Subgroups — C₅×#81013 #14430918

Order 1920.

724 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5729	C₂	1	1	yes	maximal, characteristic
2	C₅×#5572	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#475	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5091	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5022	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4861	C₂	1	1	yes	maximal, characteristic
7	C₅×#4860	C₂	1	1	yes	maximal, characteristic
8	C₅×#4857	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#4854	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4839	C₂	1	1	yes	maximal, characteristic
11	C₅×#4829	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#4802	C₂	1	1	yes	maximal, characteristic
13	C₅×D₃×#103	C₂	1	1	yes	maximal, characteristic
14	C₅×#4799	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#4793	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3082	—	3	1	no	maximal, Hall
17	C₂×C₅×D₃×Q₈	C₂²	1	1	yes	characteristic
18	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
20	C₅×#946	—	2	1	no	—
21	C₅×Q₈×Dic₃	C₂²	1	1	yes	characteristic
22	C₅×#944	—	2	1	no	—
23	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
24	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
25	C₅×#896	—	2	1	no	—
26	C₅×#892	—	2	1	no	—
27	C₅×#892	C₂²	1	1	yes	characteristic
28	C₅×#892	C₂²	1	1	yes	characteristic
29	C₅×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₅×#890	C₂²	1	1	yes	characteristic
31	C₅×#889	—	2	1	no	—
32	C₅×#888	C₂²	1	1	yes	characteristic
33	C₅×#887	—	2	1	no	—
34	C₅×#887	C₂²	1	1	yes	characteristic
35	C₅×#872	—	2	1	no	—
36	C₅×#872	C₂²	1	1	yes	characteristic
37	C₅×#870	C₂²	1	1	yes	characteristic
38	C₄×C₅×Dic₆	—	2	1	no	—
39	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
40	C₃×C₅×#106	C₂²	1	1	yes	characteristic
41	C₃×C₅×#106	C₂²	1	1	yes	characteristic
42	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
43	C₃×C₅×#103	C₂²	1	1	yes	characteristic
44	C₃×C₅×#103	C₂²	1	1	yes	characteristic
45	C₅×#835	C₂²	1	1	yes	characteristic
46	C₅×#835	C₂²	1	1	yes	characteristic
47	C₅×#818	C₂²	1	1	yes	characteristic
48	C₅×#817	C₂²	1	1	yes	characteristic
49	C₅×#816	C₂²	1	1	yes	characteristic
50	C₅×#816	C₂²	1	1	yes	characteristic
51	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
52	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
53	C₅×#810	C₂²	1	1	yes	characteristic
54	C₅×#810	C₂²	1	1	yes	characteristic
55	C₅×#808	C₂²	1	1	yes	characteristic
56	C₅×#807	C₂²	1	1	yes	characteristic
57	C₅×#807	C₂²	1	1	yes	characteristic
58	C₅×#807	C₂²	1	1	yes	characteristic
59	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
60	#81013	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
61	C₅×#544	—	3	1	no	—
62	C₅×#519	—	3	1	no	—
