Subgroups — C₅×#79941 #14419583

Order 1920.

744 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5580	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#446	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5024	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4840	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4840	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4836	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4836	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4834	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#4833	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4708	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4706	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#4706	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×D₃×#97	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#4689	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×C₈×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#2968	—	3	1	no	maximal, Hall
17	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
18	C₅×#947	C₄	1	1	yes	characteristic
19	C₅×#946	C₄	1	1	yes	characteristic
20	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
21	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
22	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
23	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
24	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
25	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
26	C₅×#898	C₄	1	1	yes	characteristic
27	C₅×#898	C₄	1	1	yes	characteristic
28	C₅×#895	C₄	1	1	yes	characteristic
29	C₅×#894	C₄	1	1	yes	characteristic
30	C₅×#894	C₄	1	1	yes	characteristic
31	C₅×#890	C₄	1	1	yes	characteristic
32	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
33	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
34	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
35	C₅×#872	C₂²	1	1	yes	characteristic
36	C₅×#872	C₂²	1	1	yes	characteristic
37	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
38	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
39	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
40	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
41	C₃×C₅×#97	C₂²	1	1	yes	characteristic
42	C₃×C₅×#97	C₂²	1	1	yes	characteristic
43	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
44	C₅×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic
45	C₅×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic
46	C₅×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic
47	C₅×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic
48	C₅×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic
49	C₅×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic
50	C₅×#815	C₂²	1	1	yes	characteristic
51	C₅×#815	C₂²	1	1	yes	characteristic
52	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic
53	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic
54	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
55	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
56	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
57	C₅×#803	C₂²	1	1	yes	characteristic
58	C₅×#803	C₂²	1	1	yes	characteristic
59	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
60	#79941	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
61	C₅×#529	—	3	1	no	—
62	C₅×#446	—	3	1	no	—
