Subgroups — C₅×#79958 #14418466

Order 1920.

728 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5578	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#446	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×Q₈×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4839	C₂	1	2	yes	maximal
5	C₅×#4837	C₂	1	1	yes	maximal, characteristic
6	C₅×#4830	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4830	C₂	1	2	yes	maximal, complemented
8	C₅×#4708	C₂	1	2	yes	maximal
9	C₅×#4701	C₂	1	2	yes	maximal, complemented
10	C₄×C₅×D₃×C₈	C₂	1	1	yes	maximal, characteristic
11	C₅×#4679	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#2960	—	3	1	no	maximal, Hall
13	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
14	C₅×#946	C₄	1	1	yes	characteristic
15	C₅×#944	C₄	1	1	yes	characteristic
16	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	—
17	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
18	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
19	C₅×#897	C₄	1	1	yes	characteristic
20	C₅×#896	C₄	1	2	yes	—
21	C₅×#889	C₄	1	2	yes	—
22	C₅×#888	C₄	1	1	yes	characteristic
23	C₅×#872	C₂²	1	2	yes	—
24	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
25	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
26	C₄×C₅×Dic₆	C₂²	1	2	yes	—
27	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	—
29	C₃×C₅×#97	C₂²	1	2	yes	—
30	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
31	C₅×#815	C₂²	1	2	yes	—
32	C₅×Dic₃⋊C₈	C₂²	1	2	yes	—
33	C₅×Dic₃⋊C₈	C₂²	1	2	yes	—
34	C₅×Dic₃⋊C₈	C₂²	1	2	yes	—
35	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic
36	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic
37	C₅×C₈×Dic₃	C₂²	1	2	yes	—
38	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
39	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	2	yes	—
40	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
41	C₄×C₅×C₃⋊C₈	C₂²	1	2	yes	—
42	#79958	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
43	C₅×#533	—	3	1	no	—
44	C₅×#446	—	3	2	no	—
45	C₅×#446	—	3	1	no	—
46	C₅×#446	D₃	1	1	yes	characteristic, complemented
47	C₅×C₈×Q₈	—	3	2	no	—
48	C₅×C₈×Q₈	—	3	1	no	—
49	C₅×C₈×Q₈	—	3	1	no	—
50	C₅×#424	—	3	2	no	—
51	C₅×#423	—	3	1	no	—
52	C₅×#405	—	3	2	no	—
53	C₂×C₄×C₅×C₈	—	3	1	no	—
54	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
58	C₂×C₅×Dic₆	C₂×C₄	1	2	yes	—
59	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
60	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
61	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
62	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
63	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
64	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
65	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
66	C₃×C₄²×C₅	C₂³	1	2	yes	—
67	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
68	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
69	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