63	C₅×#479	—	3	1	no	—
64	C₅×#479	—	3	1	no	—
65	C₅×#479	—	3	1	no	—
66	C₅×#479	—	3	1	no	—
67	C₅×#477	—	3	1	no	—
68	C₅×#477	—	3	1	no	—
69	C₅×#475	—	3	1	no	—
70	C₅×#475	D₃	1	1	yes	characteristic, complemented
71	C₅×#428	—	3	1	no	—
72	C₅×#427	—	3	1	no	—
73	C₅×#424	—	3	1	no	—
74	C₅×#419	—	3	1	no	—
75	C₂×C₅×#103	—	3	1	no	—
76	C₂×C₃×C₅×Q₈	—	2	1	no	—
77	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
78	C₅×D₃×Q₈	—	2	2	no	—
79	C₅×D₃×Q₈	Q₈	1	4	yes	complemented
80	C₂×C₄×C₅×D₃	—	2	1	no	—
81	C₂×C₄×C₅×D₃	—	2	1	no	—
82	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
83	C₂×C₅×Dic₆	—	2	1	no	—
84	C₂×C₅×Dic₆	—	2	1	no	—
85	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
86	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
87	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
88	C₃×C₅×C₄⋊C₄	—	2	1	no	—
89	C₃×C₅×C₄⋊C₄	—	2	1	no	—
90	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
91	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
92	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
93	C₃×C₄²×C₅	—	2	1	no	—
94	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
95	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
96	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
97	C₅×(C₂×D₃)⋊C₄	D₄	1	1	yes	characteristic
98	C₅×(C₂×D₃)⋊C₄	D₄	1	1	yes	characteristic
99	C₅×C₄⋊Dic₃	—	2	1	no	—
100	C₅×C₄⋊Dic₃	—	2	1	no	—
101	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
102	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
103	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
104	C₅×Dic₃⋊C₄	—	2	1	no	—
105	C₅×Dic₃⋊C₄	—	2	1	no	—
106	C₅×Dic₃⋊C₄	—	2	1	no	—
107	C₅×Dic₃⋊C₄	—	2	1	no	—
108	C₅×Dic₃⋊C₄	—	2	1	no	—
109	C₅×Dic₃⋊C₄	—	2	1	no	—
110	C₅×Dic₃⋊C₄	—	2	1	no	—
111	C₅×Dic₃⋊C₄	D₄	1	1	yes	characteristic
112	C₅×Dic₃⋊C₄	D₄	1	1	yes	characteristic
113	C₄×C₅×Dic₃	—	2	1	no	—
114	C₄×C₅×Dic₃	—	2	1	no	—
115	C₄×C₅×Dic₃	—	2	1	no	—
116	C₄×C₅×Dic₃	—	2	1	no	—
117	C₄×C₅×Dic₃	—	2	1	no	—
118	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
119	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
120	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
121	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
122	C₅×D₃×C₈	—	2	2	no	—
123	#5729	C₂×C₅	1	1	yes	characteristic
124	#5572	C₂×C₅	1	1	yes	characteristic
125	C₃×#475	C₂×C₅	1	1	yes	characteristic, complemented
126	#5091	C₂×C₅	1	1	yes	characteristic, complemented
127	#5022	C₂×C₅	1	1	yes	characteristic, complemented
128	#4861	C₂×C₅	1	1	yes	characteristic
129	#4860	C₂×C₅	1	1	yes	characteristic
130	#4857	C₂×C₅	1	1	yes	characteristic, complemented
131	#4854	C₂×C₅	1	1	yes	characteristic, complemented
132	#4839	C₂×C₅	1	1	yes	characteristic
133	#4829	C₂×C₅	1	1	yes	characteristic, complemented
134	#4802	C₂×C₅	1	1	yes	characteristic
