Subgroups — C₅×#68894 #14299940

Order 1920.

724 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#893	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#821	C₂	1	1	yes	maximal, characteristic
3	C₅×#4984	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#809	C₂	1	1	yes	maximal, characteristic
5	C₂×C₅×#807	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#340	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4550	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1862	—	3	1	no	maximal, Hall
9	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
10	C₂²×C₄×C₅×D₃	—	2	1	no	—
11	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
14	C₂×C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
15	C₂×C₅×C₄⋊Dic₃	—	2	1	no	—
16	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
18	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
19	C₅×#893	—	2	2	no	—
20	C₅×#893	—	2	2	no	—
21	C₅×C₃⋊#95	—	2	1	no	—
22	C₅×#821	—	2	2	no	—
23	C₅×#809	C₄	1	4	yes	complemented
24	C₅×#807	—	2	2	no	—
25	#68894	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
26	C₂×C₄×C₅×D₄	—	3	1	no	—
27	C₂×C₅×#107	—	3	1	no	—
28	C₂×C₅×#102	—	3	1	no	—
29	C₂×C₅×#102	—	3	1	no	—
30	C₅×#389	—	3	1	no	—
31	C₅×#340	D₃	1	1	yes	characteristic, complemented
32	C₅×#336	—	3	1	no	—
33	C₂³×C₅×D₃	—	2	1	no	—
34	C₂²×C₃×C₄×C₅	—	2	1	no	—
35	C₂²×C₃×C₄×C₅	—	2	1	no	—
36	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
37	C₂²×C₅×Dic₃	—	2	1	no	—
38	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
39	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
40	C₂×C₅×D₁₂	—	2	1	no	—
41	C₂×C₅×D₁₂	—	2	1	no	—
42	C₂×C₅×D₁₂	—	2	1	no	—
43	C₂×C₅×D₁₂	C₂×C₄	1	2	yes	—
44	C₂×C₅×D₁₂	D₄	1	2	yes	—
45	C₂×C₅×D₁₂	Q₈	1	2	yes	—
46	C₂×C₄×C₅×D₃	—	2	4	no	—
47	C₂×C₄×C₅×D₃	—	4	2	no	—
48	C₂×C₄×C₅×D₃	—	4	2	no	—
49	C₂×C₃×C₅×C₈	—	2	1	no	—
50	C₂×C₃×C₅×C₈	—	2	1	no	—
51	C₂×C₃×C₅×C₈	—	2	1	no	—
52	C₃×C₅×C₄⋊C₄	—	2	1	no	—
53	C₃×C₅×C₄⋊C₄	—	2	1	no	—
54	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	complemented
55	C₃×C₅×C₄⋊C₄	D₄	1	2	yes	—
56	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
57	C₅×C₄⋊Dic₃	—	2	1	no	—
58	C₅×C₄⋊Dic₃	—	2	1	no	—
59	C₅×C₄⋊Dic₃	—	4	2	no	—
60	C₄×C₅×Dic₃	—	2	1	no	—
61	C₄×C₅×Dic₃	—	2	1	no	—
62	C₂×C₅×C₃⋊C₈	—	2	1	no	—
63	C₂×C₅×C₃⋊C₈	—	2	1	no	—
64	C₂×C₅×C₃⋊C₈	C₂×C₄	1	2	yes	complemented
65	C₂×#893	C₂×C₅	1	1	yes	characteristic
66	C₂×#821	C₂×C₅	1	1	yes	characteristic
67	#4984	C₂×C₅	1	1	yes	characteristic, complemented
