Subgroups — C₅×#82537 #14417003

Order 1920.

1012 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#518	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#932	C₂	1	1	yes	maximal, characteristic
3	C₅×#5523	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#832	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5018	C₂	1	2	yes	maximal, complemented
6	C₄×C₅×#214	C₂	1	2	yes	maximal, complemented
7	C₅×#5014	C₂	1	2	yes	maximal, complemented
8	C₄×C₅×#213	C₂	1	2	yes	maximal, complemented
9	C₅×#5002	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4997	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4995	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#2946	—	3	1	no	maximal, Hall
13	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
14	C₂×C₅×#235	C₂²	1	1	yes	characteristic
15	C₃×C₄×C₅×D₄	—	2	1	no	—
16	C₃×C₄×C₅×D₄	—	2	1	no	—
17	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
18	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
19	C₃×C₅×#117	C₂²	1	1	yes	characteristic
20	C₃×C₅×#117	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₅×C₂²⋊C₄	—	2	2	no	—
22	C₂×C₅×#214	C₂²	1	2	yes	—
23	C₅×#932	C₄	1	8	yes	complemented
24	C₂×C₅×#213	C₂²	1	2	yes	—
25	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
26	C₂×C₅×#208	C₂²	1	1	yes	characteristic
27	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
28	C₅×#892	—	2	1	no	—
29	C₅×D₃×C₄⋊C₄	—	2	1	no	—
30	C₅×#67⋊C₄	—	2	2	no	—
31	C₄×C₅×D₁₂	C₂²	1	2	yes	complemented
32	C₄×C₅×Dic₆	C₂²	1	2	yes	complemented
33	C₅×#832	C₂²	1	2	yes	—
34	C₅×#832	C₂²	1	2	yes	—
35	C₅×#810	C₂²	1	1	yes	characteristic, complemented
36	C₅×#810	C₂²	1	1	yes	characteristic, complemented
37	C₅×#809	C₂²	1	1	yes	characteristic, complemented
38	C₅×#809	C₂²	1	1	yes	characteristic, complemented
39	C₅×#808	C₂²	1	2	yes	complemented
40	C₅×#807	C₂²	1	2	yes	complemented
41	C₅×#803	C₂²	1	2	yes	complemented
42	C₄×C₅×C₃⋊C₈	C₂²	1	2	yes	complemented
43	#82537	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
44	C₂×C₅×AGL(1,ℤ/8)	—	3	1	no	—
45	C₅×#520	—	3	1	no	—
46	C₅×#518	D₃	1	1	yes	characteristic, complemented
47	C₅×#442	—	3	2	no	—
48	C₅×#440	—	3	2	no	—
49	C₄×C₅×SD₁₆	—	3	2	no	—
50	C₄×C₅×D₈	—	3	2	no	—
51	C₅×#428	—	3	1	no	—
52	C₅×#416	—	3	1	no	—
53	C₂×C₅×#102	—	3	1	no	—
54	C₅×#405	—	3	1	no	—
55	C₂⁴×C₃×C₅	—	2	1	no	—
56	C₂×C₃×C₅×D₄	—	2	1	no	—
57	C₂×C₃×C₅×D₄	—	2	2	no	—
58	C₂×C₃×C₅×D₄	C₂×C₄	1	4	yes	complemented
59	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
60	C₂²×C₃×C₄×C₅	—	2	2	no	—
61	C₂²×C₃×C₄×C₅	—	2	2	no	—
62	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