135	D₃×#103	C₂×C₅	1	1	yes	characteristic
136	#4799	C₂×C₅	1	1	yes	characteristic, complemented
137	#4793	C₂×C₅	1	1	yes	characteristic, complemented
138	C₂²×C₅×Q₈	—	3	1	no	—
139	C₂×C₅×M₁₆	—	3	1	no	—
140	C₂²×C₅×C₈	—	3	1	no	—
141	C₅×C₄⋊Q₈	—	3	1	no	—
142	C₅×C₄⋊Q₈	—	6	1	no	—
143	C₅×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic
144	C₅×#125	—	3	1	no	—
145	C₅×#125	—	3	1	no	—
146	C₅×#125	—	6	1	no	—
147	C₅×C₂²⋊Q₈	—	6	1	no	—
148	C₅×C₂²⋊Q₈	—	6	1	no	—
149	C₄×C₅×Q₈	—	3	1	no	—
150	C₄×C₅×Q₈	—	3	1	no	—
151	C₄×C₅×Q₈	—	3	1	no	—
152	C₄×C₅×Q₈	—	6	1	no	—
153	C₄×C₅×Q₈	—	6	1	no	—
154	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
155	C₅×#117	—	3	1	no	—
156	C₅×#117	—	3	1	no	—
157	C₅×#117	—	3	1	no	—
158	C₅×#117	—	6	1	no	—
159	C₅×#117	—	6	1	no	—
160	C₂×C₅×C₄⋊C₄	—	3	1	no	—
161	C₅×#107	—	3	1	no	—
162	C₅×#107	—	3	1	no	—
163	C₅×#107	—	3	1	no	—
164	C₅×#107	—	3	1	no	—
165	C₅×#106	—	3	1	no	—
166	C₅×#106	—	3	1	no	—
167	C₅×#106	C₂×D₃	1	1	yes	characteristic
168	C₅×#106	C₂×D₃	1	1	yes	characteristic
169	C₅×C₄⋊C₈	—	3	1	no	—
170	C₅×C₄⋊C₈	—	3	1	no	—
171	C₅×C₄⋊C₈	—	3	1	no	—
172	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
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×#103	—	3	1	no	—
178	C₅×#103	—	3	1	no	—
179	C₅×#103	C₂×D₃	1	1	yes	characteristic
180	C₅×#103	C₂×D₃	1	1	yes	characteristic
181	#3082	—	3	1	no	Sylow
182	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
183	C₃×C₅×Q₈	—	2	1	no	—
184	C₃×C₅×Q₈	—	8	1	no	—
185	C₃×C₅×Q₈	C₂×Q₈	1	2	yes	—
186	C₂×C₃×C₄×C₅	—	2	1	no	—
187	C₂×C₃×C₄×C₅	—	2	1	no	—
188	C₂×C₃×C₄×C₅	—	2	1	no	—
189	C₂×C₃×C₄×C₅	—	2	1	no	—
190	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
191	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
192	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
193	C₂×C₅×Dic₃	—	2	1	no	—
194	C₂×C₅×Dic₃	—	2	1	no	—
195	C₂×C₅×Dic₃	—	2	1	no	—
196	C₂×C₅×Dic₃	—	2	1	no	—
197	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
198	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
199	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
200	C₄×C₅×D₃	—	2	4	no	—
201	C₄×C₅×D₃	—	8	1	no	—
202	C₄×C₅×D₃	C₂×Q₈	1	2	yes	—
203	C₄×C₅×D₃	#41	1	2	yes	—
204	C₅×Dic₆	—	2	1	no	—
205	C₅×Dic₆	—	2	4	no	—
206	C₅×Dic₆	—	8	1	no	—
207	C₅×Dic₆	C₂×Q₈	1	2	yes	—
208	C₃×C₅×C₈	—	2	1	no	—
209	C₃×C₅×C₈	—	2	1	no	—
210	C₅×C₃⋊C₈	—	2	1	no	—
211	C₅×C₃⋊C₈	—	2	1	no	—
212	C₂×D₃×Q₈	C₂²×C₅	1	1	yes	characteristic
213	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
214	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
215	#946	—	2	1	no	—
216	Q₈×Dic₃	C₂²×C₅	1	1	yes	characteristic
217	#944	—	2	1	no	—
218	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	1	yes	characteristic
219	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
220	#896	—	2	1	no	—
