Subgroups — C₅×#80159 #14458623

Order 1920.

816 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5806	C₂	1	1	yes	maximal, characteristic
2	C₅×#5642	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#450	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#832	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5173	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5171	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5166	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×Dic₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#5051	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4779	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4772	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#4768	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#4763	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#67⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#4721	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3296	—	3	1	no	maximal, Hall
17	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
18	C₂×C₅×#237	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
21	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
22	C₅×#953	—	2	1	no	—
23	C₂×C₅×#217	—	2	1	no	—
24	C₅×#946	C₂²	1	1	yes	characteristic, complemented
25	C₅×Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₅×#216	C₂²	1	1	yes	characteristic, complemented
27	C₅×#939	—	2	1	no	—
28	C₅×#938	C₂²	1	1	yes	characteristic
29	C₅×#936	C₂²	1	1	yes	characteristic
30	C₅×#935	—	2	1	no	—
31	C₅×D₄×Dic₃	C₂²	1	1	yes	characteristic
32	C₄×C₅×#67	C₂²	1	1	yes	characteristic
33	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
34	C₅×#924	C₂²	1	1	yes	characteristic
35	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
36	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic, complemented
37	C₅×#898	—	2	1	no	—
38	C₅×#892	C₂²	1	1	yes	characteristic, complemented
39	C₅×#890	—	2	1	no	—
40	C₅×#890	C₂²	1	1	yes	characteristic, complemented
41	C₅×#886	—	2	1	no	—
42	C₅×#877	—	2	1	no	—
43	C₃×C₅×#102	C₂²	1	1	yes	characteristic
44	C₃×C₅×#102	C₂²	1	1	yes	characteristic
45	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
46	C₅×#835	C₂²	1	1	yes	characteristic, complemented
47	C₅×#832	C₂²	1	1	yes	characteristic
48	C₅×#832	C₂²	1	1	yes	characteristic
49	C₅×#832	C₂²	1	1	yes	characteristic
50	C₅×#832	C₂²	1	1	yes	characteristic
51	C₅×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic, complemented
52	C₅×#817	C₂²	1	1	yes	characteristic, complemented
53	C₅×#817	C₂²	1	1	yes	characteristic, complemented
54	C₅×#816	C₂²	1	1	yes	characteristic, complemented
55	C₅×#816	C₂²	1	1	yes	characteristic, complemented
56	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
57	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
58	C₅×#810	C₂²	1	1	yes	characteristic, complemented
59	C₅×#807	C₂²	1	1	yes	characteristic, complemented
60	#80159	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
61	C₅×#552	—	3	1	no	—
62	C₅×#546	—	3	1	no	—
63	C₅×#488	—	3	1	no	—
64	C₅×#483	—	3	1	no	—
65	C₅×#482	—	3	1	no	—
66	C₅×#478	—	3	1	no	—
67	C₅×#467	—	3	1	no	—
68	C₅×#465	—	3	1	no	—
69	C₅×#464	—	3	1	no	—
70	C₅×#452	—	3	1	no	—
71	C₅×#450	D₃	1	1	yes	characteristic, complemented