63	C₂×C₅×#67	—	2	1	no	—
64	C₂²×C₅×Dic₃	—	2	1	no	—
65	C₅×#235	—	2	2	no	—
66	C₅×#235	C₂×C₄	1	4	yes	complemented
67	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
68	C₂×C₄×C₅×D₃	—	2	1	no	—
69	C₂×C₄×C₅×D₃	—	2	2	no	—
70	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
71	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
72	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
73	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
74	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
75	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
76	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
77	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
78	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
79	C₃×C₄²×C₅	—	2	1	no	—
80	C₃×C₄²×C₅	C₂³	1	2	yes	—
81	C₅×#214	C₂×C₄	1	8	yes	complemented
82	C₅×#213	C₂×C₄	1	8	yes	complemented
83	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
84	C₅×C₄⋊Dic₃	—	2	1	no	—
85	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
86	C₅×Dic₃⋊C₄	—	2	2	no	—
87	C₄×C₅×Dic₃	—	2	2	no	—
88	C₅×#208	C₂×C₄	1	4	yes	complemented
89	C₂×C₅×C₃⋊C₈	—	2	2	no	—
90	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
91	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
92	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
93	C₃×#518	C₂×C₅	1	1	yes	characteristic, complemented
94	C₂×#932	C₂×C₅	1	1	yes	characteristic
95	#5523	C₂×C₅	1	1	yes	characteristic, complemented
96	C₂×#832	C₂×C₅	1	1	yes	characteristic, complemented
97	#5018	C₂×C₅	1	2	yes	complemented
98	C₄×#214	C₂×C₅	1	2	yes	complemented
99	#5014	C₂×C₅	1	2	yes	complemented
100	C₄×#213	C₂×C₅	1	2	yes	complemented
101	#5002	C₂×C₅	1	1	yes	characteristic, complemented
102	#4997	C₂×C₅	1	1	yes	characteristic, complemented
103	#4995	C₂×C₅	1	1	yes	characteristic, complemented
104	C₂×C₅×#41	—	3	1	no	—
105	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
106	C₅×AGL(1,ℤ/8)	—	3	8	no	—
107	C₂×C₅×SD₁₆	—	3	2	no	—
108	C₂×C₅×D₈	—	3	2	no	—
109	C₂×C₅×M₁₆	—	3	1	no	—
110	C₂²×C₅×C₈	—	3	1	no	—
111	C₄×C₅×Q₈	—	3	2	no	—
112	C₄×C₅×D₄	—	2	1	no	—
113	C₄×C₅×D₄	—	2	1	no	—
114	C₄×C₅×D₄	—	3	2	no	—
115	C₄×C₅×D₄	—	6	2	no	—
116	C₄×C₅×D₄	C₂×D₃	1	2	yes	—
117	C₄×C₅×D₄	C₂×D₃	1	2	yes	—
118	C₅×#117	—	6	1	no	—
119	C₅×#117	C₂×D₃	1	1	yes	characteristic
120	C₅×#117	C₂×D₃	1	1	yes	characteristic
121	C₂×C₅×C₄⋊C₄	—	3	1	no	—
122	C₂×C₅×C₄⋊C₄	—	6	1	no	—
123	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
124	C₅×#107	—	3	2	no	—
125	C₅×#106	—	3	2	no	—
126	C₅×#103	—	3	1	no	—
127	C₅×#103	—	3	1	no	—
