Subgroups — C₄×C₅×#918 #14416829

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#918	C₂	1	1	yes	maximal, characteristic
2	C₄×C₅×#239	C₂	1	1	yes	maximal, characteristic
3	C₄×C₅×D₃×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₄×C₅×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5184	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄×C₅×#216	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×C₅×#215	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4889	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#4881	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4817	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4803	C₂	1	1	yes	maximal, characteristic
12	C₅×#4802	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#4789	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₅×#204	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₅×ΓL(1,𝔽₂₅)	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₅×#137	—	3	1	no	maximal, Hall
17	C₂×C₅×#239	C₂²	1	1	yes	characteristic
18	C₂×C₅×D₃×Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
20	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
21	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
22	C₅×Q₈×Dic₃	C₂²	1	1	yes	characteristic
23	C₅×Q₈×Dic₃	C₂²	1	1	yes	characteristic
24	C₂×C₅×#216	C₂²	1	1	yes	characteristic
25	C₂×C₅×#215	C₂²	1	1	yes	characteristic
26	C₅×#918	C₄	1	8	yes	direct product factor
27	C₂×C₅×#204	C₂²	1	1	yes	characteristic
28	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
29	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
30	C₅×#893	—	2	1	no	—
31	C₅×#893	C₂²	1	1	yes	characteristic
32	C₅×#892	—	2	1	no	—
33	C₅×#892	C₂²	1	1	yes	characteristic
34	C₅×D₃×C₄⋊C₄	—	2	1	no	—
35	C₅×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₅×#887	—	2	1	no	—
37	C₅×#887	C₂²	1	1	yes	characteristic
38	C₄×C₅×D₁₂	—	2	1	no	—
39	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
40	C₄²×C₅×D₃	—	2	1	no	—
41	C₄²×C₅×D₃	—	2	1	no	—
42	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
43	C₄×C₅×Dic₆	—	2	1	no	—
44	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
45	C₃×C₅×#107	C₂²	1	1	yes	characteristic
46	C₃×C₅×#103	C₂²	1	1	yes	characteristic
47	C₃×C₅×#103	C₂²	1	1	yes	characteristic
48	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
49	C₅×#835	C₂²	1	1	yes	characteristic
50	C₅×#835	C₂²	1	1	yes	characteristic
51	C₅×#821	C₂²	1	1	yes	characteristic
52	C₅×#817	C₂²	1	1	yes	characteristic
53	C₅×#816	C₂²	1	1	yes	characteristic
54	C₅×#815	C₂²	1	1	yes	characteristic
55	C₅×#815	C₂²	1	1	yes	characteristic
56	C₅×#810	C₂²	1	1	yes	characteristic
57	C₅×#809	C₂²	1	1	yes	characteristic
58	C₅×#808	C₂²	1	1	yes	characteristic
59	C₅×#807	C₂²	1	1	yes	characteristic
60	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
61	C₄×#918	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
62	C₂×C₅×#137	—	3	1	no	—
63	C₄×C₅×#41	—	3	1	no	—
64	C₂×C₄×C₅×Q₈	—	3	1	no	—
65	C₅×#441	—	3	1	no	—
66	C₅×#441	—	3	1	no	—
67	C₅×#440	—	3	1	no	—
68	C₅×#440	—	3	1	no	—
69	C₄×C₅×Q₁₆	—	3	1	no	—
70	C₄×C₅×Q₁₆	D₃	1	1	yes	characteristic, complemented
71	C₄×C₅×SD₁₆	—	3	1	no	—
72	C₄×C₅×SD₁₆	—	3	1	no	—
73	C₅×#428	—	3	1	no	—
74	C₅×#419	—	3	1	no	—
75	C₅×#417	—	3	1	no	—