63	C₅×#446	D₃	1	1	yes	characteristic, complemented
64	C₅×#435	—	3	1	no	—
65	C₅×#435	—	3	1	no	—
66	C₅×#435	—	3	1	no	—
67	C₅×#435	—	3	1	no	—
68	C₅×C₈×D₄	—	3	1	no	—
69	C₅×C₈×D₄	—	3	1	no	—
70	C₅×#433	—	3	1	no	—
71	C₅×#433	—	3	1	no	—
72	C₅×#431	—	3	1	no	—
73	C₅×#405	—	3	1	no	—
74	C₅×#405	—	3	1	no	—
75	C₂×C₅×#97	—	3	1	no	—
76	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
77	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
78	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
79	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
81	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
83	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
84	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
85	C₂×C₃×C₅×C₈	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	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
89	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
90	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
91	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
92	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
93	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
94	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
95	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
96	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
97	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
98	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
99	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
100	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
101	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
102	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
103	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
104	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
105	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
106	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
107	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
108	C₅×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
109	C₅×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
110	C₅×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
111	C₅×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
112	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
113	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
114	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
115	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
116	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
117	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
118	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
119	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
120	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
121	C₅×D₃×C₈	—	2	2	no	—
122	C₅×D₃×C₈	—	2	2	no	—
123	C₅×D₃×C₈	—	2	2	no	—
124	C₅×D₃×C₈	—	2	2	no	—
125	#5580	C₂×C₅	1	1	yes	characteristic
126	C₃×#446	C₂×C₅	1	1	yes	characteristic, complemented
127	#5024	C₂×C₅	1	1	yes	characteristic, complemented
128	#4840	C₂×C₅	1	1	yes	characteristic, complemented
129	#4840	C₂×C₅	1	1	yes	characteristic, complemented
130	#4836	C₂×C₅	1	1	yes	characteristic, complemented
131	#4836	C₂×C₅	1	1	yes	characteristic, complemented
132	#4834	C₂×C₅	1	1	yes	characteristic, complemented
133	#4833	C₂×C₅	1	1	yes	characteristic, complemented
134	#4708	C₂×C₅	1	1	yes	characteristic, complemented