72	C₄×C₅×SD₁₆	—	3	1	no	—
73	C₅×C₈×D₄	—	3	1	no	—
74	C₅×#416	—	3	1	no	—
75	C₂×C₅×#102	—	3	1	no	—
76	C₂⁴×C₃×C₅	—	2	1	no	—
77	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
78	C₂×C₃×C₅×D₄	—	2	2	no	—
79	C₂×C₃×C₅×D₄	—	2	1	no	—
80	C₂×C₃×C₅×D₄	—	4	1	no	—
81	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
82	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
83	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
84	C₂×C₅×#67	—	2	1	no	—
85	C₂×C₅×#67	—	2	1	no	—
86	C₂×C₅×#67	D₄	1	1	yes	characteristic
87	C₂²×C₅×Dic₃	—	2	1	no	—
88	C₂²×C₅×Dic₃	—	2	1	no	—
89	C₂²×C₅×Dic₃	—	2	1	no	—
90	C₅×#237	—	2	2	no	—
91	C₅×#237	—	4	1	no	—
92	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
93	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
94	C₃×C₅×SD₁₆	—	2	2	no	—
95	C₃×C₅×SD₁₆	—	4	1	no	—
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	C₂³	1	1	yes	characteristic
100	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
101	C₅×#217	—	2	1	no	—
102	C₅×#217	—	2	1	no	—
103	C₅×#217	—	2	1	no	—
104	C₅×#217	—	2	1	no	—
105	C₅×#217	—	2	1	no	—
106	C₅×#217	D₄	1	1	yes	characteristic
107	C₅×#216	—	4	1	no	—
108	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
109	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
110	C₅×(C₂×D₃)⋊C₄	D₄	1	1	yes	characteristic
111	C₅×C₄⋊Dic₃	—	2	1	no	—
112	C₅×C₄⋊Dic₃	—	2	1	no	—
113	C₅×C₄⋊Dic₃	—	2	1	no	—
114	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
115	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
116	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
117	C₅×Dic₃⋊C₄	—	2	1	no	—
118	C₅×Dic₃⋊C₄	—	2	1	no	—
119	C₅×Dic₃⋊C₄	—	2	1	no	—
120	C₅×Dic₃⋊C₄	D₄	1	1	yes	characteristic
121	C₄×C₅×Dic₃	—	2	1	no	—
122	C₄×C₅×Dic₃	—	2	1	no	—
123	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
124	C₂×C₅×C₃⋊C₈	—	4	1	no	—
125	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
126	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
127	C₅×D₃×C₈	—	4	1	no	—
128	#5806	C₂×C₅	1	1	yes	characteristic
129	#5642	C₂×C₅	1	1	yes	characteristic, complemented
130	C₃×#450	C₂×C₅	1	1	yes	characteristic, complemented
131	C₂×#832	C₂×C₅	1	1	yes	characteristic, complemented
132	#5173	C₂×C₅	1	1	yes	characteristic, complemented
133	#5171	C₂×C₅	1	1	yes	characteristic, complemented
134	#5166	C₂×C₅	1	1	yes	characteristic, complemented
135	Dic₃×SD₁₆	C₂×C₅	1	1	yes	characteristic, complemented
136	#5051	C₂×C₅	1	1	yes	characteristic, complemented
137	#4779	C₂×C₅	1	1	yes	characteristic, complemented
138	#4772	C₂×C₅	1	1	yes	characteristic, complemented
139	#4768	C₂×C₅	1	1	yes	characteristic, complemented
140	#4763	C₂×C₅	1	1	yes	characteristic, complemented
141	#67⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
142	#4721	C₂×C₅	1	1	yes	characteristic, complemented
143	C₂×C₅×#41	—	3	1	no	—
144	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
145	C₂×C₅×Q₁₆	—	3	1	no	—
146	C₂×C₅×SD₁₆	C₂×D₃	1	1	yes	characteristic
147	C₂×C₅×SD₁₆	C₂×D₃	1	1	yes	characteristic
148	C₂²×C₅×C₈	—	3	1	no	—
149	C₂²×C₅×C₈	—	3	1	no	—
150	C₅×#126	—	6	1	no	—
151	C₅×#125	—	3	1	no	—
152	C₅×#125	—	6	1	no	—
153	C₅×#124	—	3	1	no	—
154	C₅×#123	—	6	1	no	—
155	C₅×#123	—	6	1	no	—
156	C₅×C₂²⋊Q₈	—	3	1	no	—
157	C₅×C₂²⋊Q₈	—	3	1	no	—
158	C₅×C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic
159	C₅×#121	—	3	1	no	—
160	C₅×#121	—	6	1	no	—
161	C₅×#120	—	6	1	no	—
162	C₄×C₅×Q₈	—	3	1	no	—
163	C₄×C₅×D₄	—	3	1	no	—
164	C₄×C₅×D₄	—	3	1	no	—
165	C₅×#117	—	3	1	no	—
166	C₅×#117	—	6	1	no	—
167	C₂×C₅×C₄⋊C₄	—	3	1	no	—
168	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
169	C₅×#107	—	3	1	no	—
170	C₅×#106	—	3	1	no	—
171	C₅×#106	—	3	1	no	—
172	C₅×C₄⋊C₈	—	3	1	no	—
173	C₅×#103	—	3	1	no	—
174	C₅×#103	—	3	1	no	—
175	C₅×#103	—	3	1	no	—
176	C₅×#103	—	3	1	no	—
177	C₅×#102	—	3	1	no	—
178	C₅×#102	—	3	1	no	—
179	C₅×#102	—	3	1	no	—
180	C₅×#102	—	3	1	no	—
181	C₅×#102	C₂×D₃	1	1	yes	characteristic
182	C₅×#102	C₂×D₃	1	1	yes	characteristic
183	C₅×C₂²⋊C₈	—	3	1	no	—
184	C₅×C₂²⋊C₈	C₂×D₃	1	1	yes	characteristic
185	C₄×C₅×C₈	—	3	1	no	—
186	#3296	—	3	1	no	Sylow
187	C₂³×C₃×C₅	—	2	1	no	—
188	C₂³×C₃×C₅	—	2	1	no	—
189	C₂³×C₃×C₅	—	4	2	no	—
190	C₂³×C₃×C₅	—	4	2	no	—
191	C₂³×C₃×C₅	—	8	1	no	—
192	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
193	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
194	C₃×C₅×Q₈	—	2	1	no	—
195	C₃×C₅×Q₈	—	2	1	no	—
196	C₃×C₅×D₄	—	2	1	no	—
197	C₃×C₅×D₄	—	2	1	no	—
198	C₃×C₅×D₄	—	2	1	no	—
199	C₃×C₅×D₄	—	4	2	no	—
200	C₃×C₅×D₄	#41	1	2	yes	—
201	C₂×C₃×C₄×C₅	—	2	1	no	—
202	C₂×C₃×C₄×C₅	—	2	1	no	—
203	C₂×C₃×C₄×C₅	—	2	1	no	—
204	C₂×C₃×C₄×C₅	—	2	1	no	—
205	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
206	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
207	C₅×#67	—	2	2	no	—
208	C₅×#67	—	4	2	no	—
209	C₅×#67	—	8	1	no	—
210	C₂×C₅×Dic₃	—	2	1	no	—
211	C₂×C₅×Dic₃	—	2	1	no	—
212	C₂×C₅×Dic₃	—	2	1	no	—
213	C₂×C₅×Dic₃	—	2	1	no	—
214	C₂×C₅×Dic₃	—	4	2	no	—
215	C₂×C₅×Dic₃	—	4	2	no	—
216	C₂×C₅×Dic₃	—	8	1	no	—
217	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
218	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
219	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
220	C₄×C₅×D₃	—	2	1	no	—
221	C₄×C₅×D₃	—	2	1	no	—
222	C₅×Dic₆	—	2	1	no	—
223	C₅×Dic₆	—	2	1	no	—
224	C₃×C₅×C₈	—	2	1	no	—
225	C₃×C₅×C₈	—	2	1	no	—
226	C₅×C₃⋊C₈	—	2	1	no	—
227	C₅×C₃⋊C₈	—	2	1	no	—
228	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
229	C₂×#237	C₂²×C₅	1	1	yes	characteristic
230	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
231	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
232	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
233	#953	—	2	1	no	—
234	C₂×#217	—	2	1	no	—
235	#946	C₂²×C₅	1	1	yes	characteristic, complemented
236	Q₈×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
237	C₂×#216	C₂²×C₅	1	1	yes	characteristic, complemented
238	#939	—	2	1	no	—
239	#938	C₂²×C₅	1	1	yes	characteristic
240	#936	C₂²×C₅	1	1	yes	characteristic
241	#935	—	2	1	no	—
242	D₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
243	C₄×#67	C₂²×C₅	1	1	yes	characteristic
244	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
245	#924	C₂²×C₅	1	1	yes	characteristic
246	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
247	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
248	#898	—	2	1	no	—
249	#892	C₂²×C₅	1	1	yes	characteristic, complemented
250	#890	—	2	1	no	—
251	#890	C₂²×C₅	1	1	yes	characteristic, complemented
252	#886	—	2	1	no	—
253	#877	—	2	1	no	—
254	C₃×#102	C₂²×C₅	1	1	yes	characteristic
