Subgroups — C₅×#79959 #14418565

Order 1920.

696 conjugacy classes of subgroups.

The subgroup lattice has 644 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×#5024	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4839	C₂	1	1	yes	maximal, characteristic
5	C₅×#4839	C₂	1	1	yes	maximal, characteristic
6	C₅×#4837	C₂	1	1	yes	maximal, characteristic
7	C₅×#4831	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4828	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#4828	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4708	C₂	1	1	yes	maximal, characteristic
11	C₅×D₃×#97	C₂	1	1	yes	maximal, characteristic
12	C₅×#4701	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#4701	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#4689	C₂	1	1	yes	maximal, characteristic
15	C₅×#4679	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#2961	—	3	1	no	maximal, Hall
17	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
18	C₅×#946	C₄	1	1	yes	characteristic
19	C₅×#944	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	C₅×#897	C₄	1	1	yes	characteristic
25	C₅×#896	C₄	1	1	yes	characteristic
26	C₅×#896	C₄	1	1	yes	characteristic
27	C₅×#889	C₄	1	1	yes	characteristic
28	C₅×#889	C₄	1	1	yes	characteristic
29	C₅×#888	C₄	1	1	yes	characteristic
30	C₅×#872	C₂²	1	1	yes	characteristic
31	C₅×#872	C₂²	1	1	yes	characteristic
32	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
33	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
34	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
35	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
36	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
37	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
38	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
39	C₃×C₅×#97	C₂²	1	1	yes	characteristic
40	C₃×C₅×#97	C₂²	1	1	yes	characteristic
41	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
42	C₅×#815	C₂²	1	1	yes	characteristic
43	C₅×#815	C₂²	1	1	yes	characteristic
44	C₅×#815	C₂²	1	1	yes	characteristic
45	C₅×#815	C₂²	1	1	yes	characteristic
46	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
47	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
48	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
49	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
50	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
51	C₅×Dic₃⋊C₈	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	#79959	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
61	C₅×#533	—	3	1	no	—
62	C₅×#446	—	3	1	no	—
63	C₅×#446	—	3	1	no	—
64	C₅×#446	—	3	1	no	—
65	C₅×#446	—	3	1	no	—
66	C₅×#446	—	3	1	no	—
67	C₅×#446	—	3	1	no	—
68	C₅×#446	—	3	1	no	—
69	C₅×#446	D₃	1	1	yes	characteristic, complemented
70	C₅×#424	—	3	1	no	—
71	C₅×#424	—	3	1	no	—
72	C₅×#423	—	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×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
80	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
81	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
82	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
83	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
84	C₂×C₃×C₅×C₈	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	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
88	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
89	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
90	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
91	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
92	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
93	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
94	C₅×(C₂×D₃)⋊C₄	C₂×C₄	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×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
98	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
99	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
100	C₅×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
101	C₅×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