128	C₅×#102	—	3	2	no	—
129	C₅×#102	—	3	2	no	—
130	C₅×#102	—	3	1	no	—
131	C₅×#102	—	3	1	no	—
132	C₅×#97	—	3	2	no	—
133	C₄×C₅×C₈	—	3	2	no	—
134	#2946	—	3	1	no	Sylow
135	C₂³×C₃×C₅	—	2	2	no	—
136	C₂³×C₃×C₅	—	2	4	no	—
137	C₂³×C₃×C₅	—	8	1	no	—
138	C₂³×C₃×C₅	—	8	1	no	—
139	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₅×D₃	—	2	1	no	—
141	C₃×C₅×D₄	—	2	4	no	—
142	C₃×C₅×D₄	—	2	2	no	—
143	C₃×C₅×D₄	C₂²×C₄	1	4	yes	—
144	C₂×C₃×C₄×C₅	—	2	1	no	—
145	C₂×C₃×C₄×C₅	—	2	1	no	—
146	C₂×C₃×C₄×C₅	—	8	2	no	—
147	C₂×C₃×C₄×C₅	—	8	2	no	—
148	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
149	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
150	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
151	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
152	C₂×C₃×C₄×C₅	#41	1	2	yes	—
153	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
154	C₅×#67	—	2	4	no	—
155	C₂×C₅×Dic₃	—	2	1	no	—
156	C₂×C₅×Dic₃	—	2	2	no	—
157	C₂×C₅×Dic₃	—	8	1	no	—
158	C₅×D₁₂	—	2	1	no	—
159	C₅×D₁₂	C₂²×C₄	1	2	yes	—
160	C₄×C₅×D₃	—	2	4	no	—
161	C₄×C₅×D₃	—	8	2	no	—
162	C₅×Dic₆	—	2	1	no	—
163	C₅×Dic₆	C₂²×C₄	1	2	yes	—
164	C₅×C₃⋊C₈	—	2	1	no	—
165	C₅×C₃⋊C₈	—	2	1	no	—
166	C₅×C₃⋊C₈	C₂²×C₄	1	4	yes	—
167	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
168	C₂×#235	C₂²×C₅	1	1	yes	characteristic
169	C₃×C₄×D₄	—	2	1	no	—
170	C₃×C₄×D₄	—	2	1	no	—
171	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
172	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
173	C₃×#117	C₂²×C₅	1	1	yes	characteristic
174	C₃×#117	C₂²×C₅	1	1	yes	characteristic
175	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
176	C₂×#214	C₂²×C₅	1	2	yes	—
177	#932	C₄×C₅	1	8	yes	complemented
178	C₂×#213	C₂²×C₅	1	2	yes	—
179	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
180	C₂×#208	C₂²×C₅	1	1	yes	characteristic
181	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
182	#892	—	2	1	no	—
183	D₃×C₄⋊C₄	—	2	1	no	—
184	#67⋊C₄	—	2	2	no	—
185	C₄×D₁₂	C₂²×C₅	1	2	yes	complemented
186	C₄×Dic₆	C₂²×C₅	1	2	yes	complemented
187	#832	C₂²×C₅	1	2	yes	—
188	#832	C₂²×C₅	1	2	yes	—
189	#810	C₂²×C₅	1	1	yes	characteristic, complemented
190	#810	C₂²×C₅	1	1	yes	characteristic, complemented
191	#809	C₂²×C₅	1	1	yes	characteristic, complemented
192	#809	C₂²×C₅	1	1	yes	characteristic, complemented
193	#808	C₂²×C₅	1	2	yes	complemented
194	#807	C₂²×C₅	1	2	yes	complemented
195	#803	C₂²×C₅	1	2	yes	complemented
196	C₄×C₃⋊C₈	C₂²×C₅	1	2	yes	complemented
197	C₂⁴×C₅	—	2	1	no	—
198	C₅×#41	—	3	4	no	—
199	C₅×#41	—	6	2	no	—
200	C₂×C₅×Q₈	—	3	1	no	—
201	C₂×C₅×D₄	—	2	2	no	—
202	C₂×C₅×D₄	—	2	1	no	—
