²⋊C₈	—	3	4	no	—
348	C₂²⋊C₈	—	3	4	no	—
349	C₂²⋊C₈	C₂×C₅×D₃	1	4	yes	complemented
350	C₂×C₃×C₅	—	4	2	no	—
351	C₂×C₃×C₅	#408	1	4	yes	complemented
352	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
353	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
354	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
355	C₅×D₃	—	2	4	no	—
356	C₅×D₃	—	4	2	no	—
357	C₂³×C₃	—	2	2	no	—
358	C₂³×C₃	—	2	2	no	—
359	C₂³×C₃	—	2	2	no	—
360	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
361	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
362	C₂²×D₃	—	2	2	no	—
363	C₂²×D₃	—	2	2	no	—
364	C₂²×D₃	—	2	2	no	—
365	C₂²×D₃	—	2	2	no	—
366	C₂²×D₃	—	2	2	no	—
367	C₂²×D₃	C₅×C₂²⋊C₄	1	4	yes	—
368	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
369	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
370	C₂×C₃×C₄	—	2	2	no	—
371	C₂×C₃×C₄	—	2	4	no	—
372	C₂×C₃×C₄	—	2	2	no	—
373	C₂×C₃×C₄	—	2	2	no	—
374	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
375	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
376	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
377	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
378	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
379	#67	—	2	8	no	—
380	#67	—	2	8	no	—
381	C₂×Dic₃	—	2	2	no	—
382	C₂×Dic₃	C₅×C₂²⋊C₄	1	4	yes	—
383	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
384	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
385	D₁₂	—	2	8	no	—
386	C₄×D₃	—	2	4	no	—
387	C₄×D₃	—	2	2	no	—
388	C₄×D₃	—	2	2	no	—
389	C₄×D₃	C₅×C₂²⋊C₄	1	8	yes	—
390	C₄×D₃	C₂×C₅×D₄	1	4	yes	—
391	C₄×D₃	C₂×C₅×D₄	1	4	yes	—
392	Dic₆	—	2	8	no	—
393	C₃×C₈	—	2	2	no	—
394	C₃×C₈	—	2	2	no	—
395	C₃⋊C₈	—	2	2	no	—
396	C₃⋊C₈	—	2	2	no	—
397	C₂²×C₅	—	2	2	no	—
398	C₂²×C₅	—	2	2	no	—
399	C₂²×C₅	—	2	2	no	—
400	C₂²×C₅	—	3	4	no	—
401	C₂²×C₅	—	4	4	no	—
402	C₂²×C₅	—	6	2	no	—
403	C₂²×C₅	—	6	2	no	—
404	C₂²×C₅	—	6	8	no	—
405	C₂²×C₅	—	6	2	no	—
406	C₂²×C₅	—	6	2	no	—
407	C₂²×C₅	—	6	2	no	—
408	C₂²×C₅	—	12	4	no	—
409	C₂²×C₅	D₃×C₂²⋊C₄	1	2	yes	—
410	C₂²×C₅	#901	1	2	yes	—
411	C₂²×C₅	#907	1	2	yes	—
412	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
413	C₄×C₅	—	2	2	no	—
414	C₄×C₅	—	3	4	no	—
415	C₄×C₅	—	6	2	no	—
416	C₄×C₅	D₃×C₂²⋊C₄	1	2	yes	—
417	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
418	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
419	C₂⁴	—	3	1	no	—
420	C₂⁴	—	3	1	no	—
421	C₂⁴	C₄×C₅×D₃	1	1	yes	characteristic
422	#41	—	6	16	no	—
423	#41	—	6	8	no	—
424	#41	—	6	8	no	—
425	C₂×Q₈	—	3	4	no	—
426	C₂×Q₈	—	6	4	no	—
427	C₂×D₄	—	3	4	no	—
428	C₂×D₄	—	3	4	no	—
429	C₂×D₄	—	3	4	no	—
430	C₂×D₄	—	6	4	no	—
431	C₂×D₄	—	6	4	no	—
432	C₂×D₄	—	6	4	no	—
433	C₂²×C₄	—	2	2	no	—
434	C₂²×C₄	—	2	2	no	—
435	C₂²×C₄	—	3	1	no	—
436	C₂²×C₄	—	3	2	no	—
437	C₂²×C₄	—	3	4	no	—
438	C₂²×C₄	—	3	4	no	—
439	C₂²×C₄	—	3	2	no	—
440	C₂²×C₄	—	3	1	no	—
441	C₂²×C₄	—	3	2	no	—
442	C₂²×C₄	—	3	2	no	—
443	C₂²×C₄	—	6	2	no	—
444	C₂²×C₄	—	6	2	no	—
445	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
446	C₂²×C₄	C₄×C₅×D₃	1	2	yes	—
447	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
448	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
449	M₁₆	—	6	8	no	—
450	C₂×C₈	—	2	2	no	—
451	C₂×C₈	—	2	2	no	—
452	C₂×C₈	—	3	2	no	—
453	C₂×C₈	—	3	2	no	—
454	C₂×C₈	—	6	8	no	—
455	C₂×C₈	—	6	2	no	—
456	C₂×C₈	—	6	2	no	—
457	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
458	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
459	C₃×C₅	C₂×#408	1	1	yes	characteristic, complemented, Hall