68	C₂×#809	C₂×C₅	1	1	yes	characteristic
69	C₂×#807	C₂×C₅	1	1	yes	characteristic, complemented
70	C₃×#340	C₂×C₅	1	1	yes	characteristic, complemented
71	#4550	C₂×C₅	1	1	yes	characteristic, complemented
72	C₂²×C₅×D₄	—	3	1	no	—
73	C₂³×C₄×C₅	—	6	1	no	—
74	C₂²×C₅×C₈	—	3	1	no	—
75	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
76	C₄×C₅×D₄	—	6	2	no	—
77	C₄×C₅×D₄	—	6	2	no	—
78	C₂×C₅×C₄⋊C₄	—	3	1	no	—
79	C₂×C₅×C₄⋊C₄	—	6	1	no	—
80	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
81	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
82	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
83	C₂×C₄²×C₅	—	3	1	no	—
84	C₅×#107	—	6	2	no	—
85	C₅×#102	—	3	4	no	—
86	C₅×#102	—	6	2	no	—
87	C₅×#95	—	6	1	no	—
88	#1862	—	3	1	no	Sylow
89	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₅×D₃	—	2	2	no	—
91	C₂²×C₅×D₃	—	2	2	no	—
92	C₂²×C₅×D₃	—	2	2	no	—
93	C₂²×C₅×D₃	—	4	1	no	—
94	C₂²×C₅×D₃	—	4	1	no	—
95	C₂²×C₅×D₃	—	4	1	no	—
96	C₂²×C₅×D₃	—	4	1	no	—
97	C₂×C₃×C₄×C₅	—	2	2	no	—
98	C₂×C₃×C₄×C₅	—	2	2	no	—
99	C₂×C₃×C₄×C₅	—	4	1	no	—
100	C₂×C₃×C₄×C₅	—	4	1	no	—
101	C₂×C₃×C₄×C₅	—	4	1	no	—
102	C₂×C₃×C₄×C₅	—	4	1	no	—
103	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
105	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
106	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
107	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
108	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
109	C₂×C₅×Dic₃	—	2	1	no	—
110	C₂×C₅×Dic₃	—	2	1	no	—
111	C₂×C₅×Dic₃	—	2	1	no	—
112	C₂×C₅×Dic₃	—	2	1	no	—
113	C₂×C₅×Dic₃	—	2	1	no	—
114	C₂×C₅×Dic₃	—	4	1	no	—
115	C₂×C₅×Dic₃	—	4	1	no	—
116	C₂×C₅×Dic₃	—	4	1	no	—
117	C₂×C₅×Dic₃	D₈	1	2	yes	—
118	C₅×D₁₂	—	2	2	no	—
119	C₅×D₁₂	—	2	2	no	—
120	C₅×D₁₂	—	2	2	no	—
121	C₅×D₁₂	C₄⋊C₄	1	4	yes	complemented
122	C₄×C₅×D₃	—	4	8	no	—
123	C₃×C₅×C₈	—	4	1	no	—
124	C₅×C₃⋊C₈	—	2	2	no	—
125	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
126	C₂²×C₄×D₃	—	2	1	no	—
127	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
128	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
129	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
130	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
131	C₂×C₄⋊Dic₃	—	2	1	no	—
132	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
133	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
134	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
135	#893	—	2	2	no	—
136	#893	—	2	2	no	—