221	#892	—	2	1	no	—
222	#892	C₂²×C₅	1	1	yes	characteristic
223	#892	C₂²×C₅	1	1	yes	characteristic
224	D₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
225	#890	C₂²×C₅	1	1	yes	characteristic
226	#889	—	2	1	no	—
227	#888	C₂²×C₅	1	1	yes	characteristic
228	#887	—	2	1	no	—
229	#887	C₂²×C₅	1	1	yes	characteristic
230	#872	—	2	1	no	—
231	#872	C₂²×C₅	1	1	yes	characteristic
232	#870	C₂²×C₅	1	1	yes	characteristic
233	C₄×Dic₆	—	2	1	no	—
234	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic
235	C₃×#106	C₂²×C₅	1	1	yes	characteristic
236	C₃×#106	C₂²×C₅	1	1	yes	characteristic
237	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
238	C₃×#103	C₂²×C₅	1	1	yes	characteristic
239	C₃×#103	C₂²×C₅	1	1	yes	characteristic
240	#835	C₂²×C₅	1	1	yes	characteristic
241	#835	C₂²×C₅	1	1	yes	characteristic
242	#818	C₂²×C₅	1	1	yes	characteristic
243	#817	C₂²×C₅	1	1	yes	characteristic
244	#816	C₂²×C₅	1	1	yes	characteristic
245	#816	C₂²×C₅	1	1	yes	characteristic
246	Dic₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
247	Dic₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
248	#810	C₂²×C₅	1	1	yes	characteristic
249	#810	C₂²×C₅	1	1	yes	characteristic
250	#808	C₂²×C₅	1	1	yes	characteristic
251	#807	C₂²×C₅	1	1	yes	characteristic
252	#807	C₂²×C₅	1	1	yes	characteristic
253	#807	C₂²×C₅	1	1	yes	characteristic
254	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic
255	C₂×C₅×Q₈	—	2	1	no	—
256	C₂×C₅×Q₈	—	3	4	no	—
257	C₂×C₅×Q₈	—	3	1	no	—
258	C₂×C₅×Q₈	—	6	1	no	—
259	C₂×C₅×Q₈	—	6	1	no	—
260	C₂×C₅×Q₈	—	6	2	no	—
261	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
262	C₂²×C₄×C₅	—	3	1	no	—
263	C₂²×C₄×C₅	—	6	1	no	—
264	C₂²×C₄×C₅	—	6	1	no	—
265	C₅×M₁₆	—	6	2	no	—
266	C₂×C₅×C₈	—	3	1	no	—
267	C₂×C₅×C₈	—	3	1	no	—
268	C₂×C₅×C₈	—	6	2	no	—
269	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
270	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
271	C₅×C₄⋊C₄	—	2	1	no	—
272	C₅×C₄⋊C₄	—	2	1	no	—
273	C₅×C₄⋊C₄	—	3	1	no	—
274	C₅×C₄⋊C₄	—	3	1	no	—
275	C₅×C₄⋊C₄	—	3	1	no	—
276	C₅×C₄⋊C₄	—	3	1	no	—
277	C₅×C₄⋊C₄	—	3	1	no	—
278	C₅×C₄⋊C₄	—	6	1	no	—
279	C₅×C₄⋊C₄	—	6	1	no	—
280	C₅×C₄⋊C₄	—	6	1	no	—
281	C₅×C₄⋊C₄	—	6	1	no	—
282	C₅×C₄⋊C₄	—	6	1	no	—
283	C₅×C₄⋊C₄	—	6	1	no	—
284	C₅×C₄⋊C₄	—	6	1	no	—
285	C₅×C₄⋊C₄	—	6	1	no	—
286	C₅×C₄⋊C₄	—	6	1	no	—
287	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
288	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
289	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
290	C₅×C₂²⋊C₄	—	3	1	no	—
291	C₅×C₂²⋊C₄	—	3	1	no	—
292	C₅×C₂²⋊C₄	—	6	1	no	—
293	C₅×C₂²⋊C₄	—	6	1	no	—
294	C₄²×C₅	—	2	1	no	—
295	C₄²×C₅	—	3	1	no	—
296	C₄²×C₅	—	6	1	no	—
297	C₄²×C₅	—	6	1	no	—
298	C₄²×C₅	—	6	1	no	—
299	C₄²×C₅	—	6	1	no	—
300	C₄²×C₅	—	6	1	no	—
301	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