135	#4706	C₂×C₅	1	1	yes	characteristic, complemented
136	#4706	C₂×C₅	1	1	yes	characteristic, complemented
137	D₃×#97	C₂×C₅	1	1	yes	characteristic, complemented
138	#4689	C₂×C₅	1	1	yes	characteristic, complemented
139	C₈×D₁₂	C₂×C₅	1	1	yes	characteristic, complemented
140	C₂×C₅×M₁₆	—	3	1	no	—
141	C₂×C₅×M₁₆	—	3	1	no	—
142	C₂²×C₅×C₈	—	3	1	no	—
143	C₂²×C₅×C₈	—	3	1	no	—
144	C₂²×C₅×C₈	—	3	1	no	—
145	C₂²×C₅×C₈	—	3	1	no	—
146	C₅×#126	—	3	1	no	—
147	C₅×#126	—	3	1	no	—
148	C₅×#125	—	3	1	no	—
149	C₅×#124	—	3	1	no	—
150	C₅×#123	—	3	1	no	—
151	C₅×#123	—	3	1	no	—
152	C₅×C₂²⋊Q₈	—	3	1	no	—
153	C₅×#121	—	3	1	no	—
154	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
155	C₄×C₅×D₄	—	3	1	no	—
156	C₄×C₅×D₄	—	3	1	no	—
157	C₄×C₅×D₄	—	3	1	no	—
158	C₅×#117	—	3	1	no	—
159	C₅×#117	—	3	1	no	—
160	C₂×C₄²×C₅	—	3	1	no	—
161	C₅×C₄⋊C₈	—	3	1	no	—
162	C₅×C₄⋊C₈	—	3	1	no	—
163	C₅×C₄⋊C₈	—	3	1	no	—
164	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
165	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
166	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
167	C₅×C₂²⋊C₈	—	3	1	no	—
168	C₅×C₂²⋊C₈	—	3	1	no	—
169	C₅×C₂²⋊C₈	—	3	1	no	—
170	C₅×C₂²⋊C₈	—	3	1	no	—
171	C₅×C₂²⋊C₈	—	3	1	no	—
172	C₅×C₂²⋊C₈	—	3	1	no	—
173	C₅×#97	—	3	1	no	—
174	C₅×#97	—	3	1	no	—
175	C₅×#97	—	3	1	no	—
176	C₅×#97	—	3	1	no	—
177	C₅×#97	C₂×D₃	1	1	yes	characteristic
178	C₅×#97	C₂×D₃	1	1	yes	characteristic
179	C₄×C₅×C₈	—	3	1	no	—
180	C₄×C₅×C₈	—	3	1	no	—
181	C₄×C₅×C₈	—	3	1	no	—
182	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
183	#2968	—	3	1	no	Sylow
184	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
185	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
186	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
187	C₃×C₅×Q₈	—	4	1	no	—
188	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
189	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
190	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
191	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
192	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
193	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
194	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
195	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
196	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
197	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
198	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
199	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
200	C₅×D₁₂	—	2	2	no	—
201	C₅×D₁₂	—	2	2	no	—
202	C₅×D₁₂	—	4	1	no	—
203	C₄×C₅×D₃	—	2	2	no	—
204	C₄×C₅×D₃	—	2	1	no	—
205	C₄×C₅×D₃	—	2	1	no	—
206	C₄×C₅×D₃	—	2	1	no	—
207	C₄×C₅×D₃	—	2	1	no	—
208	C₄×C₅×D₃	—	2	1	no	—
209	C₄×C₅×D₃	—	2	1	no	—
210	C₄×C₅×D₃	—	4	1	no	—
211	C₃×C₅×C₈	—	2	1	no	—
212	C₃×C₅×C₈	—	2	1	no	—
213	C₃×C₅×C₈	—	2	1	no	—
214	C₃×C₅×C₈	#41	1	2	yes	—
215	C₅×C₃⋊C₈	—	2	1	no	—
216	C₅×C₃⋊C₈	—	2	1	no	—
217	C₅×C₃⋊C₈	—	2	1	no	—
218	C₅×C₃⋊C₈	#41	1	2	yes	—
219	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
220	#947	C₄×C₅	1	1	yes	characteristic
221	#946	C₄×C₅	1	1	yes	characteristic
222	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	1	yes	characteristic
223	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	1	yes	characteristic
224	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
225	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
226	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