76	C₄×C₅×M₁₆	—	3	1	no	—
77	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
78	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
79	C₅×#239	—	2	2	no	—
80	C₅×#239	C₂×C₄	1	4	yes	—
81	C₅×D₃×Q₈	—	2	2	no	—
82	C₅×D₃×Q₈	C₂×C₄	1	4	yes	complemented
83	C₂×C₅×D₁₂	—	2	1	no	—
84	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
85	C₂×C₄×C₅×D₃	—	2	1	no	—
86	C₂×C₄×C₅×D₃	—	2	1	no	—
87	C₂×C₄×C₅×D₃	—	2	1	no	—
88	C₂×C₄×C₅×D₃	—	2	1	no	—
89	C₂×C₄×C₅×D₃	—	2	1	no	—
90	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
91	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
92	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
93	C₂×C₅×Dic₆	—	2	1	no	—
94	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
95	C₃×C₅×Q₁₆	C₂×C₄	1	4	yes	complemented
96	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
97	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
98	C₃×C₅×C₄⋊C₄	—	2	1	no	—
99	C₃×C₅×C₄⋊C₄	—	2	1	no	—
100	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
101	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
102	C₃×C₄²×C₅	—	2	1	no	—
103	C₃×C₄²×C₅	—	2	1	no	—
104	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
105	C₅×#216	C₂×C₄	1	4	yes	complemented
106	C₅×#215	C₂×C₄	1	4	yes	complemented
107	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
108	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
109	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
110	C₅×C₄⋊Dic₃	—	2	1	no	—
111	C₅×C₄⋊Dic₃	—	2	1	no	—
112	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
113	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
114	C₅×Dic₃⋊C₄	—	2	1	no	—
115	C₅×Dic₃⋊C₄	—	2	1	no	—
116	C₅×Dic₃⋊C₄	—	2	1	no	—
117	C₄×C₅×Dic₃	—	2	1	no	—
118	C₄×C₅×Dic₃	—	2	1	no	—
119	C₄×C₅×Dic₃	—	2	1	no	—
120	C₄×C₅×Dic₃	—	2	1	no	—
121	C₄×C₅×Dic₃	—	2	1	no	—
122	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
123	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
124	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
125	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
126	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
127	C₅×#204	C₂×C₄	1	4	yes	complemented
128	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
129	C₅×ΓL(1,𝔽₂₅)	C₂×C₄	1	4	yes	complemented
130	C₂×#918	C₂×C₅	1	1	yes	characteristic
131	C₄×#239	C₂×C₅	1	1	yes	characteristic
132	C₄×D₃×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
133	C₃×C₄×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
134	#5184	C₂×C₅	1	1	yes	characteristic, complemented
135	C₄×#216	C₂×C₅	1	1	yes	characteristic, complemented
136	C₄×#215	C₂×C₅	1	1	yes	characteristic, complemented
137	#4889	C₂×C₅	1	1	yes	characteristic, complemented
138	#4881	C₂×C₅	1	1	yes	characteristic, complemented
139	#4817	C₂×C₅	1	1	yes	characteristic, complemented
140	#4803	C₂×C₅	1	1	yes	characteristic
141	#4802	C₂×C₅	1	1	yes	characteristic, complemented
142	#4789	C₂×C₅	1	1	yes	characteristic, complemented
143	C₄×#204	C₂×C₅	1	1	yes	characteristic, complemented
144	C₄×ΓL(1,𝔽₂₅)	C₂×C₅	1	1	yes	characteristic, complemented
145	C₂×C₅×#41	—	3	1	no	—
146	C₂²×C₅×Q₈	—	3	1	no	—
147	C₅×#137	—	3	8	no	—
148	C₂×C₅×Q₁₆	—	3	1	no	—
149	C₂×C₅×Q₁₆	C₂×D₃	1	1	yes	characteristic
150	C₂×C₅×SD₁₆	—	3	1	no	—