302	#544	—	3	1	no	—
303	#519	—	3	1	no	—
304	#479	—	3	1	no	—
305	#479	—	3	1	no	—
306	#479	—	3	1	no	—
307	#479	—	3	1	no	—
308	#477	—	3	1	no	—
309	#477	—	3	1	no	—
310	#475	—	3	1	no	—
311	#475	C₅×D₃	1	1	yes	characteristic, complemented
312	#428	—	3	1	no	—
313	#427	—	3	1	no	—
314	#424	—	3	1	no	—
315	#419	—	3	1	no	—
316	C₂×#103	—	3	1	no	—
317	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
318	C₂×C₅×D₃	—	2	1	no	—
319	C₂×C₅×D₃	—	2	1	no	—
320	C₂×C₅×D₃	C₂²⋊Q₈	1	2	yes	—
321	C₃×C₄×C₅	—	2	2	no	—
322	C₃×C₄×C₅	—	2	1	no	—
323	C₃×C₄×C₅	—	2	1	no	—
324	C₃×C₄×C₅	—	4	1	no	—
325	C₃×C₄×C₅	—	4	1	no	—
326	C₃×C₄×C₅	—	4	1	no	—
327	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
328	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
329	C₅×Dic₃	—	2	2	no	—
330	C₅×Dic₃	—	2	1	no	—
331	C₅×Dic₃	—	2	1	no	—
332	C₅×Dic₃	—	4	1	no	—
333	C₅×Dic₃	—	4	1	no	—
334	C₅×Dic₃	—	4	1	no	—
335	C₅×Dic₃	C₂²⋊Q₈	1	2	yes	—
336	C₂×C₃×Q₈	—	2	1	no	—
337	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
338	D₃×Q₈	—	2	2	no	—
339	D₃×Q₈	C₅×Q₈	1	4	yes	complemented
340	C₂×C₄×D₃	—	2	1	no	—
341	C₂×C₄×D₃	—	2	1	no	—
342	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
343	C₂×Dic₆	—	2	1	no	—
344	C₂×Dic₆	—	2	1	no	—
345	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
346	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
347	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
348	C₃×C₄⋊C₄	—	2	1	no	—
349	C₃×C₄⋊C₄	—	2	1	no	—
350	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
351	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
352	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
353	C₃×C₄²	—	2	1	no	—
354	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
355	(C₂×D₃)⋊C₄	—	2	1	no	—
356	(C₂×D₃)⋊C₄	—	2	1	no	—
357	(C₂×D₃)⋊C₄	C₅×D₄	1	1	yes	characteristic
358	(C₂×D₃)⋊C₄	C₅×D₄	1	1	yes	characteristic
359	C₄⋊Dic₃	—	2	1	no	—
360	C₄⋊Dic₃	—	2	1	no	—
361	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
362	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
363	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
364	Dic₃⋊C₄	—	2	1	no	—
365	Dic₃⋊C₄	—	2	1	no	—
366	Dic₃⋊C₄	—	2	1	no	—
367	Dic₃⋊C₄	—	2	1	no	—
368	Dic₃⋊C₄	—	2	1	no	—
369	Dic₃⋊C₄	—	2	1	no	—
370	Dic₃⋊C₄	—	2	1	no	—
371	Dic₃⋊C₄	C₅×D₄	1	1	yes	characteristic
372	Dic₃⋊C₄	C₅×D₄	1	1	yes	characteristic
373	C₄×Dic₃	—	2	1	no	—
374	C₄×Dic₃	—	2	1	no	—
375	C₄×Dic₃	—	2	1	no	—
376	C₄×Dic₃	—	2	1	no	—
377	C₄×Dic₃	—	2	1	no	—
378	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
379	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
380	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
381	ΓL(1,𝔽₂₅)	—	2	2	no	—
382	D₃×C₈	—	2	2	no	—
383	C₂³×C₅	—	3	1	no	—
384	C₅×Q₈	—	2	1	no	—
385	C₅×Q₈	—	3	2	no	—
386	C₅×Q₈	—	6	4	no	—