70	C₅×C₄⋊Dic₃	C₂×C₄	1	2	yes	—
71	C₅×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
72	C₅×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
73	C₅×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
74	C₅×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
75	C₅×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
76	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
77	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
78	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
79	C₄×C₅×Dic₃	C₂³	1	2	yes	—
80	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
81	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
82	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
83	C₅×ΓL(1,𝔽₂₅)	—	2	4	no	—
84	C₅×D₃×C₈	—	2	2	no	—
85	C₅×D₃×C₈	Q₈	1	4	yes	complemented
86	#5578	C₂×C₅	1	1	yes	characteristic
87	C₃×#446	C₂×C₅	1	1	yes	characteristic, complemented
88	Q₈×C₃⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
89	#4839	C₂×C₅	1	2	yes	—
90	#4837	C₂×C₅	1	1	yes	characteristic
91	#4830	C₂×C₅	1	1	yes	characteristic, complemented
92	#4830	C₂×C₅	1	2	yes	complemented
93	#4708	C₂×C₅	1	2	yes	—
94	#4701	C₂×C₅	1	2	yes	complemented
95	C₄×D₃×C₈	C₂×C₅	1	1	yes	characteristic
96	#4679	C₂×C₅	1	1	yes	characteristic, complemented
97	C₂×C₅×M₁₆	—	3	2	no	—
98	C₂²×C₅×C₈	—	3	1	no	—
99	C₂²×C₅×C₈	—	3	1	no	—
100	C₅×C₄⋊Q₈	—	3	1	no	—
101	C₅×C₄⋊Q₈	—	3	1	no	—
102	C₅×#125	—	3	2	no	—
103	C₅×C₂²⋊Q₈	—	3	1	no	—
104	C₅×C₂²⋊Q₈	—	3	2	no	—
105	C₅×C₂²⋊Q₈	—	3	1	no	—
106	C₄×C₅×Q₈	—	3	2	no	—
107	C₄×C₅×Q₈	—	3	1	no	—
108	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
109	C₅×#117	—	3	2	no	—
110	C₂×C₄²×C₅	—	3	1	no	—
111	C₅×C₄⋊C₈	—	3	2	no	—
112	C₅×C₄⋊C₈	—	3	2	no	—
113	C₅×C₄⋊C₈	—	3	2	no	—
114	C₅×C₄⋊C₈	—	3	1	no	—
115	C₅×C₄⋊C₈	—	3	2	no	—
116	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
117	C₅×C₄⋊C₈	C₂×D₃	1	2	yes	—
118	C₅×#97	—	3	2	no	—
119	C₅×#97	C₂×D₃	1	2	yes	—
120	C₄×C₅×C₈	—	3	1	no	—
121	C₄×C₅×C₈	—	3	1	no	—
122	C₄×C₅×C₈	—	3	2	no	—
123	C₄×C₅×C₈	—	3	1	no	—
124	C₄×C₅×C₈	—	3	2	no	—
125	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
126	#2960	—	3	1	no	Sylow
127	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
128	C₃×C₅×Q₈	—	2	2	no	—
129	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
131	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
132	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
134	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
136	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
137	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
139	C₄×C₅×D₃	—	2	2	no	—
140	C₄×C₅×D₃	—	2	2	no	—
141	C₄×C₅×D₃	C₂×Q₈	1	2	yes	—
142	C₄×C₅×D₃	#41	1	2	yes	—
143	C₅×Dic₆	—	2	2	no	—
144	C₅×Dic₆	—	2	4	no	—
145	C₃×C₅×C₈	—	2	1	no	—
146	C₃×C₅×C₈	—	2	2	no	—
147	C₃×C₅×C₈	C₂×Q₈	1	2	yes	—
148	C₅×C₃⋊C₈	—	2	1	no	—
149	C₅×C₃⋊C₈	—	2	2	no	—
150	C₅×C₃⋊C₈	C₂×Q₈	1	2	yes	—
151	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