151	C₂×C₅×SD₁₆	—	3	1	no	—
152	C₂×C₅×M₁₆	—	3	1	no	—
153	C₂×C₅×M₁₆	—	3	1	no	—
154	C₄×C₅×Q₈	—	3	1	no	—
155	C₄×C₅×Q₈	—	3	1	no	—
156	C₄×C₅×Q₈	—	3	1	no	—
157	C₄×C₅×Q₈	—	3	1	no	—
158	C₄×C₅×Q₈	—	6	1	no	—
159	C₄×C₅×Q₈	—	6	1	no	—
160	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
161	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
162	C₄×C₅×D₄	—	3	1	no	—
163	C₄×C₅×D₄	—	3	1	no	—
164	C₄×C₅×D₄	—	6	1	no	—
165	C₄×C₅×D₄	—	6	1	no	—
166	C₅×#117	—	3	1	no	—
167	C₅×#117	—	6	1	no	—
168	C₂×C₅×C₄⋊C₄	—	3	1	no	—
169	C₂×C₅×C₄⋊C₄	—	6	1	no	—
170	C₂×C₄²×C₅	—	3	1	no	—
171	C₂×C₄²×C₅	—	6	1	no	—
172	C₂×C₄²×C₅	—	6	1	no	—
173	C₅×#107	—	3	1	no	—
174	C₅×#107	C₂×D₃	1	1	yes	characteristic
175	C₅×#106	—	3	1	no	—
176	C₅×#106	—	3	1	no	—
177	C₅×#103	—	3	1	no	—
178	C₅×#103	—	3	1	no	—
179	C₅×#103	—	3	1	no	—
180	C₅×#103	—	3	1	no	—
181	C₅×#103	C₂×D₃	1	1	yes	characteristic
182	C₅×#103	C₂×D₃	1	1	yes	characteristic
183	C₅×#102	—	3	1	no	—
184	C₅×#102	—	3	1	no	—
185	C₅×#97	—	3	1	no	—
186	C₅×#97	—	3	1	no	—
187	C₄×C₅×C₈	—	3	1	no	—
188	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
189	C₄×#137	—	3	1	no	Sylow
190	C₂²×C₅×D₃	—	2	1	no	—
191	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
192	C₃×C₅×Q₈	—	2	1	no	—
193	C₃×C₅×Q₈	—	2	1	no	—
194	C₃×C₅×Q₈	C₂²×C₄	1	2	yes	—
195	C₃×C₅×Q₈	C₂²×C₄	1	2	yes	—
196	C₂×C₃×C₄×C₅	—	2	1	no	—
197	C₂×C₃×C₄×C₅	—	2	1	no	—
198	C₂×C₃×C₄×C₅	—	2	1	no	—
199	C₂×C₃×C₄×C₅	—	2	1	no	—
200	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
201	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
202	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
203	C₂×C₅×Dic₃	—	2	1	no	—
204	C₂×C₅×Dic₃	—	2	1	no	—
205	C₂×C₅×Dic₃	—	2	1	no	—
206	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
207	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
208	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
209	C₅×D₁₂	—	2	4	no	—
210	C₅×D₁₂	—	2	1	no	—
211	C₅×D₁₂	C₂²×C₄	1	2	yes	—
212	C₄×C₅×D₃	—	2	4	no	—
213	C₄×C₅×D₃	—	2	2	no	—
214	C₄×C₅×D₃	—	2	4	no	—
215	C₄×C₅×D₃	—	4	1	no	—
216	C₄×C₅×D₃	—	4	2	no	—
217	C₄×C₅×D₃	—	4	2	no	—
218	C₄×C₅×D₃	—	4	2	no	—
219	C₄×C₅×D₃	C₂²×C₄	1	2	yes	—
220	C₄×C₅×D₃	#41	1	2	yes	—
221	C₅×Dic₆	—	2	1	no	—
222	C₅×Dic₆	—	2	4	no	—
223	C₅×Dic₆	C₂²×C₄	1	2	yes	—
224	C₃×C₅×C₈	—	2	1	no	—
225	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
226	C₅×C₃⋊C₈	—	2	1	no	—
227	C₅×C₃⋊C₈	C₂²×C₄	1	2	yes	—
228	C₂×#239	C₂²×C₅	1	1	yes	characteristic
229	C₂×D₃×Q₈	C₂²×C₅	1	1	yes	characteristic
230	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic
231	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
232	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
233	Q₈×Dic₃	C₂²×C₅	1	1	yes	characteristic
234	Q₈×Dic₃	C₂²×C₅	1	1	yes	characteristic
235	C₂×#216	C₂²×C₅	1	1	yes	characteristic
236	C₂×#215	C₂²×C₅	1	1	yes	characteristic
237	#918	C₄×C₅	1	8	yes	direct product factor
238	C₂×#204	C₂²×C₅	1	1	yes	characteristic
239	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	1	yes	characteristic
240	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	1	yes	characteristic
241	#893	—	2	1	no	—
242	#893	C₂²×C₅	1	1	yes	characteristic
243	#892	—	2	1	no	—
244	#892	C₂²×C₅	1	1	yes	characteristic
245	D₃×C₄⋊C₄	—	2	1	no	—
246	D₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