137	C₃⋊#95	—	2	1	no	—
138	#821	—	2	2	no	—
139	#809	C₄×C₅	1	4	yes	complemented
140	#807	—	2	2	no	—
141	C₂⁴×C₅	—	6	1	no	—
142	C₂×C₅×D₄	—	3	2	no	—
143	C₂×C₅×D₄	—	3	2	no	—
144	C₂×C₅×D₄	—	3	2	no	—
145	C₂×C₅×D₄	—	6	1	no	—
146	C₂×C₅×D₄	—	6	1	no	—
147	C₂×C₅×D₄	—	6	1	no	—
148	C₂²×C₄×C₅	—	2	1	no	—
149	C₂²×C₄×C₅	—	2	1	no	—
150	C₂²×C₄×C₅	—	3	1	no	—
151	C₂²×C₄×C₅	—	3	1	no	—
152	C₂²×C₄×C₅	—	6	4	no	—
153	C₂²×C₄×C₅	—	6	1	no	—
154	C₂²×C₄×C₅	—	12	2	no	—
155	C₂²×C₄×C₅	—	12	2	no	—
156	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
157	C₂×C₅×C₈	—	2	1	no	—
158	C₂×C₅×C₈	—	2	1	no	—
159	C₂×C₅×C₈	—	2	1	no	—
160	C₂×C₅×C₈	—	3	2	no	—
161	C₂×C₅×C₈	—	6	1	no	—
162	C₂×C₅×C₈	—	6	1	no	—
163	C₅×C₄⋊C₄	—	2	1	no	—
164	C₅×C₄⋊C₄	—	2	1	no	—
165	C₅×C₄⋊C₄	—	6	1	no	—
166	C₅×C₄⋊C₄	—	6	1	no	—
167	C₅×C₄⋊C₄	—	12	2	no	—
168	C₅×C₄⋊C₄	C₄×D₃	1	2	yes	complemented
169	C₅×C₄⋊C₄	D₁₂	1	2	yes	—
170	C₅×C₂²⋊C₄	—	6	4	no	—
171	C₄²×C₅	—	6	1	no	—
172	C₄²×C₅	—	6	1	no	—
173	C₂×C₄×D₄	—	3	1	no	—
174	C₂×#107	—	3	1	no	—
175	C₂×#102	—	3	1	no	—
176	C₂×#102	—	3	1	no	—
177	#389	—	3	1	no	—
178	#340	C₅×D₃	1	1	yes	characteristic, complemented
179	#336	—	3	1	no	—
180	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
181	C₂²×C₃×C₅	#120	1	1	yes	characteristic
182	C₂²×C₃×C₅	C₂²⋊Q₈	1	1	yes	characteristic
183	C₂²×C₃×C₅	C₂×D₈	1	1	yes	characteristic
184	C₂²×C₃×C₅	#135	1	1	yes	characteristic
185	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
186	C₂²×C₃×C₅	#137	1	1	yes	characteristic
187	C₂×C₅×D₃	—	2	4	no	—
188	C₂×C₅×D₃	—	4	2	no	—
189	C₂×C₅×D₃	—	4	2	no	—
190	C₂×C₅×D₃	—	4	2	no	—
191	C₂×C₅×D₃	—	4	2	no	—
192	C₂×C₅×D₃	—	4	2	no	—
193	C₂×C₅×D₃	—	4	2	no	—
194	C₃×C₄×C₅	—	4	2	no	—
195	C₃×C₄×C₅	—	4	2	no	—
196	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
197	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
198	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
199	C₃×C₄×C₅	#123	1	1	yes	characteristic
200	C₅×Dic₃	—	2	2	no	—
201	C₅×Dic₃	—	4	1	no	—
202	C₅×Dic₃	—	8	1	no	—
203	C₂³×D₃	—	2	1	no	—
204	C₂²×C₃×C₄	—	2	1	no	—
205	C₂²×C₃×C₄	—	2	1	no	—
206	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
207	C₂²×Dic₃	—	2	1	no	—
208	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
209	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
210	C₂×D₁₂	—	2	1	no	—
211	C₂×D₁₂	—	2	1	no	—
212	C₂×D₁₂	—	2	1	no	—
213	C₂×D₁₂	C₂×C₄×C₅	1	2	yes	—
214	C₂×D₁₂	C₅×D₄	1	2	yes	—
215	C₂×D₁₂	C₅×Q₈	1	2	yes	—
216	C₂×C₄×D₃	—	2	4	no	—
217	C₂×C₄×D₃	—	4	2	no	—