227	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
228	#898	C₄×C₅	1	1	yes	characteristic
229	#898	C₄×C₅	1	1	yes	characteristic
230	#895	C₄×C₅	1	1	yes	characteristic
231	#894	C₄×C₅	1	1	yes	characteristic
232	#894	C₄×C₅	1	1	yes	characteristic
233	#890	C₄×C₅	1	1	yes	characteristic
234	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
235	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
236	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
237	#872	C₂²×C₅	1	1	yes	characteristic
238	#872	C₂²×C₅	1	1	yes	characteristic
239	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
240	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
241	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
242	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
243	C₃×#97	C₂²×C₅	1	1	yes	characteristic
244	C₃×#97	C₂²×C₅	1	1	yes	characteristic
245	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
246	(C₂×D₃)⋊C₈	C₂²×C₅	1	1	yes	characteristic
247	(C₂×D₃)⋊C₈	C₂²×C₅	1	1	yes	characteristic
248	(C₂×D₃)⋊C₈	C₂²×C₅	1	1	yes	characteristic
249	(C₂×D₃)⋊C₈	C₂²×C₅	1	1	yes	characteristic
250	(C₂×D₃)⋊C₈	C₂²×C₅	1	1	yes	characteristic
251	(C₂×D₃)⋊C₈	C₂²×C₅	1	1	yes	characteristic
252	#815	C₂²×C₅	1	1	yes	characteristic
253	#815	C₂²×C₅	1	1	yes	characteristic
254	C₈×Dic₃	C₂²×C₅	1	1	yes	characteristic
255	C₈×Dic₃	C₂²×C₅	1	1	yes	characteristic
256	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic
257	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic
258	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic
259	#803	C₂²×C₅	1	1	yes	characteristic
260	#803	C₂²×C₅	1	1	yes	characteristic
261	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
262	C₂×C₅×Q₈	C₄×D₃	1	1	yes	characteristic
263	C₂×C₅×D₄	—	3	1	no	—
264	C₂×C₅×D₄	—	3	1	no	—
265	C₂×C₅×D₄	—	3	1	no	—
266	C₂²×C₄×C₅	—	3	1	no	—
267	C₂²×C₄×C₅	—	3	1	no	—
268	C₂²×C₄×C₅	—	3	1	no	—
269	C₂²×C₄×C₅	—	3	1	no	—
270	C₂²×C₄×C₅	—	3	1	no	—
271	C₅×M₁₆	—	6	2	no	—
272	C₅×M₁₆	—	6	2	no	—
273	C₂×C₅×C₈	—	3	1	no	—
274	C₂×C₅×C₈	—	3	1	no	—
275	C₂×C₅×C₈	—	3	1	no	—
276	C₂×C₅×C₈	—	3	1	no	—
277	C₂×C₅×C₈	—	6	2	no	—
278	C₂×C₅×C₈	—	6	2	no	—
279	C₂×C₅×C₈	—	6	2	no	—
280	C₂×C₅×C₈	—	6	2	no	—
281	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
282	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
283	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
284	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
285	C₅×C₄⋊C₄	—	3	1	no	—
286	C₅×C₄⋊C₄	—	3	1	no	—
287	C₅×C₄⋊C₄	—	3	1	no	—
288	C₅×C₄⋊C₄	—	3	1	no	—
289	C₅×C₄⋊C₄	—	3	1	no	—
290	C₅×C₄⋊C₄	—	3	1	no	—
291	C₅×C₄⋊C₄	—	3	1	no	—
292	C₅×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
293	C₅×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
294	C₅×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
295	C₅×C₂²⋊C₄	—	3	1	no	—
296	C₅×C₂²⋊C₄	—	3	1	no	—
297	C₅×C₂²⋊C₄	—	3	1	no	—
298	C₅×C₂²⋊C₄	—	3	1	no	—
299	C₅×C₂²⋊C₄	—	3	1	no	—
300	C₅×C₂²⋊C₄	—	3	1	no	—
301	C₅×C₂²⋊C₄	—	3	1	no	—
302	C₅×C₂²⋊C₄	—	3	1	no	—
303	C₅×C₂²⋊C₄	—	3	1	no	—
304	C₅×C₂²⋊C₄	—	3	1	no	—
305	C₄²×C₅	—	3	1	no	—
306	C₄²×C₅	—	3	1	no	—
307	C₄²×C₅	—	3	1	no	—
308	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
309	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
310	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
311	#529	—	3	1	no	—
312	#446	—	3	1	no	—
313	#446	C₅×D₃	1	1	yes	characteristic, complemented