152	#946	C₄×C₅	1	1	yes	characteristic
153	#944	C₄×C₅	1	1	yes	characteristic
154	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	2	yes	—
155	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
156	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
157	#897	C₄×C₅	1	1	yes	characteristic
158	#896	C₄×C₅	1	2	yes	—
159	#889	C₄×C₅	1	2	yes	—
160	#888	C₄×C₅	1	1	yes	characteristic
161	#872	C₂²×C₅	1	2	yes	—
162	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
163	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic
164	C₄×Dic₆	C₂²×C₅	1	2	yes	—
165	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
166	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	—
167	C₃×#97	C₂²×C₅	1	2	yes	—
168	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
169	#815	C₂²×C₅	1	2	yes	—
170	Dic₃⋊C₈	C₂²×C₅	1	2	yes	—
171	Dic₃⋊C₈	C₂²×C₅	1	2	yes	—
172	Dic₃⋊C₈	C₂²×C₅	1	2	yes	—
173	C₈×Dic₃	C₂²×C₅	1	1	yes	characteristic
174	C₈×Dic₃	C₂²×C₅	1	1	yes	characteristic
175	C₈×Dic₃	C₂²×C₅	1	2	yes	—
176	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic
177	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	2	yes	—
178	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
179	C₄×C₃⋊C₈	C₂²×C₅	1	2	yes	—
180	C₂×C₅×Q₈	—	3	2	no	—
181	C₂×C₅×Q₈	—	3	1	no	—
182	C₂×C₅×Q₈	C₄×D₃	1	1	yes	characteristic
183	C₂²×C₄×C₅	—	3	1	no	—
184	C₂²×C₄×C₅	—	3	1	no	—
185	C₂²×C₄×C₅	—	3	1	no	—
186	C₅×M₁₆	—	6	4	no	—
187	C₂×C₅×C₈	—	3	1	no	—
188	C₂×C₅×C₈	—	3	4	no	—
189	C₂×C₅×C₈	—	3	1	no	—
190	C₂×C₅×C₈	—	3	2	no	—
191	C₂×C₅×C₈	—	6	2	no	—
192	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
193	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
194	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
195	C₅×C₄⋊C₄	—	3	2	no	—
196	C₅×C₄⋊C₄	—	3	2	no	—
197	C₅×C₄⋊C₄	—	3	2	no	—
198	C₅×C₄⋊C₄	—	3	2	no	—
199	C₅×C₄⋊C₄	—	3	2	no	—
200	C₅×C₄⋊C₄	—	3	2	no	—
201	C₅×C₄⋊C₄	—	3	1	no	—
202	C₅×C₄⋊C₄	C₄×D₃	1	2	yes	—
203	C₅×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
204	C₅×C₂²⋊C₄	—	3	2	no	—
205	C₅×C₂²⋊C₄	—	3	2	no	—
206	C₄²×C₅	—	3	1	no	—
207	C₄²×C₅	—	3	1	no	—
208	C₄²×C₅	—	3	1	no	—
209	C₄²×C₅	—	3	2	no	—
210	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
211	C₄²×C₅	C₂²×D₃	1	2	yes	—
212	#533	—	3	1	no	—
213	#446	—	3	2	no	—
214	#446	—	3	1	no	—
215	#446	C₅×D₃	1	1	yes	characteristic, complemented
216	C₈×Q₈	—	3	1	no	—
217	C₈×Q₈	—	3	2	no	—
218	C₈×Q₈	—	3	1	no	—
219	#424	—	3	2	no	—
220	#423	—	3	1	no	—
221	#405	—	3	2	no	—
222	C₂×C₄×C₈	—	3	1	no	—
223	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
224	C₂×C₅×D₃	—	2	1	no	—
225	C₂×C₅×D₃	—	2	1	no	—
226	C₂×C₅×D₃	C₄×Q₈	1	2	yes	—
227	C₃×C₄×C₅	—	2	2	no	—
228	C₃×C₄×C₅	—	2	1	no	—
229	C₃×C₄×C₅	—	2	2	no	—
230	C₃×C₄×C₅	#131	1	2	yes	—
231	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
232	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
233	C₅×Dic₃	—	2	2	no	—
234	C₅×Dic₃	—	2	2	no	—
235	C₅×Dic₃	—	2	1	no	—
236	C₅×Dic₃	C₄×Q₈	1	2	yes	—