387	C₅×Q₈	—	6	1	no	—
388	C₅×Q₈	—	8	1	no	—
389	C₅×Q₈	—	24	1	no	—
390	C₅×Q₈	D₃×Q₈	1	2	yes	—
391	C₂×C₄×C₅	—	2	1	no	—
392	C₂×C₄×C₅	—	2	1	no	—
393	C₂×C₄×C₅	—	2	1	no	—
394	C₂×C₄×C₅	—	2	1	no	—
395	C₂×C₄×C₅	—	3	1	no	—
396	C₂×C₄×C₅	—	3	2	no	—
397	C₂×C₄×C₅	—	3	2	no	—
398	C₂×C₄×C₅	—	3	1	no	—
399	C₂×C₄×C₅	—	3	1	no	—
400	C₂×C₄×C₅	—	6	4	no	—
401	C₂×C₄×C₅	—	6	1	no	—
402	C₂×C₄×C₅	—	6	1	no	—
403	C₂×C₄×C₅	—	6	1	no	—
404	C₂×C₄×C₅	—	6	1	no	—
405	C₂×C₄×C₅	—	24	1	no	—
406	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
407	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
408	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
409	C₅×C₈	—	2	1	no	—
410	C₅×C₈	—	2	1	no	—
411	C₅×C₈	—	6	1	no	—
412	C₅×C₈	—	6	1	no	—
413	C₂²×Q₈	—	3	1	no	—
414	C₂×M₁₆	—	3	1	no	—
415	C₂²×C₈	—	3	1	no	—
416	C₄⋊Q₈	—	3	1	no	—
417	C₄⋊Q₈	—	6	1	no	—
418	C₄⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic
419	#125	—	3	1	no	—
420	#125	—	3	1	no	—
421	#125	—	6	1	no	—
422	C₂²⋊Q₈	—	6	1	no	—
423	C₂²⋊Q₈	—	6	1	no	—
424	C₄×Q₈	—	3	1	no	—
425	C₄×Q₈	—	3	1	no	—
426	C₄×Q₈	—	3	1	no	—
427	C₄×Q₈	—	6	1	no	—
428	C₄×Q₈	—	6	1	no	—
429	C₄×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
430	#117	—	3	1	no	—
431	#117	—	3	1	no	—
432	#117	—	3	1	no	—
433	#117	—	6	1	no	—
434	#117	—	6	1	no	—
435	C₂×C₄⋊C₄	—	3	1	no	—
436	#107	—	3	1	no	—
437	#107	—	3	1	no	—
438	#107	—	3	1	no	—
439	#107	—	3	1	no	—
440	#106	—	3	1	no	—
441	#106	—	3	1	no	—
442	#106	C₂×C₅×D₃	1	1	yes	characteristic
443	#106	C₂×C₅×D₃	1	1	yes	characteristic
444	C₄⋊C₈	—	3	1	no	—
445	C₄⋊C₈	—	3	1	no	—
446	C₄⋊C₈	—	3	1	no	—
447	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
448	#103	—	3	1	no	—
449	#103	—	3	1	no	—
450	#103	—	3	1	no	—
451	#103	—	3	1	no	—
452	#103	—	3	1	no	—
453	#103	—	3	1	no	—
454	#103	C₂×C₅×D₃	1	1	yes	characteristic
455	#103	C₂×C₅×D₃	1	1	yes	characteristic
456	C₂×C₃×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
457	C₂×C₃×C₅	#577	1	1	yes	characteristic
458	C₂×C₃×C₅	#578	1	1	yes	characteristic
459	C₅×D₃	—	2	2	no	—
460	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
461	C₃×Q₈	—	2	1	no	—
462	C₃×Q₈	—	8	1	no	—
463	C₃×Q₈	C₂×C₅×Q₈	1	2	yes	—
464	C₂×C₃×C₄	—	2	1	no	—
465	C₂×C₃×C₄	—	2	1	no	—
466	C₂×C₃×C₄	—	2	1	no	—
467	C₂×C₃×C₄	—	2	1	no	—
468	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
469	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
470	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
471	C₂×Dic₃	—	2	1	no	—
472	C₂×Dic₃	—	2	1	no	—
473	C₂×Dic₃	—	2	1	no	—
474	C₂×Dic₃	—	2	1	no	—
475	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
476	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
477	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
478	C₄×D₃	—	2	4	no	—
479	C₄×D₃	—	8	1	no	—
480	C₄×D₃	C₂×C₅×Q₈	1	2	yes	—
481	C₄×D₃	C₅×#41	1	2	yes	—