314	#435	—	3	1	no	—
315	#435	—	3	1	no	—
316	#435	—	3	1	no	—
317	#435	—	3	1	no	—
318	C₈×D₄	—	3	1	no	—
319	C₈×D₄	—	3	1	no	—
320	#433	—	3	1	no	—
321	#433	—	3	1	no	—
322	#431	—	3	1	no	—
323	#405	—	3	1	no	—
324	#405	—	3	1	no	—
325	C₂×#97	—	3	1	no	—
326	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
327	C₂×C₅×D₃	—	2	1	no	—
328	C₂×C₅×D₃	—	2	1	no	—
329	C₂×C₅×D₃	—	2	1	no	—
330	C₂×C₅×D₃	—	2	1	no	—
331	C₂×C₅×D₃	—	2	1	no	—
332	C₂×C₅×D₃	—	2	1	no	—
333	C₂×C₅×D₃	—	2	1	no	—
334	C₂×C₅×D₃	—	2	1	no	—
335	C₂×C₅×D₃	#131	1	2	yes	—
336	C₃×C₄×C₅	—	2	1	no	—
337	C₃×C₄×C₅	—	2	1	no	—
338	C₃×C₄×C₅	—	2	1	no	—
339	C₃×C₄×C₅	—	2	1	no	—
340	C₃×C₄×C₅	—	2	1	no	—
341	C₃×C₄×C₅	—	2	1	no	—
342	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
343	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
344	C₅×Dic₃	—	2	1	no	—
345	C₅×Dic₃	—	2	1	no	—
346	C₅×Dic₃	—	2	1	no	—
347	C₅×Dic₃	—	2	1	no	—
348	C₅×Dic₃	—	2	1	no	—
349	C₂×C₃×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
350	C₂×D₁₂	C₂×C₄×C₅	1	1	yes	characteristic
351	C₂×D₁₂	C₂×C₄×C₅	1	1	yes	characteristic
352	C₂×D₁₂	C₂×C₄×C₅	1	1	yes	characteristic
353	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
354	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
355	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
356	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
357	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
358	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
359	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
360	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
361	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
362	C₃×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
363	C₃×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
364	C₃×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
365	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
366	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
367	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
368	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
369	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
370	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
371	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
372	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
373	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
374	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
375	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
376	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
377	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
378	C₄⋊Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
379	C₄⋊Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
380	C₄⋊Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
381	Dic₃⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
382	Dic₃⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
383	Dic₃⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
384	Dic₃⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
385	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
386	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
387	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
388	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
389	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
390	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