460	C₂²×C₃	—	2	2	no	—
461	C₂²×C₃	—	2	2	no	—
462	C₂²×C₃	—	2	2	no	—
463	C₂²×C₃	—	4	4	no	—
464	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	2	yes	—
465	C₂²×C₃	C₅×#131	1	2	yes	—
466	C₂²×C₃	C₅×#131	1	2	yes	—
467	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
468	C₂×D₃	—	2	8	no	—
469	C₂×D₃	—	2	2	no	—
470	C₂×D₃	—	2	2	no	—
471	C₂×D₃	—	2	2	no	—
472	C₂×D₃	—	2	2	no	—
473	C₂×D₃	—	2	2	no	—
474	C₂×D₃	—	4	4	no	—
475	C₂×D₃	C₂×C₅×C₂²⋊C₄	1	4	yes	—
476	C₃×C₄	—	2	2	no	—
477	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
478	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
479	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
480	Dic₃	—	2	2	no	—
481	Dic₃	C₂×C₅×C₂²⋊C₄	1	4	yes	—
482	C₂×C₅	—	4	2	no	—
483	C₂×C₅	—	6	4	no	—
484	C₂×C₅	—	12	2	no	—
485	C₂×C₅	#4727	1	4	yes	direct product factor
486	C₂×C₅	C₂×D₃×C₂²⋊C₄	1	1	yes	characteristic
487	C₂×C₅	C₂×#901	1	1	yes	characteristic
488	C₂×C₅	C₂×#907	1	1	yes	characteristic
489	C₂³	—	2	2	no	—
490	C₂³	—	2	2	no	—
491	C₂³	—	2	2	no	—
492	C₂³	—	3	4	no	—
493	C₂³	—	3	2	no	—
494	C₂³	—	3	2	no	—
495	C₂³	—	6	2	no	—
496	C₂³	—	6	2	no	—
497	C₂³	—	6	2	no	—
498	C₂³	—	6	2	no	—
499	C₂³	—	6	2	no	—
500	C₂³	C₂×C₄×C₅×D₃	1	2	yes	—
501	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
502	Q₈	—	6	8	no	—
503	D₄	—	6	8	no	—
504	D₄	—	6	8	no	—
505	D₄	—	6	8	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	4	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	3	4	no	—
511	C₂×C₄	—	3	2	no	—
512	C₂×C₄	—	3	8	no	—
513	C₂×C₄	—	3	4	no	—
514	C₂×C₄	—	3	4	no	—
515	C₂×C₄	—	3	2	no	—
516	C₂×C₄	—	6	2	no	—
517	C₂×C₄	—	6	4	no	—
518	C₂×C₄	—	6	2	no	—
519	C₂×C₄	—	6	2	no	—
520	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
521	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
522	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
523	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
524	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
525	C₈	—	2	2	no	—
526	C₈	—	2	2	no	—
527	C₈	—	6	2	no	—
528	C₈	—	6	2	no	—
529	C₂×C₃	—	4	2	no	—
530	C₂×C₃	C₅×#408	1	4	yes	complemented
531	C₂×C₃	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
532	C₂×C₃	C₂×C₅×#131	1	1	yes	characteristic
533	C₂×C₃	C₂×C₅×#131	1	1	yes	characteristic
534	D₃	—	2	4	no	—
535	D₃	—	4	2	no	—
536	C₅	C₂×#4727	1	1	yes	characteristic, direct product factor, Sylow
537	C₂²	—	2	2	no	—
538	C₂²	—	2	2	no	—
539	C₂²	—	2	2	no	—
540	C₂²	—	3	4	no	—
541	C₂²	—	4	4	no	—
542	C₂²	—	6	8	no	—
543	C₂²	—	6	2	no	—
544	C₂²	—	6	2	no	—
545	C₂²	—	6	2	no	—
546	C₂²	—	6	2	no	—
547	C₂²	—	6	2	no	—
548	C₂²	—	12	4	no	—
549	C₂²	C₅×D₃×C₂²⋊C₄	1	2	yes	—
550	C₂²	C₅×#901	1	2	yes	—
551	C₂²	C₅×#907	1	2	yes	—
552	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
553	C₄	—	2	2	no	—
554	C₄	—	3	4	no	—
555	C₄	—	6	2	no	—
556	C₄	C₅×D₃×C₂²⋊C₄	1	2	yes	—
557	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
558	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
559	C₃	C₂×C₅×#408	1	1	yes	characteristic, complemented, Sylow
560	C₂	—	4	2	no	—
561	C₂	—	6	4	no	—
562	C₂	—	12	2	no	—
563	C₂	C₅×#4727	1	4	yes	direct product factor
564	C₂	C₂×C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
565	C₂	C₂×C₅×#901	1	1	yes	characteristic
566	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×C₂²⋊C₈	C₂
socle	C₂³×C₃×C₅	C₂²×C₄
prime radical	C₂²×C₅×#235	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₂×C₅×C₂²⋊C₈	D₃
hypocenter	C₃	C₂×C₅×#408
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×C₂²⋊C₈