482	Dic₆	—	2	1	no	—
483	Dic₆	—	2	4	no	—
484	Dic₆	—	8	1	no	—
485	Dic₆	C₂×C₅×Q₈	1	2	yes	—
486	C₃×C₈	—	2	1	no	—
487	C₃×C₈	—	2	1	no	—
488	C₃⋊C₈	—	2	1	no	—
489	C₃⋊C₈	—	2	1	no	—
490	C₂²×C₅	—	3	2	no	—
491	C₂²×C₅	—	6	1	no	—
492	C₂²×C₅	—	6	1	no	—
493	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
494	C₄×C₅	—	2	1	no	—
495	C₄×C₅	—	2	1	no	—
496	C₄×C₅	—	2	2	no	—
497	C₄×C₅	—	3	2	no	—
498	C₄×C₅	—	4	1	no	—
499	C₄×C₅	—	4	1	no	—
500	C₄×C₅	—	4	1	no	—
501	C₄×C₅	—	6	1	no	—
502	C₄×C₅	—	6	1	no	—
503	C₄×C₅	—	6	2	no	—
504	C₄×C₅	—	12	1	no	—
505	C₄×C₅	—	12	1	no	—
506	C₄×C₅	—	12	1	no	—
507	C₄×C₅	C₂×D₃×Q₈	1	1	yes	characteristic
508	C₄×C₅	D₃×#41	1	1	yes	characteristic
509	C₂×Q₈	—	2	1	no	—
510	C₂×Q₈	—	3	4	no	—
511	C₂×Q₈	—	3	1	no	—
512	C₂×Q₈	—	6	1	no	—
513	C₂×Q₈	—	6	1	no	—
514	C₂×Q₈	—	6	2	no	—
515	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
516	C₂²×C₄	—	3	1	no	—
517	C₂²×C₄	—	6	1	no	—
518	C₂²×C₄	—	6	1	no	—
519	M₁₆	—	6	2	no	—
520	C₂×C₈	—	3	1	no	—
521	C₂×C₈	—	3	1	no	—
522	C₂×C₈	—	6	2	no	—
523	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
524	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
525	C₄⋊C₄	—	2	1	no	—
526	C₄⋊C₄	—	2	1	no	—
527	C₄⋊C₄	—	3	1	no	—
528	C₄⋊C₄	—	3	1	no	—
529	C₄⋊C₄	—	3	1	no	—
530	C₄⋊C₄	—	3	1	no	—
531	C₄⋊C₄	—	3	1	no	—
532	C₄⋊C₄	—	6	1	no	—
533	C₄⋊C₄	—	6	1	no	—
534	C₄⋊C₄	—	6	1	no	—
535	C₄⋊C₄	—	6	1	no	—
536	C₄⋊C₄	—	6	1	no	—
537	C₄⋊C₄	—	6	1	no	—
538	C₄⋊C₄	—	6	1	no	—
539	C₄⋊C₄	—	6	1	no	—
540	C₄⋊C₄	—	6	1	no	—
541	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
542	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
543	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
544	C₂²⋊C₄	—	3	1	no	—
545	C₂²⋊C₄	—	3	1	no	—
546	C₂²⋊C₄	—	6	1	no	—
547	C₂²⋊C₄	—	6	1	no	—
548	C₄²	—	2	1	no	—
549	C₄²	—	3	1	no	—
550	C₄²	—	6	1	no	—
551	C₄²	—	6	1	no	—
552	C₄²	—	6	1	no	—
553	C₄²	—	6	1	no	—
554	C₄²	—	6	1	no	—
555	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
556	C₃×C₅	#3082	1	1	yes	characteristic, complemented, Hall
557	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
558	C₂×D₃	—	2	1	no	—
559	C₂×D₃	—	2	1	no	—
560	C₂×D₃	C₅×C₂²⋊Q₈	1	2	yes	—
561	C₃×C₄	—	2	2	no	—
562	C₃×C₄	—	2	1	no	—
563	C₃×C₄	—	2	1	no	—
564	C₃×C₄	—	4	1	no	—
565	C₃×C₄	—	4	1	no	—
566	C₃×C₄	—	4	1	no	—
567	C₃×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
568	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
569	Dic₃	—	2	2	no	—
570	Dic₃	—	2	1	no	—
571	Dic₃	—	2	1	no	—
572	Dic₃	—	4	1	no	—
573	Dic₃	—	4	1	no	—
574	Dic₃	—	4	1	no	—
575	Dic₃	C₅×C₂²⋊Q₈	1	2	yes	—
576	C₂×C₅	—	6	2	no	—
577	C₂×C₅	D₃×C₂²⋊Q₈	1	1	yes	characteristic
578	C₂×C₅	#5762	1	1	yes	characteristic
579	C₂×C₅	#5779	1	1	yes	characteristic
580	C₂³	—	3	1	no	—
581	Q₈	—	2	1	no	—
582	Q₈	—	3	2	no	—
583	Q₈	—	6	4	no	—
584	Q₈	—	6	1	no	—