237	C₅×Dic₃	#131	1	2	yes	—
238	C₂×C₃×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
239	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
240	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
241	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
242	C₂×Dic₆	C₂×C₄×C₅	1	2	yes	—
243	C₂×Dic₆	C₂×C₄×C₅	1	1	yes	characteristic
244	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
245	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
246	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
247	C₃×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
248	C₃×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
249	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
250	C₃×C₄²	C₂³×C₅	1	2	yes	—
251	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	2	yes	—
252	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	2	yes	—
253	C₄⋊Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
254	C₄⋊Dic₃	C₂×C₄×C₅	1	2	yes	—
255	Dic₃⋊C₄	C₂×C₄×C₅	1	2	yes	—
256	Dic₃⋊C₄	C₂×C₄×C₅	1	2	yes	—
257	Dic₃⋊C₄	C₂×C₄×C₅	1	2	yes	—
258	Dic₃⋊C₄	C₂×C₄×C₅	1	2	yes	—
259	Dic₃⋊C₄	C₂×C₄×C₅	1	2	yes	—
260	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
261	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
262	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
263	C₄×Dic₃	C₂³×C₅	1	2	yes	—
264	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
265	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
266	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
267	ΓL(1,𝔽₂₅)	—	2	4	no	—
268	D₃×C₈	—	2	2	no	—
269	D₃×C₈	C₅×Q₈	1	4	yes	complemented
270	C₂³×C₅	—	3	1	no	—
271	C₅×Q₈	—	2	2	no	—
272	C₅×Q₈	—	6	4	no	—
273	C₅×Q₈	—	6	2	no	—
274	C₂×C₄×C₅	—	3	1	no	—
275	C₂×C₄×C₅	—	3	1	no	—
276	C₂×C₄×C₅	—	3	2	no	—
277	C₂×C₄×C₅	—	3	2	no	—
278	C₂×C₄×C₅	—	3	1	no	—
279	C₂×C₄×C₅	—	3	2	no	—
280	C₂×C₄×C₅	—	3	2	no	—
281	C₂×C₄×C₅	—	6	2	no	—
282	C₂×C₄×C₅	—	6	2	no	—
283	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
284	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
285	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
286	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
287	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
288	C₅×C₈	—	2	1	no	—
289	C₅×C₈	—	2	2	no	—
290	C₅×C₈	—	3	2	no	—
291	C₅×C₈	—	6	1	no	—
292	C₅×C₈	—	6	2	no	—
293	C₅×C₈	D₃×Q₈	1	2	yes	—
294	C₂×M₁₆	—	3	2	no	—
295	C₂²×C₈	—	3	1	no	—
296	C₂²×C₈	—	3	1	no	—
297	C₄⋊Q₈	—	3	1	no	—
298	C₄⋊Q₈	—	3	1	no	—
299	#125	—	3	2	no	—
300	C₂²⋊Q₈	—	3	1	no	—
301	C₂²⋊Q₈	—	3	2	no	—
302	C₂²⋊Q₈	—	3	1	no	—
303	C₄×Q₈	—	3	2	no	—
304	C₄×Q₈	—	3	1	no	—
305	C₄×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
306	#117	—	3	2	no	—
307	C₂×C₄²	—	3	1	no	—
308	C₄⋊C₈	—	3	2	no	—
309	C₄⋊C₈	—	3	2	no	—
310	C₄⋊C₈	—	3	2	no	—
311	C₄⋊C₈	—	3	1	no	—
312	C₄⋊C₈	—	3	2	no	—
313	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
314	C₄⋊C₈	C₂×C₅×D₃	1	2	yes	—
315	#97	—	3	2	no	—
316	#97	C₂×C₅×D₃	1	2	yes	—
317	C₄×C₈	—	3	1	no	—