255	C₃×#102	C₂²×C₅	1	1	yes	characteristic
256	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
257	#835	C₂²×C₅	1	1	yes	characteristic, complemented
258	#832	C₂²×C₅	1	1	yes	characteristic
259	#832	C₂²×C₅	1	1	yes	characteristic
260	#832	C₂²×C₅	1	1	yes	characteristic
261	#832	C₂²×C₅	1	1	yes	characteristic
262	(C₂×D₃)⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
263	#817	C₂²×C₅	1	1	yes	characteristic, complemented
264	#817	C₂²×C₅	1	1	yes	characteristic, complemented
265	#816	C₂²×C₅	1	1	yes	characteristic, complemented
266	#816	C₂²×C₅	1	1	yes	characteristic, complemented
267	Dic₃⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
268	C₈×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
269	#810	C₂²×C₅	1	1	yes	characteristic, complemented
270	#807	C₂²×C₅	1	1	yes	characteristic, complemented
271	C₂⁴×C₅	—	2	1	no	—
272	C₅×#41	—	6	2	no	—
273	C₅×#41	—	12	1	no	—
274	C₂×C₅×Q₈	—	3	1	no	—
275	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
276	C₂×C₅×D₄	—	2	2	no	—
277	C₂×C₅×D₄	—	2	1	no	—
278	C₂×C₅×D₄	—	3	1	no	—
279	C₂×C₅×D₄	—	4	1	no	—
280	C₂×C₅×D₄	—	6	1	no	—
281	C₂×C₅×D₄	—	6	1	no	—
282	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
283	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
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	C₂²×D₃	1	1	yes	characteristic
289	C₅×Q₁₆	—	12	1	no	—
290	C₅×SD₁₆	—	2	2	no	—
291	C₅×SD₁₆	—	4	1	no	—
292	C₂×C₅×C₈	—	3	1	no	—
293	C₂×C₅×C₈	—	3	1	no	—
294	C₂×C₅×C₈	—	12	1	no	—
295	C₂×C₅×C₈	—	12	1	no	—
296	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
297	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
298	C₅×C₄⋊C₄	—	2	1	no	—
299	C₅×C₄⋊C₄	—	3	1	no	—
300	C₅×C₄⋊C₄	—	3	1	no	—
301	C₅×C₄⋊C₄	—	3	1	no	—
302	C₅×C₄⋊C₄	—	3	1	no	—
303	C₅×C₄⋊C₄	—	6	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×C₂²⋊C₄	—	2	1	no	—
311	C₅×C₂²⋊C₄	—	3	1	no	—
312	C₅×C₂²⋊C₄	—	3	1	no	—
313	C₅×C₂²⋊C₄	—	6	1	no	—
314	C₅×C₂²⋊C₄	—	6	1	no	—
315	C₅×C₂²⋊C₄	—	6	1	no	—
316	C₅×C₂²⋊C₄	—	6	1	no	—
317	C₅×C₂²⋊C₄	—	6	1	no	—
318	C₅×C₂²⋊C₄	—	6	1	no	—
319	C₅×C₂²⋊C₄	—	6	1	no	—
320	C₄²×C₅	—	3	1	no	—
321	C₄²×C₅	—	6	1	no	—
322	C₄²×C₅	—	6	1	no	—
323	#552	—	3	1	no	—
324	#546	—	3	1	no	—
325	#488	—	3	1	no	—
326	#483	—	3	1	no	—
327	#482	—	3	1	no	—
328	#478	—	3	1	no	—
329	#467	—	3	1	no	—
330	#465	—	3	1	no	—
331	#464	—	3	1	no	—
332	#452	—	3	1	no	—
333	#450	C₅×D₃	1	1	yes	characteristic, complemented
334	C₄×SD₁₆	—	3	1	no	—
335	C₈×D₄	—	3	1	no	—
336	#416	—	3	1	no	—
337	C₂×#102	—	3	1	no	—
338	C₂²×C₃×C₅	—	2	1	no	—
339	C₂²×C₃×C₅	—	2	1	no	—
340	C₂²×C₃×C₅	—	2	2	no	—
341	C₂²×C₃×C₅	—	4	1	no	—
342	C₂²×C₃×C₅	—	4	1	no	—
343	C₂²×C₃×C₅	—	4	1	no	—
344	C₂²×C₃×C₅	—	4	1	no	—
345	C₂²×C₃×C₅	—	4	1	no	—
346	C₂²×C₃×C₅	—	8	4	no	—
347	C₂²×C₃×C₅	#135	1	2	yes	—
348	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
349	C₂×C₅×D₃	—	2	1	no	—
350	C₂×C₅×D₃	—	2	1	no	—
351	C₂×C₅×D₃	—	2	1	no	—
352	C₃×C₄×C₅	—	2	1	no	—
353	C₃×C₄×C₅	—	4	1	no	—
354	C₃×C₄×C₅	—	4	1	no	—
355	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
356	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
357	C₅×Dic₃	—	2	1	no	—
358	C₅×Dic₃	—	2	1	no	—
359	C₅×Dic₃	—	2	1	no	—
360	C₅×Dic₃	—	4	1	no	—
361	C₅×Dic₃	—	4	1	no	—
362	C₅×Dic₃	—	4	1	no	—
363	C₅×Dic₃	—	4	1	no	—
364	C₂⁴×C₃	—	2	1	no	—