218	C₂×C₄×D₃	—	4	2	no	—
219	C₂×C₃×C₈	—	2	1	no	—
220	C₂×C₃×C₈	—	2	1	no	—
221	C₂×C₃×C₈	—	2	1	no	—
222	C₃×C₄⋊C₄	—	2	1	no	—
223	C₃×C₄⋊C₄	—	2	1	no	—
224	C₃×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	complemented
225	C₃×C₄⋊C₄	C₅×D₄	1	2	yes	—
226	(C₂×D₃)⋊C₄	—	2	4	no	—
227	C₄⋊Dic₃	—	2	1	no	—
228	C₄⋊Dic₃	—	2	1	no	—
229	C₄⋊Dic₃	—	4	2	no	—
230	C₄×Dic₃	—	2	1	no	—
231	C₄×Dic₃	—	2	1	no	—
232	C₂×C₃⋊C₈	—	2	1	no	—
233	C₂×C₃⋊C₈	—	2	1	no	—
234	C₂×C₃⋊C₈	C₂×C₄×C₅	1	2	yes	complemented
235	C₂³×C₅	—	6	2	no	—
236	C₂³×C₅	—	6	2	no	—
237	C₂³×C₅	—	6	2	no	—
238	C₂³×C₅	—	12	1	no	—
239	C₂³×C₅	—	12	1	no	—
240	C₂³×C₅	—	12	1	no	—
241	C₂³×C₅	—	12	1	no	—
242	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
243	C₅×D₄	—	3	4	no	—
244	C₅×D₄	—	6	2	no	—
245	C₅×D₄	—	6	2	no	—
246	C₅×D₄	—	6	2	no	—
247	C₂×C₄×C₅	—	2	2	no	—
248	C₂×C₄×C₅	—	2	2	no	—
249	C₂×C₄×C₅	—	3	2	no	—
250	C₂×C₄×C₅	—	4	1	no	—
251	C₂×C₄×C₅	—	4	1	no	—
252	C₂×C₄×C₅	—	4	1	no	—
253	C₂×C₄×C₅	—	4	1	no	—
254	C₂×C₄×C₅	—	6	1	no	—
255	C₂×C₄×C₅	—	6	1	no	—
256	C₂×C₄×C₅	—	6	1	no	—
257	C₂×C₄×C₅	—	6	1	no	—
258	C₂×C₄×C₅	—	6	1	no	—
259	C₂×C₄×C₅	—	12	8	no	—
260	C₂×C₄×C₅	—	12	1	no	—
261	C₂×C₄×C₅	—	12	1	no	—
262	C₂×C₄×C₅	—	12	1	no	—
263	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
264	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
265	C₂×C₄×C₅	#235	1	1	yes	characteristic
266	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
267	C₂×C₄×C₅	#237	1	1	yes	characteristic
268	C₂×C₄×C₅	D₃×Q₈	1	1	yes	characteristic
269	C₅×C₈	—	4	1	no	—
270	C₅×C₈	—	6	2	no	—
271	C₂²×D₄	—	3	1	no	—
272	C₂³×C₄	—	6	1	no	—
273	C₂²×C₈	—	3	1	no	—
274	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
275	C₄×D₄	—	6	2	no	—
276	C₄×D₄	—	6	2	no	—
277	C₂×C₄⋊C₄	—	3	1	no	—
278	C₂×C₄⋊C₄	—	6	1	no	—
279	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
280	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
281	C₂×C₂²⋊C₄	—	6	1	no	—
282	C₂×C₄²	—	3	1	no	—
283	#107	—	6	2	no	—
284	#102	—	3	4	no	—
285	#102	—	6	2	no	—
286	#95	—	6	1	no	—
287	C₂×C₃×C₅	#385	1	1	yes	characteristic
288	C₂×C₃×C₅	C₄×D₈	1	1	yes	characteristic
289	C₂×C₃×C₅	#440	1	1	yes	characteristic
290	C₂×C₃×C₅	#447	1	1	yes	characteristic
291	C₂×C₃×C₅	#452	1	1	yes	characteristic
292	C₂×C₃×C₅	#474	1	1	yes	characteristic
293	C₂×C₃×C₅	#478	1	1	yes	characteristic
294	C₅×D₃	—	4	4	no	—
295	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
296	C₂²×D₃	—	2	2	no	—
297	C₂²×D₃	—	2	2	no	—