102	C₅×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
103	C₅×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
104	C₅×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
105	C₅×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
106	C₅×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
107	C₅×Dic₃⋊C₄	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	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
111	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
112	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
113	C₄×C₅×Dic₃	C₂³	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	Q₈	1	4	yes	complemented
123	#5578	C₂×C₅	1	1	yes	characteristic
124	C₃×#446	C₂×C₅	1	1	yes	characteristic, complemented
125	#5024	C₂×C₅	1	1	yes	characteristic, complemented
126	#4839	C₂×C₅	1	1	yes	characteristic
127	#4839	C₂×C₅	1	1	yes	characteristic
128	#4837	C₂×C₅	1	1	yes	characteristic
129	#4831	C₂×C₅	1	1	yes	characteristic, complemented
130	#4828	C₂×C₅	1	1	yes	characteristic, complemented
131	#4828	C₂×C₅	1	1	yes	characteristic, complemented
132	#4708	C₂×C₅	1	1	yes	characteristic
133	D₃×#97	C₂×C₅	1	1	yes	characteristic
134	#4701	C₂×C₅	1	1	yes	characteristic, complemented
135	#4701	C₂×C₅	1	1	yes	characteristic, complemented
136	#4689	C₂×C₅	1	1	yes	characteristic
137	#4679	C₂×C₅	1	1	yes	characteristic, complemented
138	C₂×C₅×M₁₆	—	3	1	no	—
139	C₂×C₅×M₁₆	—	3	1	no	—
140	C₂²×C₅×C₈	—	3	1	no	—
141	C₂²×C₅×C₈	—	3	1	no	—
142	C₅×C₄⋊Q₈	—	3	1	no	—
143	C₅×C₄⋊Q₈	—	3	1	no	—
144	C₅×#125	—	3	1	no	—
145	C₅×#125	—	3	1	no	—
146	C₅×C₂²⋊Q₈	—	3	1	no	—
147	C₅×C₂²⋊Q₈	—	3	1	no	—
148	C₅×C₂²⋊Q₈	—	3	1	no	—
149	C₅×C₂²⋊Q₈	—	3	1	no	—
150	C₄×C₅×Q₈	—	3	1	no	—
151	C₄×C₅×Q₈	—	3	1	no	—
152	C₄×C₅×Q₈	—	3	1	no	—
153	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
154	C₅×#117	—	3	1	no	—
155	C₅×#117	—	3	1	no	—
156	C₂×C₄²×C₅	—	3	1	no	—
157	C₅×C₄⋊C₈	—	3	1	no	—
158	C₅×C₄⋊C₈	—	3	1	no	—
159	C₅×C₄⋊C₈	—	3	1	no	—
160	C₅×C₄⋊C₈	—	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	—	3	1	no	—
165	C₅×C₄⋊C₈	—	3	1	no	—
166	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
167	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
168	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
169	C₅×#97	—	3	1	no	—
170	C₅×#97	—	3	1	no	—
171	C₅×#97	—	3	1	no	—
172	C₅×#97	—	3	1	no	—
173	C₅×#97	—	3	1	no	—
174	C₅×#97	—	3	1	no	—
175	C₅×#97	C₂×D₃	1	1	yes	characteristic
176	C₅×#97	C₂×D₃	1	1	yes	characteristic
177	C₄×C₅×C₈	—	3	1	no	—
178	C₄×C₅×C₈	—	3	1	no	—
179	C₄×C₅×C₈	—	3	1	no	—
180	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
181	#2961	—	3	1	no	Sylow
182	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
183	C₃×C₅×Q₈	—	4	1	no	—
184	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
185	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
186	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
187	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
191	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
192	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
193	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
194	C₂×C₅×Dic₃	C₂²×C₄	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	C₄×C₅×D₃	—	4	1	no	—
199	C₄×C₅×D₃	—	4	1	no	—
200	C₄×C₅×D₃	C₂×Q₈	1	2	yes	—
201	C₄×C₅×D₃	#41	1	2	yes	—
202	C₅×Dic₆	—	4	1	no	—
203	C₅×Dic₆	—	4	1	no	—
204	C₅×Dic₆	—	4	1	no	—
205	C₃×C₅×C₈	—	2	1	no	—
206	C₃×C₅×C₈	—	2	1	no	—
207	C₃×C₅×C₈	—	2	1	no	—
208	C₃×C₅×C₈	C₂×Q₈	1	2	yes	—
209	C₅×C₃⋊C₈	—	2	1	no	—
210	C₅×C₃⋊C₈	—	2	1	no	—
211	C₅×C₃⋊C₈	—	2	1	no	—
212	C₅×C₃⋊C₈	C₂×Q₈	1	2	yes	—
213	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
214	#946	C₄×C₅	1	1	yes	characteristic
215	#944	C₄×C₅	1	1	yes	characteristic
216	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	1	yes	characteristic
217	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	1	yes	characteristic
218	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
219	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