365	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
366	C₂×C₃×D₄	—	2	2	no	—
367	C₂×C₃×D₄	—	2	1	no	—
368	C₂×C₃×D₄	—	4	1	no	—
369	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
370	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
371	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
372	C₂×#67	—	2	1	no	—
373	C₂×#67	—	2	1	no	—
374	C₂×#67	C₅×D₄	1	1	yes	characteristic
375	C₂²×Dic₃	—	2	1	no	—
376	C₂²×Dic₃	—	2	1	no	—
377	C₂²×Dic₃	—	2	1	no	—
378	#237	—	2	2	no	—
379	#237	—	4	1	no	—
380	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
381	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
382	C₃×SD₁₆	—	2	2	no	—
383	C₃×SD₁₆	—	4	1	no	—
384	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
385	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
386	C₃×C₄⋊C₄	—	2	1	no	—
387	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
388	C₃×C₂²⋊C₄	—	2	1	no	—
389	#217	—	2	1	no	—
390	#217	—	2	1	no	—
391	#217	—	2	1	no	—
392	#217	—	2	1	no	—
393	#217	—	2	1	no	—
394	#217	C₅×D₄	1	1	yes	characteristic
395	#216	—	4	1	no	—
396	(C₂×D₃)⋊C₄	—	2	1	no	—
397	(C₂×D₃)⋊C₄	—	2	1	no	—
398	(C₂×D₃)⋊C₄	C₅×D₄	1	1	yes	characteristic
399	C₄⋊Dic₃	—	2	1	no	—
400	C₄⋊Dic₃	—	2	1	no	—
401	C₄⋊Dic₃	—	2	1	no	—
402	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
403	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
404	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
405	Dic₃⋊C₄	—	2	1	no	—
406	Dic₃⋊C₄	—	2	1	no	—
407	Dic₃⋊C₄	—	2	1	no	—
408	Dic₃⋊C₄	C₅×D₄	1	1	yes	characteristic
409	C₄×Dic₃	—	2	1	no	—
410	C₄×Dic₃	—	2	1	no	—
411	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
412	C₂×C₃⋊C₈	—	4	1	no	—
413	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
414	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
415	D₃×C₈	—	4	1	no	—
416	C₂³×C₅	—	2	1	no	—
417	C₂³×C₅	—	2	1	no	—
418	C₂³×C₅	—	3	1	no	—
419	C₂³×C₅	—	4	2	no	—
420	C₂³×C₅	—	4	2	no	—
421	C₂³×C₅	—	8	1	no	—
422	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
423	C₅×Q₈	—	2	1	no	—
424	C₅×Q₈	—	2	1	no	—
425	C₅×Q₈	—	6	1	no	—
426	C₅×Q₈	—	6	1	no	—
427	C₅×D₄	—	2	1	no	—
428	C₅×D₄	—	2	1	no	—
429	C₅×D₄	—	2	1	no	—
430	C₅×D₄	—	4	2	no	—
431	C₅×D₄	—	6	2	no	—
432	C₅×D₄	—	12	2	no	—
433	C₅×D₄	—	24	1	no	—
434	C₅×D₄	#237	1	2	yes	—
435	C₂×C₄×C₅	—	2	1	no	—
436	C₂×C₄×C₅	—	2	1	no	—
437	C₂×C₄×C₅	—	2	1	no	—
438	C₂×C₄×C₅	—	2	1	no	—
439	C₂×C₄×C₅	—	3	1	no	—
440	C₂×C₄×C₅	—	3	1	no	—
441	C₂×C₄×C₅	—	3	1	no	—
442	C₂×C₄×C₅	—	6	1	no	—
443	C₂×C₄×C₅	—	6	1	no	—
444	C₂×C₄×C₅	—	6	1	no	—
445	C₂×C₄×C₅	—	6	1	no	—
446	C₂×C₄×C₅	—	6	1	no	—
447	C₂×C₄×C₅	—	6	1	no	—
448	C₂×C₄×C₅	—	12	2	no	—
449	C₂×C₄×C₅	—	12	2	no	—
450	C₂×C₄×C₅	—	24	1	no	—
451	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
452	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
453	C₅×C₈	—	2	1	no	—
454	C₅×C₈	—	2	1	no	—
455	C₅×C₈	—	6	1	no	—
456	C₅×C₈	—	6	1	no	—
457	C₂×#41	—	3	1	no	—
458	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
459	C₂×Q₁₆	—	3	1	no	—
460	C₂×SD₁₆	C₂×C₅×D₃	1	1	yes	characteristic
461	C₂×SD₁₆	C₂×C₅×D₃	1	1	yes	characteristic
462	C₂²×C₈	—	3	1	no	—
463	C₂²×C₈	—	3	1	no	—
464	#126	—	6	1	no	—
465	#125	—	3	1	no	—
466	#125	—	6	1	no	—
467	#124	—	3	1	no	—
468	#123	—	6	1	no	—
469	#123	—	6	1	no	—
470	C₂²⋊Q₈	—	3	1	no	—
471	C₂²⋊Q₈	—	3	1	no	—