298	C₂²×D₃	—	2	2	no	—
299	C₂²×D₃	—	4	1	no	—
300	C₂²×D₃	—	4	1	no	—
301	C₂²×D₃	—	4	1	no	—
302	C₂²×D₃	—	4	1	no	—
303	C₂×C₃×C₄	—	2	2	no	—
304	C₂×C₃×C₄	—	2	2	no	—
305	C₂×C₃×C₄	—	4	1	no	—
306	C₂×C₃×C₄	—	4	1	no	—
307	C₂×C₃×C₄	—	4	1	no	—
308	C₂×C₃×C₄	—	4	1	no	—
309	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
310	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
311	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
312	C₂×C₃×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
313	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
314	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
315	C₂×Dic₃	—	2	1	no	—
316	C₂×Dic₃	—	2	1	no	—
317	C₂×Dic₃	—	2	1	no	—
318	C₂×Dic₃	—	2	1	no	—
319	C₂×Dic₃	—	2	1	no	—
320	C₂×Dic₃	—	4	1	no	—
321	C₂×Dic₃	—	4	1	no	—
322	C₂×Dic₃	—	4	1	no	—
323	C₂×Dic₃	C₅×D₈	1	2	yes	—
324	D₁₂	—	2	2	no	—
325	D₁₂	—	2	2	no	—
326	D₁₂	—	2	2	no	—
327	D₁₂	C₅×C₄⋊C₄	1	4	yes	complemented
328	C₄×D₃	—	4	8	no	—
329	C₃×C₈	—	4	1	no	—
330	C₃⋊C₈	—	2	2	no	—
331	C₂²×C₅	—	6	4	no	—
332	C₂²×C₅	—	12	2	no	—
333	C₂²×C₅	—	12	2	no	—
334	C₂²×C₅	—	12	2	no	—
335	C₂²×C₅	—	12	2	no	—
336	C₂²×C₅	—	12	2	no	—
337	C₂²×C₅	—	12	2	no	—
338	C₂²×C₅	#67⋊C₄	1	1	yes	characteristic
339	C₂²×C₅	#882	1	1	yes	characteristic
340	C₂²×C₅	#896	1	1	yes	characteristic
341	C₂²×C₅	D₃×D₈	1	1	yes	characteristic
342	C₂²×C₅	#914	1	1	yes	characteristic
343	C₂²×C₅	#916	1	1	yes	characteristic
344	C₂²×C₅	#918	1	1	yes	characteristic
345	C₄×C₅	—	4	2	no	—
346	C₄×C₅	—	4	2	no	—
347	C₄×C₅	—	6	2	no	—
348	C₄×C₅	—	12	1	no	—
349	C₄×C₅	—	24	1	no	—
350	C₄×C₅	C₄×D₁₂	1	1	yes	characteristic
351	C₄×C₅	#883	1	1	yes	characteristic
352	C₄×C₅	D₃×C₄⋊C₄	1	1	yes	characteristic
353	C₄×C₅	#897	1	1	yes	characteristic
354	C₂⁴	—	6	1	no	—
355	C₂×D₄	—	3	2	no	—
356	C₂×D₄	—	3	2	no	—
357	C₂×D₄	—	3	2	no	—
358	C₂×D₄	—	6	1	no	—
359	C₂×D₄	—	6	1	no	—
360	C₂×D₄	—	6	1	no	—
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	3	1	no	—
364	C₂²×C₄	—	3	1	no	—
365	C₂²×C₄	—	6	4	no	—
366	C₂²×C₄	—	6	1	no	—
367	C₂²×C₄	—	12	2	no	—
368	C₂²×C₄	—	12	2	no	—
369	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
370	C₂×C₈	—	2	1	no	—
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	—	3	2	no	—
374	C₂×C₈	—	6	1	no	—
375	C₂×C₈	—	6	1	no	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	6	1	no	—
379	C₄⋊C₄	—	6	1	no	—
380	C₄⋊C₄	—	12	2	no	—
381	C₄⋊C₄	C₄×C₅×D₃	1	2	yes	complemented
382	C₄⋊C₄	C₅×D₁₂	1	2	yes	—
383	C₂²⋊C₄	—	6	4	no	—
384	C₄²	—	6	1	no	—