391	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
392	ΓL(1,𝔽₂₅)	—	2	2	no	—
393	ΓL(1,𝔽₂₅)	—	2	2	no	—
394	D₃×C₈	—	2	2	no	—
395	D₃×C₈	—	2	2	no	—
396	D₃×C₈	—	2	2	no	—
397	D₃×C₈	—	2	2	no	—
398	C₂³×C₅	—	3	1	no	—
399	C₂³×C₅	—	3	1	no	—
400	C₂³×C₅	—	3	1	no	—
401	C₅×Q₈	—	4	1	no	—
402	C₅×D₄	—	6	2	no	—
403	C₅×D₄	—	6	2	no	—
404	C₅×D₄	—	12	1	no	—
405	C₂×C₄×C₅	—	3	1	no	—
406	C₂×C₄×C₅	—	3	1	no	—
407	C₂×C₄×C₅	—	3	1	no	—
408	C₂×C₄×C₅	—	3	1	no	—
409	C₂×C₄×C₅	—	3	1	no	—
410	C₂×C₄×C₅	—	6	2	no	—
411	C₂×C₄×C₅	—	6	1	no	—
412	C₂×C₄×C₅	—	6	1	no	—
413	C₂×C₄×C₅	—	6	1	no	—
414	C₂×C₄×C₅	—	6	1	no	—
415	C₂×C₄×C₅	—	6	1	no	—
416	C₂×C₄×C₅	—	6	1	no	—
417	C₂×C₄×C₅	—	12	1	no	—
418	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
419	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
420	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
421	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
422	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
423	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
424	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
425	C₅×C₈	—	2	1	no	—
426	C₅×C₈	—	2	1	no	—
427	C₅×C₈	—	2	1	no	—
428	C₅×C₈	—	3	2	no	—
429	C₅×C₈	—	6	1	no	—
430	C₅×C₈	—	6	1	no	—
431	C₅×C₈	—	6	1	no	—
432	C₅×C₈	#239	1	2	yes	—
433	C₂×M₁₆	—	3	1	no	—
434	C₂×M₁₆	—	3	1	no	—
435	C₂²×C₈	—	3	1	no	—
436	C₂²×C₈	—	3	1	no	—
437	C₂²×C₈	—	3	1	no	—
438	C₂²×C₈	—	3	1	no	—
439	#126	—	3	1	no	—
440	#126	—	3	1	no	—
441	#125	—	3	1	no	—
442	#124	—	3	1	no	—
443	#123	—	3	1	no	—
444	#123	—	3	1	no	—
445	C₂²⋊Q₈	—	3	1	no	—
446	#121	—	3	1	no	—
447	C₄×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
448	C₄×D₄	—	3	1	no	—
449	C₄×D₄	—	3	1	no	—
450	C₄×D₄	—	3	1	no	—
451	#117	—	3	1	no	—
452	#117	—	3	1	no	—
453	C₂×C₄²	—	3	1	no	—
454	C₄⋊C₈	—	3	1	no	—
455	C₄⋊C₈	—	3	1	no	—
456	C₄⋊C₈	—	3	1	no	—
457	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
458	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
459	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
460	C₂²⋊C₈	—	3	1	no	—
461	C₂²⋊C₈	—	3	1	no	—
462	C₂²⋊C₈	—	3	1	no	—
463	C₂²⋊C₈	—	3	1	no	—
464	C₂²⋊C₈	—	3	1	no	—
465	C₂²⋊C₈	—	3	1	no	—
466	#97	—	3	1	no	—
467	#97	—	3	1	no	—
468	#97	—	3	1	no	—
469	#97	—	3	1	no	—
470	#97	C₂×C₅×D₃	1	1	yes	characteristic
471	#97	C₂×C₅×D₃	1	1	yes	characteristic
472	C₄×C₈	—	3	1	no	—
473	C₄×C₈	—	3	1	no	—
474	C₄×C₈	—	3	1	no	—
475	C₄×C₈	C₂×C₅×D₃	1	1	yes	characteristic
476	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
477	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
478	C₂×C₃×C₅	#568	1	1	yes	characteristic
479	C₅×D₃	—	2	2	no	—
480	C₅×D₃	—	4	1	no	—
481	C₅×D₃	—	4	1	no	—
482	C₂²×D₃	C₂²×C₄×C₅	1	1	yes	characteristic
483	C₂²×D₃	C₂²×C₄×C₅	1	1	yes	characteristic
484	C₂²×D₃	C₂²×C₄×C₅	1	1	yes	characteristic
485	C₃×Q₈	—	4	1	no	—
486	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
487	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
488	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
489	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
490	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
491	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
492	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
493	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
494	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
495	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