472	C₂²⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic
473	#121	—	3	1	no	—
474	#121	—	6	1	no	—
475	#120	—	6	1	no	—
476	C₄×Q₈	—	3	1	no	—
477	C₄×D₄	—	3	1	no	—
478	C₄×D₄	—	3	1	no	—
479	#117	—	3	1	no	—
480	#117	—	6	1	no	—
481	C₂×C₄⋊C₄	—	3	1	no	—
482	C₂×C₂²⋊C₄	—	6	1	no	—
483	#107	—	3	1	no	—
484	#106	—	3	1	no	—
485	#106	—	3	1	no	—
486	C₄⋊C₈	—	3	1	no	—
487	#103	—	3	1	no	—
488	#103	—	3	1	no	—
489	#103	—	3	1	no	—
490	#103	—	3	1	no	—
491	#102	—	3	1	no	—
492	#102	—	3	1	no	—
493	#102	—	3	1	no	—
494	#102	—	3	1	no	—
495	#102	C₂×C₅×D₃	1	1	yes	characteristic
496	#102	C₂×C₅×D₃	1	1	yes	characteristic
497	C₂²⋊C₈	—	3	1	no	—
498	C₂²⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
499	C₄×C₈	—	3	1	no	—
500	C₂×C₃×C₅	—	2	2	no	—
501	C₂×C₃×C₅	—	4	2	no	—
502	C₂×C₃×C₅	—	8	1	no	—
503	C₂×C₃×C₅	#546	1	1	yes	characteristic
504	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
505	C₂×C₃×C₅	#577	1	1	yes	characteristic
506	C₅×D₃	—	4	1	no	—
507	C₂³×C₃	—	2	1	no	—
508	C₂³×C₃	—	2	1	no	—
509	C₂³×C₃	—	4	2	no	—
510	C₂³×C₃	—	4	2	no	—
511	C₂³×C₃	—	8	1	no	—
512	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
513	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
514	C₃×Q₈	—	2	1	no	—
515	C₃×Q₈	—	2	1	no	—
516	C₃×D₄	—	2	1	no	—
517	C₃×D₄	—	2	1	no	—
518	C₃×D₄	—	2	1	no	—
519	C₃×D₄	—	4	2	no	—
520	C₃×D₄	C₅×#41	1	2	yes	—
521	C₂×C₃×C₄	—	2	1	no	—
522	C₂×C₃×C₄	—	2	1	no	—
523	C₂×C₃×C₄	—	2	1	no	—
524	C₂×C₃×C₄	—	2	1	no	—
525	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
526	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
527	#67	—	2	2	no	—
528	#67	—	4	2	no	—
529	#67	—	8	1	no	—
530	C₂×Dic₃	—	2	1	no	—
531	C₂×Dic₃	—	2	1	no	—
532	C₂×Dic₃	—	2	1	no	—
533	C₂×Dic₃	—	2	1	no	—
534	C₂×Dic₃	—	4	2	no	—
535	C₂×Dic₃	—	4	2	no	—
536	C₂×Dic₃	—	8	1	no	—
537	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
538	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
539	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
540	C₄×D₃	—	2	1	no	—
541	C₄×D₃	—	2	1	no	—
542	Dic₆	—	2	1	no	—
543	Dic₆	—	2	1	no	—
544	C₃×C₈	—	2	1	no	—
545	C₃×C₈	—	2	1	no	—
546	C₃⋊C₈	—	2	1	no	—
547	C₃⋊C₈	—	2	1	no	—
548	C₂²×C₅	—	2	1	no	—
549	C₂²×C₅	—	2	1	no	—
550	C₂²×C₅	—	2	2	no	—
551	C₂²×C₅	—	4	1	no	—
552	C₂²×C₅	—	4	1	no	—
553	C₂²×C₅	—	4	1	no	—
554	C₂²×C₅	—	4	1	no	—
555	C₂²×C₅	—	4	1	no	—
556	C₂²×C₅	—	6	1	no	—
557	C₂²×C₅	—	6	1	no	—
558	C₂²×C₅	—	6	1	no	—
559	C₂²×C₅	—	8	4	no	—
560	C₂²×C₅	#916	1	2	yes	—
561	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
562	C₄×C₅	—	2	1	no	—
563	C₄×C₅	—	4	1	no	—
564	C₄×C₅	—	4	1	no	—
565	C₄×C₅	—	6	1	no	—
566	C₄×C₅	—	6	1	no	—
567	C₄×C₅	—	6	1	no	—
568	C₄×C₅	—	12	1	no	—
569	C₄×C₅	—	12	1	no	—
570	C₄×C₅	—	12	1	no	—
571	C₄×C₅	—	12	1	no	—
572	C₄×C₅	C₂×#237	1	1	yes	characteristic
573	C₄×C₅	#1004	1	1	yes	characteristic
574	C₂⁴	—	2	1	no	—
575	#41	—	6	2	no	—
576	#41	—	12	1	no	—
577	C₂×Q₈	—	3	1	no	—
578	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
579	C₂×D₄	—	2	2	no	—
580	C₂×D₄	—	2	1	no	—
581	C₂×D₄	—	3	1	no	—
582	C₂×D₄	—	4	1	no	—
583	C₂×D₄	—	6	1	no	—
584	C₂×D₄	—	6	1	no	—
585	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
586	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
587	C₂²×C₄	—	3	1	no	—
588	C₂²×C₄	—	6	1	no	—
589	C₂²×C₄	—	6	1	no	—
590	C₂²×C₄	—	6	1	no	—