Complements

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

N	H ≅ G/N	type
2. C₂²×C₅×ΓL(1,𝔽₂₅)	C₂	semidirect
3. C₂²×C₅×D₃×C₈	C₂	semidirect
4. C₂×C₃×C₅×C₂²⋊C₈	C₂	semidirect
5. C₂×C₅×#830	C₂	semidirect
6. C₂×C₅×(C₂×D₃)⋊C₈	C₂	semidirect
7. C₂×C₅×(C₂×D₃)⋊C₈	C₂	semidirect
8. C₅×#4727	C₂	direct (N × H)
26. C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	semidirect
28. C₂×C₅×D₃×C₈	C₂²	semidirect
29. C₃×C₅×C₂²⋊C₈	C₂²	semidirect
30. C₅×#830	C₂²	semidirect
31. C₅×(C₂×D₃)⋊C₈	C₂²	semidirect
32. C₅×(C₂×D₃)⋊C₈	C₂²	semidirect
33. C₂×#4727	C₅	direct (N × H)
41. C₂×C₅×C₂²⋊C₈	D₃	semidirect
83. C₂²×ΓL(1,𝔽₂₅)	C₂×C₅	semidirect
84. C₂²×D₃×C₈	C₂×C₅	semidirect
85. C₂×C₃×C₂²⋊C₈	C₂×C₅	semidirect
86. C₂×#830	C₂×C₅	semidirect
87. C₂×(C₂×D₃)⋊C₈	C₂×C₅	semidirect
88. C₂×(C₂×D₃)⋊C₈	C₂×C₅	semidirect
89. #4727	C₂×C₅	direct (N × H)
112. C₅×C₂²⋊C₈	C₂×D₃	semidirect
170. C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	semidirect
172. C₂×D₃×C₈	C₂²×C₅	semidirect
173. C₃×C₂²⋊C₈	C₂²×C₅	semidirect
174. #830	C₂²×C₅	semidirect
175. (C₂×D₃)⋊C₈	C₂²×C₅	semidirect
176. (C₂×D₃)⋊C₈	C₂²×C₅	semidirect
224. C₂×C₂²⋊C₈	C₅×D₃	semidirect
349. C₂²⋊C₈	C₂×C₅×D₃	semidirect
351. C₂×C₃×C₅	#408	semidirect
459. C₃×C₅	C₂×#408	semidirect
485. C₂×C₅	#4727	direct (N × H)
530. C₂×C₃	C₅×#408	semidirect
536. C₅	C₂×#4727	direct (N × H)
559. C₃	C₂×C₅×#408	semidirect
563. C₂	C₅×#4727	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×#235	2
C₂²×C₅×ΓL(1,𝔽₂₅)	2
C₂²×C₅×D₃×C₈	2
C₂×C₃×C₅×C₂²⋊C₈	2
C₂×C₅×#830	2
C₂×C₅×(C₂×D₃)⋊C₈	2
C₅×#4727	2
C₂×C₅×#408	3
C₂×#4727	5

Subgroups — C2×C5×#4727 #14411677

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#4727 #14411677