247	#887	—	2	1	no	—
248	#887	C₂²×C₅	1	1	yes	characteristic
249	C₄×D₁₂	—	2	1	no	—
250	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
251	C₄²×D₃	—	2	1	no	—
252	C₄²×D₃	—	2	1	no	—
253	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
254	C₄×Dic₆	—	2	1	no	—
255	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic
256	C₃×#107	C₂²×C₅	1	1	yes	characteristic
257	C₃×#103	C₂²×C₅	1	1	yes	characteristic
258	C₃×#103	C₂²×C₅	1	1	yes	characteristic
259	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
260	#835	C₂²×C₅	1	1	yes	characteristic
261	#835	C₂²×C₅	1	1	yes	characteristic
262	#821	C₂²×C₅	1	1	yes	characteristic
263	#817	C₂²×C₅	1	1	yes	characteristic
264	#816	C₂²×C₅	1	1	yes	characteristic
265	#815	C₂²×C₅	1	1	yes	characteristic
266	#815	C₂²×C₅	1	1	yes	characteristic
267	#810	C₂²×C₅	1	1	yes	characteristic
268	#809	C₂²×C₅	1	1	yes	characteristic
269	#808	C₂²×C₅	1	1	yes	characteristic
270	#807	C₂²×C₅	1	1	yes	characteristic
271	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
272	C₅×#41	—	3	4	no	—
273	C₅×#41	—	6	2	no	—
274	C₂×C₅×Q₈	—	3	4	no	—
275	C₂×C₅×Q₈	—	3	1	no	—
276	C₂×C₅×Q₈	—	6	1	no	—
277	C₂×C₅×Q₈	—	6	2	no	—
278	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
279	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
280	C₂×C₅×D₄	—	3	1	no	—
281	C₂×C₅×D₄	—	6	1	no	—
282	C₂²×C₄×C₅	—	3	1	no	—
283	C₂²×C₄×C₅	—	3	1	no	—
284	C₂²×C₄×C₅	—	3	1	no	—
285	C₂²×C₄×C₅	—	6	1	no	—
286	C₂²×C₄×C₅	—	6	1	no	—
287	C₂²×C₄×C₅	—	6	1	no	—
288	C₂²×C₄×C₅	—	6	1	no	—
289	C₂²×C₄×C₅	—	6	1	no	—
290	C₅×Q₁₆	—	3	4	no	—
291	C₅×Q₁₆	C₄×D₃	1	4	yes	complemented
292	C₅×SD₁₆	—	3	4	no	—
293	C₅×SD₁₆	—	3	4	no	—
294	C₅×M₁₆	—	3	4	no	—
295	C₅×M₁₆	—	6	2	no	—
296	C₂×C₅×C₈	—	3	1	no	—
297	C₂×C₅×C₈	—	3	1	no	—
298	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
299	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
300	C₅×C₄⋊C₄	—	2	1	no	—
301	C₅×C₄⋊C₄	—	2	1	no	—
302	C₅×C₄⋊C₄	—	3	1	no	—
303	C₅×C₄⋊C₄	—	3	1	no	—
304	C₅×C₄⋊C₄	—	6	1	no	—
305	C₅×C₄⋊C₄	—	6	1	no	—
306	C₅×C₄⋊C₄	—	6	1	no	—
307	C₅×C₄⋊C₄	—	6	1	no	—
308	C₅×C₄⋊C₄	—	6	1	no	—
309	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
310	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
311	C₅×C₂²⋊C₄	—	6	1	no	—
312	C₅×C₂²⋊C₄	—	6	1	no	—
313	C₅×C₂²⋊C₄	—	6	1	no	—
314	C₄²×C₅	—	2	1	no	—
315	C₄²×C₅	—	2	1	no	—
316	C₄²×C₅	—	3	1	no	—
317	C₄²×C₅	—	3	1	no	—
318	C₄²×C₅	—	3	1	no	—
319	C₄²×C₅	—	6	1	no	—
320	C₄²×C₅	—	6	1	no	—
321	C₄²×C₅	—	6	1	no	—
322	C₄²×C₅	—	6	1	no	—
323	C₄²×C₅	—	6	1	no	—
324	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
325	C₂×#137	—	3	1	no	—
326	C₄×#41	—	3	1	no	—
327	C₂×C₄×Q₈	—	3	1	no	—
328	#441	—	3	1	no	—
329	#441	—	3	1	no	—
330	#440	—	3	1	no	—
331	#440	—	3	1	no	—
332	C₄×Q₁₆	—	3	1	no	—
333	C₄×Q₁₆	C₅×D₃	1	1	yes	characteristic, complemented
334	C₄×SD₁₆	—	3	1	no	—
335	C₄×SD₁₆	—	3	1	no	—
336	#428	—	3	1	no	—
337	#419	—	3	1	no	—
338	#417	—	3	1	no	—
339	C₄×M₁₆	—	3	1	no	—
340	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
341	C₂×C₅×D₃	—	2	1	no	—
342	C₂×C₅×D₃	—	2	1	no	—
343	C₂×C₅×D₃	—	2	2	no	—
344	C₂×C₅×D₃	—	4	1	no	—
345	C₂×C₅×D₃	—	4	1	no	—
346	C₂×C₅×D₃	C₄×D₄	1	2	yes	—
347	C₃×C₄×C₅	—	2	2	no	—
348	C₃×C₄×C₅	—	2	2	no	—
349	C₃×C₄×C₅	—	2	1	no	—
350	C₃×C₄×C₅	—	4	1	no	—