591	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
592	Q₁₆	—	12	1	no	—
593	SD₁₆	—	2	2	no	—
594	SD₁₆	—	4	1	no	—
595	C₂×C₈	—	3	1	no	—
596	C₂×C₈	—	3	1	no	—
597	C₂×C₈	—	12	1	no	—
598	C₂×C₈	—	12	1	no	—
599	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
600	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
601	C₄⋊C₄	—	2	1	no	—
602	C₄⋊C₄	—	3	1	no	—
603	C₄⋊C₄	—	3	1	no	—
604	C₄⋊C₄	—	3	1	no	—
605	C₄⋊C₄	—	3	1	no	—
606	C₄⋊C₄	—	6	1	no	—
607	C₄⋊C₄	—	6	1	no	—
608	C₄⋊C₄	—	6	1	no	—
609	C₄⋊C₄	—	6	1	no	—
610	C₄⋊C₄	—	6	1	no	—
611	C₄⋊C₄	—	6	1	no	—
612	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
613	C₂²⋊C₄	—	2	1	no	—
614	C₂²⋊C₄	—	3	1	no	—
615	C₂²⋊C₄	—	3	1	no	—
616	C₂²⋊C₄	—	6	1	no	—
617	C₂²⋊C₄	—	6	1	no	—
618	C₂²⋊C₄	—	6	1	no	—
619	C₂²⋊C₄	—	6	1	no	—
620	C₂²⋊C₄	—	6	1	no	—
621	C₂²⋊C₄	—	6	1	no	—
622	C₂²⋊C₄	—	6	1	no	—
623	C₄²	—	3	1	no	—
624	C₄²	—	6	1	no	—
625	C₄²	—	6	1	no	—
626	C₃×C₅	#3296	1	1	yes	characteristic, complemented, Hall
627	C₂²×C₃	—	2	1	no	—
628	C₂²×C₃	—	2	1	no	—
629	C₂²×C₃	—	2	2	no	—
630	C₂²×C₃	—	4	1	no	—
631	C₂²×C₃	—	4	1	no	—
632	C₂²×C₃	—	4	1	no	—
633	C₂²×C₃	—	4	1	no	—
634	C₂²×C₃	—	4	1	no	—
635	C₂²×C₃	—	8	4	no	—
636	C₂²×C₃	C₅×#135	1	2	yes	—
637	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
638	C₂×D₃	—	2	1	no	—
639	C₂×D₃	—	2	1	no	—
640	C₂×D₃	—	2	1	no	—
641	C₃×C₄	—	2	1	no	—
642	C₃×C₄	—	4	1	no	—
643	C₃×C₄	—	4	1	no	—
644	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
645	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
646	Dic₃	—	2	1	no	—
647	Dic₃	—	2	1	no	—
648	Dic₃	—	2	1	no	—
649	Dic₃	—	4	1	no	—
650	Dic₃	—	4	1	no	—
651	Dic₃	—	4	1	no	—
652	Dic₃	—	4	1	no	—
653	C₂×C₅	—	2	2	no	—
654	C₂×C₅	—	4	2	no	—
655	C₂×C₅	—	8	1	no	—
656	C₂×C₅	—	12	1	no	—
657	C₂×C₅	#5591	1	1	yes	characteristic
658	C₂×C₅	C₂×#916	1	1	yes	characteristic
659	C₂×C₅	#5775	1	1	yes	characteristic
660	C₂³	—	2	1	no	—
661	C₂³	—	2	1	no	—
662	C₂³	—	3	1	no	—
663	C₂³	—	4	2	no	—
664	C₂³	—	4	2	no	—
665	C₂³	—	8	1	no	—
666	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
667	Q₈	—	2	1	no	—
668	Q₈	—	2	1	no	—
669	Q₈	—	6	1	no	—
670	Q₈	—	6	1	no	—
671	D₄	—	2	1	no	—
672	D₄	—	2	1	no	—
673	D₄	—	2	1	no	—
674	D₄	—	4	2	no	—
675	D₄	—	6	2	no	—
676	D₄	—	12	2	no	—
677	D₄	—	24	1	no	—
678	D₄	C₅×#237	1	2	yes	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	3	1	no	—
684	C₂×C₄	—	3	1	no	—
685	C₂×C₄	—	3	1	no	—
686	C₂×C₄	—	6	1	no	—
687	C₂×C₄	—	6	1	no	—
688	C₂×C₄	—	6	1	no	—
689	C₂×C₄	—	6	1	no	—
690	C₂×C₄	—	6	1	no	—
691	C₂×C₄	—	6	1	no	—
692	C₂×C₄	—	12	2	no	—
693	C₂×C₄	—	12	2	no	—
694	C₂×C₄	—	24	1	no	—
695	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
696	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
697	C₈	—	2	1	no	—
698	C₈	—	2	1	no	—
699	C₈	—	6	1	no	—
700	C₈	—	6	1	no	—
701	C₂×C₃	—	2	2	no	—
702	C₂×C₃	—	4	2	no	—
703	C₂×C₃	—	8	1	no	—
704	C₂×C₃	C₅×#546	1	1	yes	characteristic
705	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
706	C₂×C₃	C₅×#577	1	1	yes	characteristic
707	D₃	—	4	1	no	—
708	C₅	#80159	1	1	yes	characteristic, direct product factor, Sylow
709	C₂²	—	2	1	no	—
710	C₂²	—	2	1	no	—
711	C₂²	—	2	2	no	—
712	C₂²	—	4	1	no	—
713	C₂²	—	4	1	no	—
714	C₂²	—	4	1	no	—
715	C₂²	—	4	1	no	—
716	C₂²	—	4	1	no	—
717	C₂²	—	6	1	no	—
718	C₂²	—	6	1	no	—