385	C₄²	—	6	1	no	—
386	C₃×C₅	#1862	1	1	yes	characteristic, complemented, Hall
387	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
388	C₂²×C₃	C₅×#120	1	1	yes	characteristic
389	C₂²×C₃	C₅×C₂²⋊Q₈	1	1	yes	characteristic
390	C₂²×C₃	C₂×C₅×D₈	1	1	yes	characteristic
391	C₂²×C₃	C₅×#135	1	1	yes	characteristic
392	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
393	C₂²×C₃	C₅×#137	1	1	yes	characteristic
394	C₂×D₃	—	2	4	no	—
395	C₂×D₃	—	4	2	no	—
396	C₂×D₃	—	4	2	no	—
397	C₂×D₃	—	4	2	no	—
398	C₂×D₃	—	4	2	no	—
399	C₂×D₃	—	4	2	no	—
400	C₂×D₃	—	4	2	no	—
401	C₃×C₄	—	4	2	no	—
402	C₃×C₄	—	4	2	no	—
403	C₃×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
404	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
405	C₃×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
406	C₃×C₄	C₅×#123	1	1	yes	characteristic
407	Dic₃	—	2	2	no	—
408	Dic₃	—	4	1	no	—
409	Dic₃	—	8	1	no	—
410	C₂×C₅	—	12	4	no	—
411	C₂×C₅	#4668	1	1	yes	characteristic
412	C₂×C₅	#4756	1	1	yes	characteristic
413	C₂×C₅	#4773	1	1	yes	characteristic
414	C₂×C₅	#4808	1	1	yes	characteristic
415	C₂×C₅	#4817	1	1	yes	characteristic
416	C₂×C₅	#4871	1	1	yes	characteristic
417	C₂×C₅	#4890	1	1	yes	characteristic
418	C₂³	—	6	2	no	—
419	C₂³	—	6	2	no	—
420	C₂³	—	6	2	no	—
421	C₂³	—	12	1	no	—
422	C₂³	—	12	1	no	—
423	C₂³	—	12	1	no	—
424	C₂³	—	12	1	no	—
425	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
426	D₄	—	3	4	no	—
427	D₄	—	6	2	no	—
428	D₄	—	6	2	no	—
429	D₄	—	6	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	3	2	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	6	1	no	—
438	C₂×C₄	—	6	1	no	—
439	C₂×C₄	—	6	1	no	—
440	C₂×C₄	—	6	1	no	—
441	C₂×C₄	—	6	1	no	—
442	C₂×C₄	—	12	8	no	—
443	C₂×C₄	—	12	1	no	—
444	C₂×C₄	—	12	1	no	—
445	C₂×C₄	—	12	1	no	—
446	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
447	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
448	C₂×C₄	C₅×#235	1	1	yes	characteristic
449	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
450	C₂×C₄	C₅×#237	1	1	yes	characteristic
451	C₂×C₄	C₅×D₃×Q₈	1	1	yes	characteristic
452	C₈	—	4	1	no	—
453	C₈	—	6	2	no	—
454	C₂×C₃	C₅×#385	1	1	yes	characteristic
455	C₂×C₃	C₄×C₅×D₈	1	1	yes	characteristic
456	C₂×C₃	C₅×#440	1	1	yes	characteristic
457	C₂×C₃	C₅×#447	1	1	yes	characteristic
458	C₂×C₃	C₅×#452	1	1	yes	characteristic
459	C₂×C₃	C₅×#474	1	1	yes	characteristic
460	C₂×C₃	C₅×#478	1	1	yes	characteristic
461	D₃	—	4	4	no	—