351	C₃×C₄×C₅	—	4	1	no	—
352	C₃×C₄×C₅	#137	1	2	yes	complemented
353	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
354	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
355	C₅×Dic₃	—	2	2	no	—
356	C₅×Dic₃	—	2	1	no	—
357	C₅×Dic₃	—	2	1	no	—
358	C₅×Dic₃	—	4	1	no	—
359	C₅×Dic₃	—	4	1	no	—
360	C₅×Dic₃	C₄×D₄	1	2	yes	—
361	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
362	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
363	#239	—	2	2	no	—
364	#239	C₂×C₄×C₅	1	4	yes	—
365	D₃×Q₈	—	2	2	no	—
366	D₃×Q₈	C₂×C₄×C₅	1	4	yes	complemented
367	C₂×D₁₂	—	2	1	no	—
368	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
369	C₂×C₄×D₃	—	2	1	no	—
370	C₂×C₄×D₃	—	2	1	no	—
371	C₂×C₄×D₃	—	2	1	no	—
372	C₂×C₄×D₃	—	2	1	no	—
373	C₂×C₄×D₃	—	2	1	no	—
374	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
375	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
376	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
377	C₂×Dic₆	—	2	1	no	—
378	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
379	C₃×Q₁₆	C₂×C₄×C₅	1	4	yes	complemented
380	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
381	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
382	C₃×C₄⋊C₄	—	2	1	no	—
383	C₃×C₄⋊C₄	—	2	1	no	—
384	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
385	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
386	C₃×C₄²	—	2	1	no	—
387	C₃×C₄²	—	2	1	no	—
388	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
389	#216	C₂×C₄×C₅	1	4	yes	complemented
390	#215	C₂×C₄×C₅	1	4	yes	complemented
391	(C₂×D₃)⋊C₄	—	2	1	no	—
392	(C₂×D₃)⋊C₄	—	2	1	no	—
393	(C₂×D₃)⋊C₄	—	2	1	no	—
394	C₄⋊Dic₃	—	2	1	no	—
395	C₄⋊Dic₃	—	2	1	no	—
396	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
397	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
398	Dic₃⋊C₄	—	2	1	no	—
399	Dic₃⋊C₄	—	2	1	no	—
400	Dic₃⋊C₄	—	2	1	no	—
401	C₄×Dic₃	—	2	1	no	—
402	C₄×Dic₃	—	2	1	no	—
403	C₄×Dic₃	—	2	1	no	—
404	C₄×Dic₃	—	2	1	no	—
405	C₄×Dic₃	—	2	1	no	—
406	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
407	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
408	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
409	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
410	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
411	#204	C₂×C₄×C₅	1	4	yes	complemented
412	ΓL(1,𝔽₂₅)	—	2	2	no	—
413	ΓL(1,𝔽₂₅)	C₂×C₄×C₅	1	4	yes	complemented
414	C₂³×C₅	—	3	1	no	—
415	C₂³×C₅	—	6	1	no	—
416	C₅×Q₈	—	2	1	no	—
417	C₅×Q₈	—	2	1	no	—
418	C₅×Q₈	—	3	2	no	—
419	C₅×Q₈	—	6	4	no	—
420	C₅×Q₈	—	6	1	no	—
421	C₅×Q₈	C₂×C₄×D₃	1	2	yes	—
422	C₅×Q₈	C₂×C₄×D₃	1	2	yes	—
423	C₅×D₄	—	3	2	no	—
424	C₅×D₄	—	6	4	no	—
425	C₅×D₄	—	6	1	no	—
426	C₂×C₄×C₅	—	2	1	no	—
427	C₂×C₄×C₅	—	2	1	no	—
428	C₂×C₄×C₅	—	2	1	no	—
429	C₂×C₄×C₅	—	2	1	no	—
430	C₂×C₄×C₅	—	3	1	no	—
431	C₂×C₄×C₅	—	3	2	no	—
432	C₂×C₄×C₅	—	3	2	no	—
433	C₂×C₄×C₅	—	3	1	no	—
434	C₂×C₄×C₅	—	3	1	no	—
435	C₂×C₄×C₅	—	6	4	no	—
436	C₂×C₄×C₅	—	6	4	no	—
437	C₂×C₄×C₅	—	6	1	no	—
438	C₂×C₄×C₅	—	6	2	no	—
439	C₂×C₄×C₅	—	6	1	no	—
440	C₂×C₄×C₅	—	6	1	no	—
441	C₂×C₄×C₅	—	12	1	no	—
442	C₂×C₄×C₅	—	12	2	no	—
443	C₂×C₄×C₅	—	12	2	no	—
444	C₂×C₄×C₅	—	12	2	no	—
445	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
446	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