203	C₂×C₅×D₄	—	3	1	no	—
204	C₂×C₅×D₄	—	6	1	no	—
205	C₂×C₅×D₄	C₄×D₃	1	4	yes	complemented
206	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
207	C₂²×C₄×C₅	—	2	2	no	—
208	C₂²×C₄×C₅	—	2	2	no	—
209	C₂²×C₄×C₅	—	6	1	no	—
210	C₂²×C₄×C₅	—	6	1	no	—
211	C₂²×C₄×C₅	—	6	2	no	—
212	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
213	C₅×SD₁₆	—	3	8	no	—
214	C₅×D₈	—	3	8	no	—
215	C₅×M₁₆	—	3	4	no	—
216	C₂×C₅×C₈	—	3	2	no	—
217	C₂×C₅×C₈	—	3	1	no	—
218	C₂×C₅×C₈	—	3	1	no	—
219	C₂×C₅×C₈	—	6	2	no	—
220	C₅×C₄⋊C₄	—	3	2	no	—
221	C₅×C₄⋊C₄	—	6	1	no	—
222	C₅×C₄⋊C₄	—	6	2	no	—
223	C₅×C₄⋊C₄	#67	1	1	yes	characteristic
224	C₅×C₄⋊C₄	#67	1	1	yes	characteristic
225	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
226	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
227	C₅×C₂²⋊C₄	—	2	1	no	—
228	C₅×C₂²⋊C₄	—	2	2	no	—
229	C₅×C₂²⋊C₄	—	2	2	no	—
230	C₅×C₂²⋊C₄	—	6	2	no	—
231	C₅×C₂²⋊C₄	#67	1	2	yes	—
232	C₄²×C₅	—	2	1	no	—
233	C₄²×C₅	—	6	2	no	—
234	C₄²×C₅	C₂²×D₃	1	2	yes	—
235	C₂×AGL(1,ℤ/8)	—	3	1	no	—
236	#520	—	3	1	no	—
237	#518	C₅×D₃	1	1	yes	characteristic, complemented
238	#442	—	3	2	no	—
239	#440	—	3	2	no	—
240	C₄×SD₁₆	—	3	2	no	—
241	C₄×D₈	—	3	2	no	—
242	#428	—	3	1	no	—
243	#416	—	3	1	no	—
244	C₂×#102	—	3	1	no	—
245	#405	—	3	1	no	—
246	C₂²×C₃×C₅	—	2	1	no	—
247	C₂²×C₃×C₅	—	2	1	no	—
248	C₂²×C₃×C₅	—	2	4	no	—
249	C₂²×C₃×C₅	—	4	2	no	—
250	C₂²×C₃×C₅	—	4	2	no	—
251	C₂²×C₃×C₅	—	8	4	no	—
252	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
253	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
254	C₂×C₅×D₃	—	2	2	no	—
255	C₂×C₅×D₃	—	4	1	no	—
256	C₂×C₅×D₃	—	4	1	no	—
257	C₃×C₄×C₅	—	2	2	no	—
258	C₃×C₄×C₅	—	2	2	no	—
259	C₃×C₄×C₅	—	4	1	no	—
260	C₃×C₄×C₅	—	4	1	no	—
261	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
262	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
263	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
264	C₅×Dic₃	—	2	2	no	—
265	C₅×Dic₃	—	4	2	no	—
266	C₂⁴×C₃	—	2	1	no	—
267	C₂×C₃×D₄	—	2	1	no	—
268	C₂×C₃×D₄	—	2	2	no	—
269	C₂×C₃×D₄	C₂×C₄×C₅	1	4	yes	complemented
270	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
271	C₂²×C₃×C₄	—	2	2	no	—
272	C₂²×C₃×C₄	—	2	2	no	—
273	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
274	C₂×#67	—	2	1	no	—
275	C₂²×Dic₃	—	2	1	no	—
276	#235	—	2	2	no	—
277	#235	C₂×C₄×C₅	1	4	yes	complemented
278	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
279	C₂×C₄×D₃	—	2	1	no	—
280	C₂×C₄×D₃	—	2	2	no	—
281	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
282	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