719	C₂²	—	6	1	no	—
720	C₂²	—	8	4	no	—
721	C₂²	C₅×#916	1	2	yes	—
722	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
723	C₄	—	2	1	no	—
724	C₄	—	4	1	no	—
725	C₄	—	4	1	no	—
726	C₄	—	6	1	no	—
727	C₄	—	6	1	no	—
728	C₄	—	6	1	no	—
729	C₄	—	12	1	no	—
730	C₄	—	12	1	no	—
731	C₄	—	12	1	no	—
732	C₄	—	12	1	no	—
733	C₄	C₂×C₅×#237	1	1	yes	characteristic
734	C₄	C₅×#1004	1	1	yes	characteristic
735	C₃	C₅×#3296	1	1	yes	characteristic, complemented, Sylow
736	C₂	—	2	2	no	—
737	C₂	—	4	2	no	—
738	C₂	—	8	1	no	—
739	C₂	—	12	1	no	—
740	C₂	C₅×#5591	1	1	yes	characteristic
741	C₂	C₂×C₅×#916	1	1	yes	characteristic
742	C₂	C₅×#5775	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂×D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#450	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₅×#5806	C₂
hypercenter	C₅×#450	D₃
hypocenter	C₃	C₅×#3296
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#450

Complements

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

N	H ≅ G/N	type
2. C₅×#5642	C₂	semidirect
3. C₃×C₅×#450	C₂	semidirect
4. C₂×C₅×#832	C₂	semidirect
5. C₅×#5173	C₂	semidirect
6. C₅×#5171	C₂	semidirect
7. C₅×#5166	C₂	semidirect
8. C₅×Dic₃×SD₁₆	C₂	semidirect
9. C₅×#5051	C₂	semidirect
10. C₅×#4779	C₂	semidirect
11. C₅×#4772	C₂	semidirect
12. C₅×#4768	C₂	semidirect
13. C₅×#4763	C₂	semidirect
14. C₅×#67⋊C₈	C₂	semidirect
15. C₅×#4721	C₂	semidirect
24. C₅×#946	C₂²	semidirect
25. C₅×Q₈×Dic₃	C₂²	semidirect
26. C₂×C₅×#216	C₂²	semidirect
36. C₂×C₅×D₃×C₈	C₂²	semidirect
38. C₅×#892	C₂²	semidirect
40. C₅×#890	C₂²	semidirect
46. C₅×#835	C₂²	semidirect
51. C₅×(C₂×D₃)⋊C₈	C₂²	semidirect
52. C₅×#817	C₂²	semidirect
53. C₅×#817	C₂²	semidirect
54. C₅×#816	C₂²	semidirect
55. C₅×#816	C₂²	semidirect
56. C₅×Dic₃⋊C₈	C₂²	semidirect
57. C₅×C₈×Dic₃	C₂²	semidirect
58. C₅×#810	C₂²	semidirect
59. C₅×#807	C₂²	semidirect
60. #80159	C₅	direct (N × H)
71. C₅×#450	D₃	semidirect
129. #5642	C₂×C₅	semidirect
130. C₃×#450	C₂×C₅	semidirect
131. C₂×#832	C₂×C₅	semidirect
132. #5173	C₂×C₅	semidirect
133. #5171	C₂×C₅	semidirect
134. #5166	C₂×C₅	semidirect
135. Dic₃×SD₁₆	C₂×C₅	semidirect
136. #5051	C₂×C₅	semidirect
137. #4779	C₂×C₅	semidirect
138. #4772	C₂×C₅	semidirect
139. #4768	C₂×C₅	semidirect
140. #4763	C₂×C₅	semidirect
141. #67⋊C₈	C₂×C₅	semidirect
142. #4721	C₂×C₅	semidirect
235. #946	C₂²×C₅	semidirect
236. Q₈×Dic₃	C₂²×C₅	semidirect
237. C₂×#216	C₂²×C₅	semidirect
247. C₂×D₃×C₈	C₂²×C₅	semidirect
249. #892	C₂²×C₅	semidirect
251. #890	C₂²×C₅	semidirect
257. #835	C₂²×C₅	semidirect
262. (C₂×D₃)⋊C₈	C₂²×C₅	semidirect
263. #817	C₂²×C₅	semidirect
264. #817	C₂²×C₅	semidirect
265. #816	C₂²×C₅	semidirect
266. #816	C₂²×C₅	semidirect
267. Dic₃⋊C₈	C₂²×C₅	semidirect
268. C₈×Dic₃	C₂²×C₅	semidirect
269. #810	C₂²×C₅	semidirect
270. #807	C₂²×C₅	semidirect
333. #450	C₅×D₃	semidirect
626. C₃×C₅	#3296	semidirect
708. C₅	#80159	direct (N × H)
735. C₃	C₅×#3296	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5806	2
C₅×#5642	2
C₃×C₅×#450	2
C₂×C₅×#832	2
C₅×#5173	2
C₅×#5171	2
C₅×#5166	2
C₅×Dic₃×SD₁₆	2
C₅×#5051	2
C₅×#4779	2
C₅×#4772	2
C₅×#4768	2
C₅×#4763	2
C₅×#67⋊C₈	2
C₅×#4721	2
C₅×#3296	3
#80159	5

Subgroups — C5×#80159 #14458623

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#80159 #14458623