447	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
448	C₅×C₈	—	2	1	no	—
449	C₅×C₈	—	3	2	no	—
450	C₅×C₈	—	6	1	no	—
451	C₅×C₈	C₂×C₄×D₃	1	2	yes	—
452	C₂×#41	—	3	1	no	—
453	C₂²×Q₈	—	3	1	no	—
454	#137	—	3	8	no	—
455	C₂×Q₁₆	—	3	1	no	—
456	C₂×Q₁₆	C₂×C₅×D₃	1	1	yes	characteristic
457	C₂×SD₁₆	—	3	1	no	—
458	C₂×SD₁₆	—	3	1	no	—
459	C₂×M₁₆	—	3	1	no	—
460	C₂×M₁₆	—	3	1	no	—
461	C₄×Q₈	—	3	1	no	—
462	C₄×Q₈	—	3	1	no	—
463	C₄×Q₈	—	3	1	no	—
464	C₄×Q₈	—	3	1	no	—
465	C₄×Q₈	—	6	1	no	—
466	C₄×Q₈	—	6	1	no	—
467	C₄×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
468	C₄×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
469	C₄×D₄	—	3	1	no	—
470	C₄×D₄	—	3	1	no	—
471	C₄×D₄	—	6	1	no	—
472	C₄×D₄	—	6	1	no	—
473	#117	—	3	1	no	—
474	#117	—	6	1	no	—
475	C₂×C₄⋊C₄	—	3	1	no	—
476	C₂×C₄⋊C₄	—	6	1	no	—
477	C₂×C₄²	—	3	1	no	—
478	C₂×C₄²	—	6	1	no	—
479	C₂×C₄²	—	6	1	no	—
480	#107	—	3	1	no	—
481	#107	C₂×C₅×D₃	1	1	yes	characteristic
482	#106	—	3	1	no	—
483	#106	—	3	1	no	—
484	#103	—	3	1	no	—
485	#103	—	3	1	no	—
486	#103	—	3	1	no	—
487	#103	—	3	1	no	—
488	#103	C₂×C₅×D₃	1	1	yes	characteristic
489	#103	C₂×C₅×D₃	1	1	yes	characteristic
490	#102	—	3	1	no	—
491	#102	—	3	1	no	—
492	#97	—	3	1	no	—
493	#97	—	3	1	no	—
494	C₄×C₈	—	3	1	no	—
495	C₄×C₈	C₂×C₅×D₃	1	1	yes	characteristic
496	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
497	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
498	C₂×C₃×C₅	#575	1	1	yes	characteristic
499	C₅×D₃	—	2	2	no	—
500	C₅×D₃	—	4	2	no	—
501	C₂²×D₃	—	2	1	no	—
502	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
503	C₃×Q₈	—	2	1	no	—
504	C₃×Q₈	—	2	1	no	—
505	C₃×Q₈	C₂²×C₄×C₅	1	2	yes	—
506	C₃×Q₈	C₂²×C₄×C₅	1	2	yes	—
507	C₂×C₃×C₄	—	2	1	no	—
508	C₂×C₃×C₄	—	2	1	no	—
509	C₂×C₃×C₄	—	2	1	no	—
510	C₂×C₃×C₄	—	2	1	no	—
511	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
512	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
513	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
514	C₂×Dic₃	—	2	1	no	—
515	C₂×Dic₃	—	2	1	no	—
516	C₂×Dic₃	—	2	1	no	—
517	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
518	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
519	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
520	D₁₂	—	2	4	no	—
521	D₁₂	—	2	1	no	—
522	D₁₂	C₂²×C₄×C₅	1	2	yes	—
523	C₄×D₃	—	2	4	no	—
524	C₄×D₃	—	2	2	no	—
525	C₄×D₃	—	2	4	no	—
526	C₄×D₃	—	4	1	no	—
527	C₄×D₃	—	4	2	no	—
528	C₄×D₃	—	4	2	no	—
529	C₄×D₃	—	4	2	no	—
530	C₄×D₃	C₂²×C₄×C₅	1	2	yes	—
531	C₄×D₃	C₅×#41	1	2	yes	—
532	Dic₆	—	2	1	no	—
533	Dic₆	—	2	4	no	—
534	Dic₆	C₂²×C₄×C₅	1	2	yes	—
535	C₃×C₈	—	2	1	no	—
536	C₃×C₈	C₂²×C₄×C₅	1	2	yes	—
537	C₃⋊C₈	—	2	1	no	—
538	C₃⋊C₈	C₂²×C₄×C₅	1	2	yes	—
539	C₂²×C₅	—	3	2	no	—
540	C₂²×C₅	—	6	1	no	—
541	C₂²×C₅	—	6	1	no	—
542	C₂²×C₅	—	6	2	no	—
543	C₂²×C₅	—	12	1	no	—
544	C₂²×C₅	—	12	1	no	—
545	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
546	C₄×C₅	—	2	1	no	—
547	C₄×C₅	—	2	2	no	—
548	C₄×C₅	—	2	2	no	—
549	C₄×C₅	—	3	2	no	—
550	C₄×C₅	—	4	1	no	—
551	C₄×C₅	—	4	1	no	—
552	C₄×C₅	—	6	1	no	—
553	C₄×C₅	—	6	1	no	—
554	C₄×C₅	—	6	2	no	—
555	C₄×C₅	—	12	1	no	—
556	C₄×C₅	—	12	1	no	—
557	C₄×C₅	#918	1	2	yes	direct product factor
558	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
559	C₄×C₅	D₃×#41	1	1	yes	characteristic