283	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
284	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
285	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
286	C₃×C₂²⋊C₄	—	2	1	no	—
287	C₃×C₂²⋊C₄	—	2	2	no	—
288	C₃×C₂²⋊C₄	—	2	2	no	—
289	C₃×C₂²⋊C₄	C₅×D₄	1	2	yes	—
290	C₃×C₄²	—	2	1	no	—
291	C₃×C₄²	C₂³×C₅	1	2	yes	—
292	#214	C₂×C₄×C₅	1	8	yes	complemented
293	#213	C₂×C₄×C₅	1	8	yes	complemented
294	(C₂×D₃)⋊C₄	—	2	2	no	—
295	C₄⋊Dic₃	—	2	1	no	—
296	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
297	Dic₃⋊C₄	—	2	2	no	—
298	C₄×Dic₃	—	2	2	no	—
299	#208	C₂×C₄×C₅	1	4	yes	complemented
300	C₂×C₃⋊C₈	—	2	2	no	—
301	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
302	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
303	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
304	C₂³×C₅	—	2	2	no	—
305	C₂³×C₅	—	2	4	no	—
306	C₂³×C₅	—	6	1	no	—
307	C₂³×C₅	—	8	1	no	—
308	C₂³×C₅	—	8	1	no	—
309	C₂³×C₅	C₂×#67	1	1	yes	characteristic
310	C₅×Q₈	—	3	2	no	—
311	C₅×Q₈	—	6	1	no	—
312	C₅×D₄	—	2	4	no	—
313	C₅×D₄	—	2	2	no	—
314	C₅×D₄	—	3	2	no	—
315	C₅×D₄	—	6	4	no	—
316	C₅×D₄	—	6	1	no	—
317	C₅×D₄	C₂×C₄×D₃	1	4	yes	—
318	C₂×C₄×C₅	—	2	1	no	—
319	C₂×C₄×C₅	—	2	1	no	—
320	C₂×C₄×C₅	—	6	1	no	—
321	C₂×C₄×C₅	—	6	4	no	—
322	C₂×C₄×C₅	—	6	2	no	—
323	C₂×C₄×C₅	—	8	2	no	—
324	C₂×C₄×C₅	—	8	2	no	—
325	C₂×C₄×C₅	—	24	2	no	—
326	C₂×C₄×C₅	—	24	1	no	—
327	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
328	C₂×C₄×C₅	#235	1	2	yes	—
329	C₂×C₄×C₅	C₂×#67	1	2	yes	—
330	C₂×C₄×C₅	C₂×#67	1	2	yes	—
331	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
332	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
333	C₅×C₈	—	3	4	no	—
334	C₅×C₈	—	6	1	no	—
335	C₅×C₈	—	6	1	no	—
336	C₂×#41	—	3	1	no	—
337	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
338	AGL(1,ℤ/8)	—	3	8	no	—
339	C₂×SD₁₆	—	3	2	no	—
340	C₂×D₈	—	3	2	no	—
341	C₂×M₁₆	—	3	1	no	—
342	C₂²×C₈	—	3	1	no	—
343	C₄×Q₈	—	3	2	no	—
344	C₄×D₄	—	2	1	no	—
345	C₄×D₄	—	2	1	no	—
346	C₄×D₄	—	3	2	no	—
347	C₄×D₄	—	6	2	no	—
348	C₄×D₄	C₂×C₅×D₃	1	2	yes	—
349	C₄×D₄	C₂×C₅×D₃	1	2	yes	—
350	#117	—	6	1	no	—
351	#117	C₂×C₅×D₃	1	1	yes	characteristic
352	#117	C₂×C₅×D₃	1	1	yes	characteristic
353	C₂×C₄⋊C₄	—	3	1	no	—
354	C₂×C₄⋊C₄	—	6	1	no	—
355	C₂×C₂²⋊C₄	—	2	2	no	—
356	#107	—	3	2	no	—
357	#106	—	3	2	no	—
358	#103	—	3	1	no	—
359	#103	—	3	1	no	—
360	#102	—	3	2	no	—
361	#102	—	3	2	no	—
362	#102	—	3	1	no	—
363	#102	—	3	1	no	—
364	#97	—	3	2	no	—
365	C₄×C₈	—	3	2	no	—
366	C₂×C₃×C₅	—	2	2	no	—
367	C₂×C₃×C₅	—	4	4	no	—
368	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
369	C₂×C₃×C₅	#576	1	1	yes	characteristic