496	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
497	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
498	D₁₂	—	2	2	no	—
499	D₁₂	—	2	2	no	—
500	D₁₂	—	4	1	no	—
501	C₄×D₃	—	2	2	no	—
502	C₄×D₃	—	2	1	no	—
503	C₄×D₃	—	2	1	no	—
504	C₄×D₃	—	2	1	no	—
505	C₄×D₃	—	2	1	no	—
506	C₄×D₃	—	2	1	no	—
507	C₄×D₃	—	2	1	no	—
508	C₄×D₃	—	4	1	no	—
509	C₃×C₈	—	2	1	no	—
510	C₃×C₈	—	2	1	no	—
511	C₃×C₈	—	2	1	no	—
512	C₃×C₈	C₅×#41	1	2	yes	—
513	C₃⋊C₈	—	2	1	no	—
514	C₃⋊C₈	—	2	1	no	—
515	C₃⋊C₈	—	2	1	no	—
516	C₃⋊C₈	C₅×#41	1	2	yes	—
517	C₂²×C₅	—	3	2	no	—
518	C₂²×C₅	—	6	1	no	—
519	C₂²×C₅	—	6	1	no	—
520	C₂²×C₅	—	6	1	no	—
521	C₂²×C₅	—	6	1	no	—
522	C₂²×C₅	—	6	1	no	—
523	C₂²×C₅	—	6	1	no	—
524	C₂²×C₅	—	6	1	no	—
525	C₂²×C₅	—	6	1	no	—
526	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
527	C₄×C₅	—	2	1	no	—
528	C₄×C₅	—	2	1	no	—
529	C₄×C₅	—	2	1	no	—
530	C₄×C₅	—	2	1	no	—
531	C₄×C₅	—	2	1	no	—
532	C₄×C₅	—	2	1	no	—
533	C₄×C₅	—	6	1	no	—
534	C₄×C₅	—	6	1	no	—
535	C₄×C₅	—	6	1	no	—
536	C₄×C₅	—	6	1	no	—
537	C₄×C₅	—	6	1	no	—
538	C₄×C₅	C₂×#239	1	1	yes	characteristic
539	C₄×C₅	D₃×#41	1	1	yes	characteristic
540	C₂×Q₈	C₄×C₅×D₃	1	1	yes	characteristic
541	C₂×D₄	—	3	1	no	—
542	C₂×D₄	—	3	1	no	—
543	C₂×D₄	—	3	1	no	—
544	C₂²×C₄	—	3	1	no	—
545	C₂²×C₄	—	3	1	no	—
546	C₂²×C₄	—	3	1	no	—
547	C₂²×C₄	—	3	1	no	—
548	C₂²×C₄	—	3	1	no	—
549	M₁₆	—	6	2	no	—
550	M₁₆	—	6	2	no	—
551	C₂×C₈	—	3	1	no	—
552	C₂×C₈	—	3	1	no	—
553	C₂×C₈	—	3	1	no	—
554	C₂×C₈	—	3	1	no	—
555	C₂×C₈	—	6	2	no	—
556	C₂×C₈	—	6	2	no	—
557	C₂×C₈	—	6	2	no	—
558	C₂×C₈	—	6	2	no	—
559	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
560	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
561	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
562	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
563	C₄⋊C₄	—	3	1	no	—
564	C₄⋊C₄	—	3	1	no	—
565	C₄⋊C₄	—	3	1	no	—
566	C₄⋊C₄	—	3	1	no	—
567	C₄⋊C₄	—	3	1	no	—
568	C₄⋊C₄	—	3	1	no	—
569	C₄⋊C₄	—	3	1	no	—
570	C₄⋊C₄	C₄×C₅×D₃	1	1	yes	characteristic
571	C₄⋊C₄	C₄×C₅×D₃	1	1	yes	characteristic
572	C₄⋊C₄	C₄×C₅×D₃	1	1	yes	characteristic
573	C₂²⋊C₄	—	3	1	no	—
574	C₂²⋊C₄	—	3	1	no	—
575	C₂²⋊C₄	—	3	1	no	—
576	C₂²⋊C₄	—	3	1	no	—
577	C₂²⋊C₄	—	3	1	no	—
578	C₂²⋊C₄	—	3	1	no	—
579	C₂²⋊C₄	—	3	1	no	—
580	C₂²⋊C₄	—	3	1	no	—
581	C₂²⋊C₄	—	3	1	no	—
582	C₂²⋊C₄	—	3	1	no	—
583	C₄²	—	3	1	no	—
584	C₄²	—	3	1	no	—
585	C₄²	—	3	1	no	—
586	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
587	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
588	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
589	C₃×C₅	#2968	1	1	yes	characteristic, complemented, Hall
590	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
591	C₂×D₃	—	2	1	no	—
592	C₂×D₃	—	2	1	no	—
593	C₂×D₃	—	2	1	no	—
594	C₂×D₃	—	2	1	no	—
595	C₂×D₃	—	2	1	no	—
596	C₂×D₃	—	2	1	no	—
597	C₂×D₃	—	2	1	no	—
598	C₂×D₃	—	2	1	no	—
599	C₂×D₃	C₅×#131	1	2	yes	—
600	C₃×C₄	—	2	1	no	—
601	C₃×C₄	—	2	1	no	—
602	C₃×C₄	—	2	1	no	—
603	C₃×C₄	—	2	1	no	—
604	C₃×C₄	—	2	1	no	—
605	C₃×C₄	—	2	1	no	—
606	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
607	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
608	Dic₃	—	2	1	no	—
609	Dic₃	—	2	1	no	—
610	Dic₃	—	2	1	no	—
611	Dic₃	—	2	1	no	—
612	Dic₃	—	2	1	no	—
613	C₂×C₅	—	6	2	no	—
614	C₂×C₅	—	12	1	no	—
615	C₂×C₅	—	12	1	no	—
616	C₂×C₅	C₄×#239	1	1	yes	characteristic
617	C₂×C₅	#5745	1	1	yes	characteristic
618	C₂×C₅	D₃×#131	1	1	yes	characteristic
619	C₂³	—	3	1	no	—