560	#41	—	3	4	no	—
561	#41	—	6	2	no	—
562	C₂×Q₈	—	3	4	no	—
563	C₂×Q₈	—	3	1	no	—
564	C₂×Q₈	—	6	1	no	—
565	C₂×Q₈	—	6	2	no	—
566	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
567	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
568	C₂×D₄	—	3	1	no	—
569	C₂×D₄	—	6	1	no	—
570	C₂²×C₄	—	3	1	no	—
571	C₂²×C₄	—	3	1	no	—
572	C₂²×C₄	—	3	1	no	—
573	C₂²×C₄	—	6	1	no	—
574	C₂²×C₄	—	6	1	no	—
575	C₂²×C₄	—	6	1	no	—
576	C₂²×C₄	—	6	1	no	—
577	C₂²×C₄	—	6	1	no	—
578	Q₁₆	—	3	4	no	—
579	Q₁₆	C₄×C₅×D₃	1	4	yes	complemented
580	SD₁₆	—	3	4	no	—
581	SD₁₆	—	3	4	no	—
582	M₁₆	—	3	4	no	—
583	M₁₆	—	6	2	no	—
584	C₂×C₈	—	3	1	no	—
585	C₂×C₈	—	3	1	no	—
586	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
587	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
588	C₄⋊C₄	—	2	1	no	—
589	C₄⋊C₄	—	2	1	no	—
590	C₄⋊C₄	—	3	1	no	—
591	C₄⋊C₄	—	3	1	no	—
592	C₄⋊C₄	—	6	1	no	—
593	C₄⋊C₄	—	6	1	no	—
594	C₄⋊C₄	—	6	1	no	—
595	C₄⋊C₄	—	6	1	no	—
596	C₄⋊C₄	—	6	1	no	—
597	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
598	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
599	C₂²⋊C₄	—	6	1	no	—
600	C₂²⋊C₄	—	6	1	no	—
601	C₂²⋊C₄	—	6	1	no	—
602	C₄²	—	2	1	no	—
603	C₄²	—	2	1	no	—
604	C₄²	—	3	1	no	—
605	C₄²	—	3	1	no	—
606	C₄²	—	3	1	no	—
607	C₄²	—	6	1	no	—
608	C₄²	—	6	1	no	—
609	C₄²	—	6	1	no	—
610	C₄²	—	6	1	no	—
611	C₄²	—	6	1	no	—
612	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
613	C₃×C₅	C₄×#137	1	1	yes	characteristic, complemented, Hall
614	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
615	C₂×D₃	—	2	1	no	—
616	C₂×D₃	—	2	1	no	—
617	C₂×D₃	—	2	2	no	—
618	C₂×D₃	—	4	1	no	—
619	C₂×D₃	—	4	1	no	—
620	C₂×D₃	C₄×C₅×D₄	1	2	yes	—
621	C₃×C₄	—	2	2	no	—
622	C₃×C₄	—	2	2	no	—
623	C₃×C₄	—	2	1	no	—
624	C₃×C₄	—	4	1	no	—
625	C₃×C₄	—	4	1	no	—
626	C₃×C₄	C₅×#137	1	2	yes	complemented
627	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
628	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
629	Dic₃	—	2	2	no	—
630	Dic₃	—	2	1	no	—
631	Dic₃	—	2	1	no	—
632	Dic₃	—	4	1	no	—
633	Dic₃	—	4	1	no	—
634	Dic₃	C₄×C₅×D₄	1	2	yes	—
635	C₂×C₅	—	6	2	no	—
636	C₂×C₅	—	12	2	no	—
637	C₂×C₅	C₄×D₃×D₄	1	1	yes	characteristic
638	C₂×C₅	C₂×#918	1	1	yes	characteristic
639	C₂×C₅	#5768	1	1	yes	characteristic
640	C₂³	—	3	1	no	—
641	C₂³	—	6	1	no	—
642	Q₈	—	2	1	no	—
643	Q₈	—	2	1	no	—
644	Q₈	—	3	2	no	—
645	Q₈	—	6	4	no	—
646	Q₈	—	6	1	no	—
647	Q₈	C₂×C₄×C₅×D₃	1	2	yes	—
648	Q₈	C₂×C₄×C₅×D₃	1	2	yes	—
649	D₄	—	3	2	no	—
650	D₄	—	6	4	no	—
651	D₄	—	6	1	no	—
652	C₂×C₄	—	2	1	no	—
653	C₂×C₄	—	2	1	no	—
654	C₂×C₄	—	2	1	no	—
655	C₂×C₄	—	2	1	no	—
656	C₂×C₄	—	3	1	no	—
657	C₂×C₄	—	3	2	no	—
658	C₂×C₄	—	3	2	no	—
659	C₂×C₄	—	3	1	no	—
660	C₂×C₄	—	3	1	no	—
661	C₂×C₄	—	6	4	no	—
662	C₂×C₄	—	6	4	no	—
663	C₂×C₄	—	6	1	no	—
664	C₂×C₄	—	6	2	no	—
665	C₂×C₄	—	6	1	no	—
666	C₂×C₄	—	6	1	no	—
667	C₂×C₄	—	12	1	no	—
668	C₂×C₄	—	12	2	no	—
669	C₂×C₄	—	12	2	no	—
670	C₂×C₄	—	12	2	no	—
671	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
672	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
673	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
674	C₈	—	2	1	no	—
675	C₈	—	3	2	no	—
676	C₈	—	6	1	no	—
677	C₈	C₂×C₄×C₅×D₃	1	2	yes	—
678	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
679	C₂×C₃	C₂×C₅×#137	1	1	yes	characteristic