370	C₂×C₃×C₅	#577	1	1	yes	characteristic
371	C₅×D₃	—	4	2	no	—
372	C₂³×C₃	—	2	2	no	—
373	C₂³×C₃	—	2	4	no	—
374	C₂³×C₃	—	8	1	no	—
375	C₂³×C₃	—	8	1	no	—
376	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
377	C₂²×D₃	—	2	1	no	—
378	C₃×D₄	—	2	4	no	—
379	C₃×D₄	—	2	2	no	—
380	C₃×D₄	C₂²×C₄×C₅	1	4	yes	—
381	C₂×C₃×C₄	—	2	1	no	—
382	C₂×C₃×C₄	—	2	1	no	—
383	C₂×C₃×C₄	—	8	2	no	—
384	C₂×C₃×C₄	—	8	2	no	—
385	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
386	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
387	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
388	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
389	C₂×C₃×C₄	C₅×#41	1	2	yes	—
390	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
391	#67	—	2	4	no	—
392	C₂×Dic₃	—	2	1	no	—
393	C₂×Dic₃	—	2	2	no	—
394	C₂×Dic₃	—	8	1	no	—
395	D₁₂	—	2	1	no	—
396	D₁₂	C₂²×C₄×C₅	1	2	yes	—
397	C₄×D₃	—	2	4	no	—
398	C₄×D₃	—	8	2	no	—
399	Dic₆	—	2	1	no	—
400	Dic₆	C₂²×C₄×C₅	1	2	yes	—
401	C₃⋊C₈	—	2	1	no	—
402	C₃⋊C₈	—	2	1	no	—
403	C₃⋊C₈	C₂²×C₄×C₅	1	4	yes	—
404	C₂²×C₅	—	2	1	no	—
405	C₂²×C₅	—	2	1	no	—
406	C₂²×C₅	—	2	4	no	—
407	C₂²×C₅	—	4	2	no	—
408	C₂²×C₅	—	4	2	no	—
409	C₂²×C₅	—	6	2	no	—
410	C₂²×C₅	—	8	4	no	—
411	C₂²×C₅	—	12	1	no	—
412	C₂²×C₅	—	12	1	no	—
413	C₂²×C₅	C₄×#67	1	2	yes	—
414	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
415	C₄×C₅	—	2	2	no	—
416	C₄×C₅	—	2	2	no	—
417	C₄×C₅	—	4	1	no	—
418	C₄×C₅	—	4	1	no	—
419	C₄×C₅	—	6	2	no	—
420	C₄×C₅	—	12	2	no	—
421	C₄×C₅	C₄×#67	1	2	yes	—
422	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
423	C₄×C₅	C₂×#235	1	1	yes	characteristic
424	C₂⁴	—	2	1	no	—
425	#41	—	3	4	no	—
426	#41	—	6	2	no	—
427	C₂×Q₈	—	3	1	no	—
428	C₂×D₄	—	2	2	no	—
429	C₂×D₄	—	2	1	no	—
430	C₂×D₄	—	3	1	no	—
431	C₂×D₄	—	6	1	no	—
432	C₂×D₄	C₄×C₅×D₃	1	4	yes	complemented
433	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
434	C₂²×C₄	—	2	2	no	—
435	C₂²×C₄	—	2	2	no	—
436	C₂²×C₄	—	6	1	no	—
437	C₂²×C₄	—	6	1	no	—
438	C₂²×C₄	—	6	2	no	—
439	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
440	SD₁₆	—	3	8	no	—
441	D₈	—	3	8	no	—
442	M₁₆	—	3	4	no	—
443	C₂×C₈	—	3	2	no	—
444	C₂×C₈	—	3	1	no	—
445	C₂×C₈	—	3	1	no	—
446	C₂×C₈	—	6	2	no	—
447	C₄⋊C₄	—	3	2	no	—
448	C₄⋊C₄	—	6	1	no	—
449	C₄⋊C₄	—	6	2	no	—
450	C₄⋊C₄	C₅×#67	1	1	yes	characteristic
451	C₄⋊C₄	C₅×#67	1	1	yes	characteristic
452	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
453	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
454	C₂²⋊C₄	—	2	1	no	—
455	C₂²⋊C₄	—	2	2	no	—
456	C₂²⋊C₄	—	2	2	no	—
457	C₂²⋊C₄	—	6	2	no	—
458	C₂²⋊C₄	C₅×#67	1	2	yes	—