318	C₄×C₈	—	3	1	no	—
319	C₄×C₈	—	3	2	no	—
320	C₄×C₈	—	3	1	no	—
321	C₄×C₈	—	3	2	no	—
322	C₄×C₈	C₂×C₅×D₃	1	1	yes	characteristic
323	C₂×C₃×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
324	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
325	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
326	C₅×D₃	—	2	2	no	—
327	C₂²×D₃	C₂²×C₄×C₅	1	1	yes	characteristic
328	C₃×Q₈	—	2	2	no	—
329	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
330	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
331	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
332	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
333	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
334	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
335	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
336	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
337	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
338	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
339	C₄×D₃	—	2	2	no	—
340	C₄×D₃	—	2	2	no	—
341	C₄×D₃	C₂×C₅×Q₈	1	2	yes	—
342	C₄×D₃	C₅×#41	1	2	yes	—
343	Dic₆	—	2	2	no	—
344	Dic₆	—	2	4	no	—
345	C₃×C₈	—	2	1	no	—
346	C₃×C₈	—	2	2	no	—
347	C₃×C₈	C₂×C₅×Q₈	1	2	yes	—
348	C₃⋊C₈	—	2	1	no	—
349	C₃⋊C₈	—	2	2	no	—
350	C₃⋊C₈	C₂×C₅×Q₈	1	2	yes	—
351	C₂²×C₅	—	3	2	no	—
352	C₂²×C₅	—	6	1	no	—
353	C₂²×C₅	—	6	1	no	—
354	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
355	C₄×C₅	—	2	2	no	—
356	C₄×C₅	—	2	1	no	—
357	C₄×C₅	—	2	2	no	—
358	C₄×C₅	—	3	2	no	—
359	C₄×C₅	—	3	2	no	—
360	C₄×C₅	—	6	1	no	—
361	C₄×C₅	—	6	2	no	—
362	C₄×C₅	—	6	2	no	—
363	C₄×C₅	#907	1	2	yes	—
364	C₄×C₅	C₂×D₃×Q₈	1	1	yes	characteristic
365	C₄×C₅	D₃×#41	1	1	yes	characteristic
366	C₂×Q₈	—	3	2	no	—
367	C₂×Q₈	—	3	1	no	—
368	C₂×Q₈	C₄×C₅×D₃	1	1	yes	characteristic
369	C₂²×C₄	—	3	1	no	—
370	C₂²×C₄	—	3	1	no	—
371	C₂²×C₄	—	3	1	no	—
372	M₁₆	—	6	4	no	—
373	C₂×C₈	—	3	1	no	—
374	C₂×C₈	—	3	4	no	—
375	C₂×C₈	—	3	1	no	—
376	C₂×C₈	—	3	2	no	—
377	C₂×C₈	—	6	2	no	—
378	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
379	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
380	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
381	C₄⋊C₄	—	3	2	no	—
382	C₄⋊C₄	—	3	2	no	—
383	C₄⋊C₄	—	3	2	no	—
384	C₄⋊C₄	—	3	2	no	—
385	C₄⋊C₄	—	3	2	no	—
386	C₄⋊C₄	—	3	2	no	—
387	C₄⋊C₄	—	3	1	no	—
388	C₄⋊C₄	C₄×C₅×D₃	1	2	yes	—
389	C₄⋊C₄	C₄×C₅×D₃	1	1	yes	characteristic
390	C₂²⋊C₄	—	3	2	no	—
391	C₂²⋊C₄	—	3	2	no	—
392	C₄²	—	3	1	no	—
393	C₄²	—	3	1	no	—
394	C₄²	—	3	1	no	—
395	C₄²	—	3	2	no	—
396	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
397	C₄²	C₂²×C₅×D₃	1	2	yes	—
398	C₃×C₅	#2960	1	1	yes	characteristic, complemented, Hall
399	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
400	C₂×D₃	—	2	1	no	—
401	C₂×D₃	—	2	1	no	—
402	C₂×D₃	C₄×C₅×Q₈	1	2	yes	—
403	C₃×C₄	—	2	2	no	—
404	C₃×C₄	—	2	1	no	—
405	C₃×C₄	—	2	2	no	—
406	C₃×C₄	C₅×#131	1	2	yes	—
407	C₃×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