680	C₂×C₃	C₅×#575	1	1	yes	characteristic
681	D₃	—	2	2	no	—
682	D₃	—	4	2	no	—
683	C₅	C₄×#918	1	1	yes	characteristic, direct product factor, Sylow
684	C₂²	—	3	2	no	—
685	C₂²	—	6	1	no	—
686	C₂²	—	6	1	no	—
687	C₂²	—	6	2	no	—
688	C₂²	—	12	1	no	—
689	C₂²	—	12	1	no	—
690	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
691	C₄	—	2	1	no	—
692	C₄	—	2	2	no	—
693	C₄	—	2	2	no	—
694	C₄	—	3	2	no	—
695	C₄	—	4	1	no	—
696	C₄	—	4	1	no	—
697	C₄	—	6	1	no	—
698	C₄	—	6	1	no	—
699	C₄	—	6	2	no	—
700	C₄	—	12	1	no	—
701	C₄	—	12	1	no	—
702	C₄	C₅×#918	1	2	yes	direct product factor
703	C₄	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
704	C₄	C₅×D₃×#41	1	1	yes	characteristic
705	C₃	C₄×C₅×#137	1	1	yes	characteristic, complemented, Sylow
706	C₂	—	6	2	no	—
707	C₂	—	12	2	no	—
708	C₂	C₄×C₅×D₃×D₄	1	1	yes	characteristic
709	C₂	C₂×C₅×#918	1	1	yes	characteristic
710	C₂	C₅×#5768	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	D₃×D₄
commutator	C₃×C₄	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₄×C₅×Q₁₆	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₅×#239	C₂²
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₄×C₅×Q₁₆	D₃
hypocenter	C₃	C₄×C₅×#137
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₄²×C₅ ◁ C₄×C₅×Q₁₆

Complements

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

N	H ≅ G/N	type
3. C₄×C₅×D₃×Q₈	C₂	semidirect
4. C₃×C₄×C₅×Q₁₆	C₂	semidirect
5. C₅×#5184	C₂	semidirect
6. C₄×C₅×#216	C₂	semidirect
7. C₄×C₅×#215	C₂	semidirect
8. C₅×#4889	C₂	semidirect
9. C₅×#4881	C₂	semidirect
10. C₅×#4817	C₂	semidirect
12. C₅×#4802	C₂	semidirect
13. C₅×#4789	C₂	semidirect
14. C₄×C₅×#204	C₂	semidirect
15. C₄×C₅×ΓL(1,𝔽₂₅)	C₂	semidirect
26. C₅×#918	C₄	direct (N × H)
61. C₄×#918	C₅	direct (N × H)
70. C₄×C₅×Q₁₆	D₃	semidirect
82. C₅×D₃×Q₈	C₂×C₄	semidirect
95. C₃×C₅×Q₁₆	C₂×C₄	semidirect
105. C₅×#216	C₂×C₄	semidirect
106. C₅×#215	C₂×C₄	semidirect
127. C₅×#204	C₂×C₄	semidirect
129. C₅×ΓL(1,𝔽₂₅)	C₂×C₄	semidirect
132. C₄×D₃×Q₈	C₂×C₅	semidirect
133. C₃×C₄×Q₁₆	C₂×C₅	semidirect
134. #5184	C₂×C₅	semidirect
135. C₄×#216	C₂×C₅	semidirect
136. C₄×#215	C₂×C₅	semidirect
137. #4889	C₂×C₅	semidirect
138. #4881	C₂×C₅	semidirect
139. #4817	C₂×C₅	semidirect
141. #4802	C₂×C₅	semidirect
142. #4789	C₂×C₅	semidirect
143. C₄×#204	C₂×C₅	semidirect
144. C₄×ΓL(1,𝔽₂₅)	C₂×C₅	semidirect
237. #918	C₄×C₅	direct (N × H)
291. C₅×Q₁₆	C₄×D₃	semidirect
333. C₄×Q₁₆	C₅×D₃	semidirect
352. C₃×C₄×C₅	#137	semidirect
366. D₃×Q₈	C₂×C₄×C₅	semidirect
379. C₃×Q₁₆	C₂×C₄×C₅	semidirect
389. #216	C₂×C₄×C₅	semidirect
390. #215	C₂×C₄×C₅	semidirect
411. #204	C₂×C₄×C₅	semidirect
413. ΓL(1,𝔽₂₅)	C₂×C₄×C₅	semidirect
557. C₄×C₅	#918	direct (N × H)
579. Q₁₆	C₄×C₅×D₃	semidirect
613. C₃×C₅	C₄×#137	semidirect
626. C₃×C₄	C₅×#137	semidirect
683. C₅	C₄×#918	direct (N × H)
702. C₄	C₅×#918	direct (N × H)
705. C₃	C₄×C₅×#137	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#918	2
C₄×C₅×#239	2
C₄×C₅×D₃×Q₈	2
C₃×C₄×C₅×Q₁₆	2
C₅×#5184	2
C₄×C₅×#216	2
C₄×C₅×#215	2
C₅×#4889	2
C₅×#4881	2
C₅×#4817	2
C₅×#4803	2
C₅×#4802	2
C₅×#4789	2
C₄×C₅×#204	2
C₄×C₅×ΓL(1,𝔽₂₅)	2
C₄×C₅×#137	3
C₄×#918	5

Subgroups — C4×C5×#918 #14416829

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₅×#918 #14416829