459	C₄²	—	2	1	no	—
460	C₄²	—	6	2	no	—
461	C₄²	C₂²×C₅×D₃	1	2	yes	—
462	C₃×C₅	#2946	1	1	yes	characteristic, complemented, Hall
463	C₂²×C₃	—	2	1	no	—
464	C₂²×C₃	—	2	1	no	—
465	C₂²×C₃	—	2	4	no	—
466	C₂²×C₃	—	4	2	no	—
467	C₂²×C₃	—	4	2	no	—
468	C₂²×C₃	—	8	4	no	—
469	C₂²×C₃	C₄×C₅×D₄	1	2	yes	—
470	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
471	C₂×D₃	—	2	2	no	—
472	C₂×D₃	—	4	1	no	—
473	C₂×D₃	—	4	1	no	—
474	C₃×C₄	—	2	2	no	—
475	C₃×C₄	—	2	2	no	—
476	C₃×C₄	—	4	1	no	—
477	C₃×C₄	—	4	1	no	—
478	C₃×C₄	C₄×C₅×D₄	1	2	yes	—
479	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
480	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
481	Dic₃	—	2	2	no	—
482	Dic₃	—	4	2	no	—
483	C₂×C₅	—	2	2	no	—
484	C₂×C₅	—	4	4	no	—
485	C₂×C₅	—	12	2	no	—
486	C₂×C₅	C₂×C₄×#67	1	1	yes	characteristic
487	C₂×C₅	#5835	1	1	yes	characteristic
488	C₂×C₅	#5836	1	1	yes	characteristic
489	C₂³	—	2	2	no	—
490	C₂³	—	2	4	no	—
491	C₂³	—	6	1	no	—
492	C₂³	—	8	1	no	—
493	C₂³	—	8	1	no	—
494	C₂³	C₂×C₅×#67	1	1	yes	characteristic
495	Q₈	—	3	2	no	—
496	Q₈	—	6	1	no	—
497	D₄	—	2	4	no	—
498	D₄	—	2	2	no	—
499	D₄	—	3	2	no	—
500	D₄	—	6	4	no	—
501	D₄	—	6	1	no	—
502	D₄	C₂×C₄×C₅×D₃	1	4	yes	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	6	1	no	—
506	C₂×C₄	—	6	4	no	—
507	C₂×C₄	—	6	2	no	—
508	C₂×C₄	—	8	2	no	—
509	C₂×C₄	—	8	2	no	—
510	C₂×C₄	—	24	2	no	—
511	C₂×C₄	—	24	1	no	—
512	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
513	C₂×C₄	C₅×#235	1	2	yes	—
514	C₂×C₄	C₂×C₅×#67	1	2	yes	—
515	C₂×C₄	C₂×C₅×#67	1	2	yes	—
516	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
517	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
518	C₈	—	3	4	no	—
519	C₈	—	6	1	no	—
520	C₈	—	6	1	no	—
521	C₂×C₃	—	2	2	no	—
522	C₂×C₃	—	4	4	no	—
523	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
524	C₂×C₃	C₅×#576	1	1	yes	characteristic
525	C₂×C₃	C₅×#577	1	1	yes	characteristic
526	D₃	—	4	2	no	—
527	C₅	#82537	1	1	yes	characteristic, direct product factor, Sylow
528	C₂²	—	2	1	no	—
529	C₂²	—	2	1	no	—
530	C₂²	—	2	4	no	—
531	C₂²	—	4	2	no	—
532	C₂²	—	4	2	no	—
533	C₂²	—	6	2	no	—
534	C₂²	—	8	4	no	—
535	C₂²	—	12	1	no	—
536	C₂²	—	12	1	no	—
537	C₂²	C₄×C₅×#67	1	2	yes	—
538	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
539	C₄	—	2	2	no	—
540	C₄	—	2	2	no	—
541	C₄	—	4	1	no	—
542	C₄	—	4	1	no	—
543	C₄	—	6	2	no	—
544	C₄	—	12	2	no	—
545	C₄	C₄×C₅×#67	1	2	yes	—
546	C₄	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
547	C₄	C₂×C₅×#235	1	1	yes	characteristic
548	C₃	C₅×#2946	1	1	yes	characteristic, complemented, Sylow
549	C₂	—	2	2	no	—
550	C₂	—	4	4	no	—