620	C₂³	—	3	1	no	—
621	C₂³	—	3	1	no	—
622	Q₈	—	4	1	no	—
623	D₄	—	6	2	no	—
624	D₄	—	6	2	no	—
625	D₄	—	12	1	no	—
626	C₂×C₄	—	3	1	no	—
627	C₂×C₄	—	3	1	no	—
628	C₂×C₄	—	3	1	no	—
629	C₂×C₄	—	3	1	no	—
630	C₂×C₄	—	3	1	no	—
631	C₂×C₄	—	6	2	no	—
632	C₂×C₄	—	6	1	no	—
633	C₂×C₄	—	6	1	no	—
634	C₂×C₄	—	6	1	no	—
635	C₂×C₄	—	6	1	no	—
636	C₂×C₄	—	6	1	no	—
637	C₂×C₄	—	6	1	no	—
638	C₂×C₄	—	12	1	no	—
639	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
640	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
641	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
642	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
643	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
644	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
645	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
646	C₈	—	2	1	no	—
647	C₈	—	2	1	no	—
648	C₈	—	2	1	no	—
649	C₈	—	3	2	no	—
650	C₈	—	6	1	no	—
651	C₈	—	6	1	no	—
652	C₈	—	6	1	no	—
653	C₈	C₅×#239	1	2	yes	—
654	C₂×C₃	C₄×C₅×#41	1	1	yes	characteristic
655	C₂×C₃	C₂×C₅×#131	1	1	yes	characteristic
656	C₂×C₃	C₅×#568	1	1	yes	characteristic
657	D₃	—	2	2	no	—
658	D₃	—	4	1	no	—
659	D₃	—	4	1	no	—
660	C₅	#79941	1	1	yes	characteristic, direct product factor, Sylow
661	C₂²	—	3	2	no	—
662	C₂²	—	6	1	no	—
663	C₂²	—	6	1	no	—
664	C₂²	—	6	1	no	—
665	C₂²	—	6	1	no	—
666	C₂²	—	6	1	no	—
667	C₂²	—	6	1	no	—
668	C₂²	—	6	1	no	—
669	C₂²	—	6	1	no	—
670	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
671	C₄	—	2	1	no	—
672	C₄	—	2	1	no	—
673	C₄	—	2	1	no	—
674	C₄	—	2	1	no	—
675	C₄	—	2	1	no	—
676	C₄	—	2	1	no	—
677	C₄	—	6	1	no	—
678	C₄	—	6	1	no	—
679	C₄	—	6	1	no	—
680	C₄	—	6	1	no	—
681	C₄	—	6	1	no	—
682	C₄	C₂×C₅×#239	1	1	yes	characteristic
683	C₄	C₅×D₃×#41	1	1	yes	characteristic
684	C₃	C₅×#2968	1	1	yes	characteristic, complemented, Sylow
685	C₂	—	6	2	no	—
686	C₂	—	12	1	no	—
687	C₂	—	12	1	no	—
688	C₂	C₄×C₅×#239	1	1	yes	characteristic
689	C₂	C₅×#5745	1	1	yes	characteristic
690	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	C₅×#895	C₄
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₅×#446	D₃
hypocenter	C₃	C₅×#2968
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×#5024	C₂	semidirect
4. C₅×#4840	C₂	semidirect
5. C₅×#4840	C₂	semidirect
6. C₅×#4836	C₂	semidirect
7. C₅×#4836	C₂	semidirect
8. C₅×#4834	C₂	semidirect
9. C₅×#4833	C₂	semidirect
10. C₅×#4708	C₂	semidirect
11. C₅×#4706	C₂	semidirect
12. C₅×#4706	C₂	semidirect
13. C₅×D₃×#97	C₂	semidirect
14. C₅×#4689	C₂	semidirect
15. C₅×C₈×D₁₂	C₂	semidirect
60. #79941	C₅	direct (N × H)
63. C₅×#446	D₃	semidirect
126. C₃×#446	C₂×C₅	semidirect
127. #5024	C₂×C₅	semidirect
128. #4840	C₂×C₅	semidirect
129. #4840	C₂×C₅	semidirect
130. #4836	C₂×C₅	semidirect
131. #4836	C₂×C₅	semidirect
132. #4834	C₂×C₅	semidirect
133. #4833	C₂×C₅	semidirect
134. #4708	C₂×C₅	semidirect
135. #4706	C₂×C₅	semidirect
136. #4706	C₂×C₅	semidirect
137. D₃×#97	C₂×C₅	semidirect
138. #4689	C₂×C₅	semidirect
139. C₈×D₁₂	C₂×C₅	semidirect
313. #446	C₅×D₃	semidirect
589. C₃×C₅	#2968	semidirect
660. C₅	#79941	direct (N × H)
684. C₃	C₅×#2968	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5580	2
C₃×C₅×#446	2
C₅×#5024	2
C₅×#4840	2
C₅×#4836	2
C₅×#4834	2
C₅×#4833	2
C₅×#4708	2
C₅×#4706	2
C₅×D₃×#97	2
C₅×#4689	2
C₅×C₈×D₁₂	2
C₅×#2968	3
#79941	5

Subgroups — C5×#79941 #14419583

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#79941 #14419583