585	Q₈	—	8	1	no	—
586	Q₈	—	24	1	no	—
587	Q₈	C₅×D₃×Q₈	1	2	yes	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	1	no	—
592	C₂×C₄	—	3	1	no	—
593	C₂×C₄	—	3	2	no	—
594	C₂×C₄	—	3	2	no	—
595	C₂×C₄	—	3	1	no	—
596	C₂×C₄	—	3	1	no	—
597	C₂×C₄	—	6	4	no	—
598	C₂×C₄	—	6	1	no	—
599	C₂×C₄	—	6	1	no	—
600	C₂×C₄	—	6	1	no	—
601	C₂×C₄	—	6	1	no	—
602	C₂×C₄	—	24	1	no	—
603	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
604	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
605	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
606	C₈	—	2	1	no	—
607	C₈	—	2	1	no	—
608	C₈	—	6	1	no	—
609	C₈	—	6	1	no	—
610	C₂×C₃	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
611	C₂×C₃	C₅×#577	1	1	yes	characteristic
612	C₂×C₃	C₅×#578	1	1	yes	characteristic
613	D₃	—	2	2	no	—
614	C₅	#81013	1	1	yes	characteristic, direct product factor, Sylow
615	C₂²	—	3	2	no	—
616	C₂²	—	6	1	no	—
617	C₂²	—	6	1	no	—
618	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
619	C₄	—	2	1	no	—
620	C₄	—	2	1	no	—
621	C₄	—	2	2	no	—
622	C₄	—	3	2	no	—
623	C₄	—	4	1	no	—
624	C₄	—	4	1	no	—
625	C₄	—	4	1	no	—
626	C₄	—	6	1	no	—
627	C₄	—	6	1	no	—
628	C₄	—	6	2	no	—
629	C₄	—	12	1	no	—
630	C₄	—	12	1	no	—
631	C₄	—	12	1	no	—
632	C₄	C₂×C₅×D₃×Q₈	1	1	yes	characteristic
633	C₄	C₅×D₃×#41	1	1	yes	characteristic
634	C₃	C₅×#3082	1	1	yes	characteristic, complemented, Sylow
635	C₂	—	6	2	no	—
636	C₂	C₅×D₃×C₂²⋊Q₈	1	1	yes	characteristic
637	C₂	C₅×#5762	1	1	yes	characteristic
638	C₂	C₅×#5779	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×#475	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂²×C₅×D₃	C₂×D₄
hypercenter	C₅×#475	D₃
hypocenter	C₃	C₅×#3082
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#475

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×#475	C₂	semidirect
4. C₅×#5091	C₂	semidirect
5. C₅×#5022	C₂	semidirect
8. C₅×#4857	C₂	semidirect
9. C₅×#4854	C₂	semidirect
11. C₅×#4829	C₂	semidirect
14. C₅×#4799	C₂	semidirect
15. C₅×#4793	C₂	semidirect
60. #81013	C₅	direct (N × H)
70. C₅×#475	D₃	semidirect
79. C₅×D₃×Q₈	Q₈	semidirect
125. C₃×#475	C₂×C₅	semidirect
126. #5091	C₂×C₅	semidirect
127. #5022	C₂×C₅	semidirect
130. #4857	C₂×C₅	semidirect
131. #4854	C₂×C₅	semidirect
133. #4829	C₂×C₅	semidirect
136. #4799	C₂×C₅	semidirect
137. #4793	C₂×C₅	semidirect
311. #475	C₅×D₃	semidirect
339. D₃×Q₈	C₅×Q₈	semidirect
556. C₃×C₅	#3082	semidirect
614. C₅	#81013	direct (N × H)
634. C₃	C₅×#3082	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5729	2
C₅×#5572	2
C₃×C₅×#475	2
C₅×#5091	2
C₅×#5022	2
C₅×#4861	2
C₅×#4860	2
C₅×#4857	2
C₅×#4854	2
C₅×#4839	2
C₅×#4829	2
C₅×#4802	2
C₅×D₃×#103	2
C₅×#4799	2
C₅×#4793	2
C₅×#3082	3
#81013	5

Subgroups — C5×#81013 #14430918

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#81013 #14430918