462	C₅	#68894	1	1	yes	characteristic, direct product factor, Sylow
463	C₂²	—	6	4	no	—
464	C₂²	—	12	2	no	—
465	C₂²	—	12	2	no	—
466	C₂²	—	12	2	no	—
467	C₂²	—	12	2	no	—
468	C₂²	—	12	2	no	—
469	C₂²	—	12	2	no	—
470	C₂²	C₅×#67⋊C₄	1	1	yes	characteristic
471	C₂²	C₅×#882	1	1	yes	characteristic
472	C₂²	C₅×#896	1	1	yes	characteristic
473	C₂²	C₅×D₃×D₈	1	1	yes	characteristic
474	C₂²	C₅×#914	1	1	yes	characteristic
475	C₂²	C₅×#916	1	1	yes	characteristic
476	C₂²	C₅×#918	1	1	yes	characteristic
477	C₄	—	4	2	no	—
478	C₄	—	4	2	no	—
479	C₄	—	6	2	no	—
480	C₄	—	12	1	no	—
481	C₄	—	24	1	no	—
482	C₄	C₄×C₅×D₁₂	1	1	yes	characteristic
483	C₄	C₅×#883	1	1	yes	characteristic
484	C₄	C₅×D₃×C₄⋊C₄	1	1	yes	characteristic
485	C₄	C₅×#897	1	1	yes	characteristic
486	C₃	C₅×#1862	1	1	yes	characteristic, complemented, Sylow
487	C₂	—	12	4	no	—
488	C₂	C₅×#4668	1	1	yes	characteristic
489	C₂	C₅×#4756	1	1	yes	characteristic
490	C₂	C₅×#4773	1	1	yes	characteristic
491	C₂	C₅×#4808	1	1	yes	characteristic
492	C₂	C₅×#4817	1	1	yes	characteristic
493	C₂	C₅×#4871	1	1	yes	characteristic
494	C₂	C₅×#4890	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	D₃×D₄
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₃×C₅×#340	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂²×C₅×D₁₂	C₂²
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₅×#340	D₃
hypocenter	C₃	C₅×#1862
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#340

Complements

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

N	H ≅ G/N	type
3. C₅×#4984	C₂	semidirect
5. C₂×C₅×#807	C₂	semidirect
6. C₃×C₅×#340	C₂	semidirect
7. C₅×#4550	C₂	semidirect
23. C₅×#809	C₄	semidirect
25. #68894	C₅	direct (N × H)
31. C₅×#340	D₃	semidirect
54. C₃×C₅×C₄⋊C₄	C₂×C₄	semidirect
64. C₂×C₅×C₃⋊C₈	C₂×C₄	semidirect
67. #4984	C₂×C₅	semidirect
69. C₂×#807	C₂×C₅	semidirect
70. C₃×#340	C₂×C₅	semidirect
71. #4550	C₂×C₅	semidirect
121. C₅×D₁₂	C₄⋊C₄	semidirect
139. #809	C₄×C₅	semidirect
168. C₅×C₄⋊C₄	C₄×D₃	semidirect
178. #340	C₅×D₃	semidirect
224. C₃×C₄⋊C₄	C₂×C₄×C₅	semidirect
234. C₂×C₃⋊C₈	C₂×C₄×C₅	semidirect
327. D₁₂	C₅×C₄⋊C₄	semidirect
381. C₄⋊C₄	C₄×C₅×D₃	semidirect
386. C₃×C₅	#1862	semidirect
462. C₅	#68894	direct (N × H)
486. C₃	C₅×#1862	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#893	2
C₂×C₅×#821	2
C₅×#4984	2
C₂×C₅×#809	2
C₂×C₅×#807	2
C₃×C₅×#340	2
C₅×#4550	2
C₅×#1862	3
#68894	5

Subgroups — C5×#68894 #14299940

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#68894 #14299940