551	C₂	—	12	2	no	—
552	C₂	C₂×C₄×C₅×#67	1	1	yes	characteristic
553	C₂	C₅×#5835	1	1	yes	characteristic
554	C₂	C₅×#5836	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂²×#67
commutator	C₃×C₄	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#518	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₅×#932	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₅×#518	D₃
hypocenter	C₃	C₅×#2946
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₅×#117 ◁ C₅×#518

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#518	C₂	semidirect
3. C₅×#5523	C₂	semidirect
4. C₂×C₅×#832	C₂	semidirect
5. C₅×#5018	C₂	semidirect
6. C₄×C₅×#214	C₂	semidirect
7. C₅×#5014	C₂	semidirect
8. C₄×C₅×#213	C₂	semidirect
9. C₅×#5002	C₂	semidirect
10. C₅×#4997	C₂	semidirect
11. C₅×#4995	C₂	semidirect
23. C₅×#932	C₄	semidirect
31. C₄×C₅×D₁₂	C₂²	semidirect
32. C₄×C₅×Dic₆	C₂²	semidirect
35. C₅×#810	C₂²	semidirect
36. C₅×#810	C₂²	semidirect
37. C₅×#809	C₂²	semidirect
38. C₅×#809	C₂²	semidirect
39. C₅×#808	C₂²	semidirect
40. C₅×#807	C₂²	semidirect
41. C₅×#803	C₂²	semidirect
42. C₄×C₅×C₃⋊C₈	C₂²	semidirect
43. #82537	C₅	direct (N × H)
46. C₅×#518	D₃	semidirect
58. C₂×C₃×C₅×D₄	C₂×C₄	semidirect
66. C₅×#235	C₂×C₄	semidirect
81. C₅×#214	C₂×C₄	semidirect
82. C₅×#213	C₂×C₄	semidirect
88. C₅×#208	C₂×C₄	semidirect
93. C₃×#518	C₂×C₅	semidirect
95. #5523	C₂×C₅	semidirect
96. C₂×#832	C₂×C₅	semidirect
97. #5018	C₂×C₅	semidirect
98. C₄×#214	C₂×C₅	semidirect
99. #5014	C₂×C₅	semidirect
100. C₄×#213	C₂×C₅	semidirect
101. #5002	C₂×C₅	semidirect
102. #4997	C₂×C₅	semidirect
103. #4995	C₂×C₅	semidirect
177. #932	C₄×C₅	semidirect
185. C₄×D₁₂	C₂²×C₅	semidirect
186. C₄×Dic₆	C₂²×C₅	semidirect
189. #810	C₂²×C₅	semidirect
190. #810	C₂²×C₅	semidirect
191. #809	C₂²×C₅	semidirect
192. #809	C₂²×C₅	semidirect
193. #808	C₂²×C₅	semidirect
194. #807	C₂²×C₅	semidirect
195. #803	C₂²×C₅	semidirect
196. C₄×C₃⋊C₈	C₂²×C₅	semidirect
205. C₂×C₅×D₄	C₄×D₃	semidirect
237. #518	C₅×D₃	semidirect
269. C₂×C₃×D₄	C₂×C₄×C₅	semidirect
277. #235	C₂×C₄×C₅	semidirect
292. #214	C₂×C₄×C₅	semidirect
293. #213	C₂×C₄×C₅	semidirect
299. #208	C₂×C₄×C₅	semidirect
432. C₂×D₄	C₄×C₅×D₃	semidirect
462. C₃×C₅	#2946	semidirect
527. C₅	#82537	direct (N × H)
548. C₃	C₅×#2946	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#518	2
C₂×C₅×#932	2
C₅×#5523	2
C₂×C₅×#832	2
C₅×#5018	2
C₄×C₅×#214	2
C₅×#5014	2
C₄×C₅×#213	2
C₅×#5002	2
C₅×#4997	2
C₅×#4995	2
C₅×#2946	3
#82537	5

Subgroups — C5×#82537 #14417003

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#82537 #14417003