408	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
409	Dic₃	—	2	2	no	—
410	Dic₃	—	2	2	no	—
411	Dic₃	—	2	1	no	—
412	Dic₃	C₄×C₅×Q₈	1	2	yes	—
413	Dic₃	C₅×#131	1	2	yes	—
414	C₂×C₅	—	6	2	no	—
415	C₂×C₅	C₄×D₃×Q₈	1	1	yes	characteristic
416	C₂×C₅	C₂×#907	1	1	yes	characteristic
417	C₂×C₅	D₃×#131	1	1	yes	characteristic
418	C₂³	—	3	1	no	—
419	Q₈	—	2	2	no	—
420	Q₈	—	6	4	no	—
421	Q₈	—	6	2	no	—
422	C₂×C₄	—	3	1	no	—
423	C₂×C₄	—	3	1	no	—
424	C₂×C₄	—	3	2	no	—
425	C₂×C₄	—	3	2	no	—
426	C₂×C₄	—	3	1	no	—
427	C₂×C₄	—	3	2	no	—
428	C₂×C₄	—	3	2	no	—
429	C₂×C₄	—	6	2	no	—
430	C₂×C₄	—	6	2	no	—
431	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
432	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
433	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
434	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
435	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
436	C₈	—	2	1	no	—
437	C₈	—	2	2	no	—
438	C₈	—	3	2	no	—
439	C₈	—	6	1	no	—
440	C₈	—	6	2	no	—
441	C₈	C₅×D₃×Q₈	1	2	yes	—
442	C₂×C₃	C₂×C₄×C₅×Q₈	1	1	yes	characteristic
443	C₂×C₃	C₂×C₅×#131	1	1	yes	characteristic
444	C₂×C₃	C₂×C₅×#131	1	1	yes	characteristic
445	D₃	—	2	2	no	—
446	C₅	#79958	1	1	yes	characteristic, direct product factor, Sylow
447	C₂²	—	3	2	no	—
448	C₂²	—	6	1	no	—
449	C₂²	—	6	1	no	—
450	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
451	C₄	—	2	2	no	—
452	C₄	—	2	1	no	—
453	C₄	—	2	2	no	—
454	C₄	—	3	2	no	—
455	C₄	—	3	2	no	—
456	C₄	—	6	1	no	—
457	C₄	—	6	2	no	—
458	C₄	—	6	2	no	—
459	C₄	C₅×#907	1	2	yes	—
460	C₄	C₂×C₅×D₃×Q₈	1	1	yes	characteristic
461	C₄	C₅×D₃×#41	1	1	yes	characteristic
462	C₃	C₅×#2960	1	1	yes	characteristic, complemented, Sylow
463	C₂	—	6	2	no	—
464	C₂	C₄×C₅×D₃×Q₈	1	1	yes	characteristic
465	C₂	C₂×C₅×#907	1	1	yes	characteristic
466	C₂	C₅×D₃×#131	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#446	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂²×C₅×D₃	C₂²×C₄
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₅×#446	D₃
hypocenter	C₃	C₅×#2960
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₅×#446

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#446	C₂	semidirect
3. C₅×Q₈×C₃⋊C₈	C₂	semidirect
6. C₅×#4830	C₂	semidirect
7. C₅×#4830	C₂	semidirect
9. C₅×#4701	C₂	semidirect
11. C₅×#4679	C₂	semidirect
42. #79958	C₅	direct (N × H)
46. C₅×#446	D₃	semidirect
85. C₅×D₃×C₈	Q₈	semidirect
87. C₃×#446	C₂×C₅	semidirect
88. Q₈×C₃⋊C₈	C₂×C₅	semidirect
91. #4830	C₂×C₅	semidirect
92. #4830	C₂×C₅	semidirect
94. #4701	C₂×C₅	semidirect
96. #4679	C₂×C₅	semidirect
215. #446	C₅×D₃	semidirect
269. D₃×C₈	C₅×Q₈	semidirect
398. C₃×C₅	#2960	semidirect
446. C₅	#79958	direct (N × H)
462. C₃	C₅×#2960	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5578	2
C₃×C₅×#446	2
C₅×Q₈×C₃⋊C₈	2
C₅×#4839	2
C₅×#4837	2
C₅×#4830	2
C₅×#4708	2
C₅×#4701	2
C₄×C₅×D₃×C₈	2
C₅×#4679	2
C₅×#2960	3
#79958	5

Subgroups — C5×#79958 #14418466

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#79958 #14418466