220	#897	C₄×C₅	1	1	yes	characteristic
221	#896	C₄×C₅	1	1	yes	characteristic
222	#896	C₄×C₅	1	1	yes	characteristic
223	#889	C₄×C₅	1	1	yes	characteristic
224	#889	C₄×C₅	1	1	yes	characteristic
225	#888	C₄×C₅	1	1	yes	characteristic
226	#872	C₂²×C₅	1	1	yes	characteristic
227	#872	C₂²×C₅	1	1	yes	characteristic
228	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
229	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic
230	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic
231	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic
232	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
233	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
234	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
235	C₃×#97	C₂²×C₅	1	1	yes	characteristic
236	C₃×#97	C₂²×C₅	1	1	yes	characteristic
237	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
238	#815	C₂²×C₅	1	1	yes	characteristic
239	#815	C₂²×C₅	1	1	yes	characteristic
240	#815	C₂²×C₅	1	1	yes	characteristic
241	#815	C₂²×C₅	1	1	yes	characteristic
242	Dic₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
243	Dic₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
244	Dic₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
245	Dic₃⋊C₈	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	C₈×Dic₃	C₂²×C₅	1	1	yes	characteristic
249	C₈×Dic₃	C₂²×C₅	1	1	yes	characteristic
250	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic
251	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic
252	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic
253	#803	C₂²×C₅	1	1	yes	characteristic
254	#803	C₂²×C₅	1	1	yes	characteristic
255	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
256	C₂×C₅×Q₈	—	3	1	no	—
257	C₂×C₅×Q₈	—	3	1	no	—
258	C₂×C₅×Q₈	—	3	1	no	—
259	C₂×C₅×Q₈	C₄×D₃	1	1	yes	characteristic
260	C₂²×C₄×C₅	—	3	1	no	—
261	C₂²×C₄×C₅	—	3	1	no	—
262	C₂²×C₄×C₅	—	3	1	no	—
263	C₅×M₁₆	—	6	2	no	—
264	C₅×M₁₆	—	6	2	no	—
265	C₂×C₅×C₈	—	3	1	no	—
266	C₂×C₅×C₈	—	3	4	no	—
267	C₂×C₅×C₈	—	3	1	no	—
268	C₂×C₅×C₈	—	3	1	no	—
269	C₂×C₅×C₈	—	3	1	no	—
270	C₂×C₅×C₈	—	6	2	no	—
271	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
272	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
273	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
274	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
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	—	3	1	no	—
279	C₅×C₄⋊C₄	—	3	1	no	—
280	C₅×C₄⋊C₄	—	3	1	no	—
281	C₅×C₄⋊C₄	—	3	1	no	—
282	C₅×C₄⋊C₄	—	3	1	no	—
283	C₅×C₄⋊C₄	—	3	1	no	—
284	C₅×C₄⋊C₄	—	3	1	no	—
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	C₄×D₃	1	1	yes	characteristic
289	C₅×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
290	C₅×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
291	C₅×C₂²⋊C₄	—	3	1	no	—
292	C₅×C₂²⋊C₄	—	3	1	no	—
293	C₅×C₂²⋊C₄	—	3	1	no	—
294	C₅×C₂²⋊C₄	—	3	1	no	—
295	C₄²×C₅	—	3	1	no	—
296	C₄²×C₅	—	3	1	no	—
297	C₄²×C₅	—	3	1	no	—
298	C₄²×C₅	—	3	1	no	—
299	C₄²×C₅	—	3	1	no	—
300	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
301	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
302	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
303	#533	—	3	1	no	—
304	#446	—	3	1	no	—
305	#446	—	3	1	no	—
306	#446	—	3	1	no	—
307	#446	—	3	1	no	—
308	#446	—	3	1	no	—
309	#446	—	3	1	no	—
310	#446	—	3	1	no	—
311	#446	C₅×D₃	1	1	yes	characteristic, complemented
312	#424	—	3	1	no	—
313	#424	—	3	1	no	—
314	#423	—	3	1	no	—
315	#405	—	3	1	no	—
316	#405	—	3	1	no	—
317	C₂×#97	—	3	1	no	—
318	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
319	C₂×C₅×D₃	—	2	1	no	—
320	C₂×C₅×D₃	—	2	1	no	—
321	C₂×C₅×D₃	C₄×Q₈	1	2	yes	—
322	C₃×C₄×C₅	—	2	1	no	—
323	C₃×C₄×C₅	—	2	1	no	—
324	C₃×C₄×C₅	—	2	1	no	—
325	C₃×C₄×C₅	—	2	1	no	—
326	C₃×C₄×C₅	—	2	1	no	—
327	C₃×C₄×C₅	—	2	1	no	—
328	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
329	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
330	C₅×Dic₃	—	2	1	no	—
331	C₅×Dic₃	—	2	1	no	—
332	C₅×Dic₃	—	2	1	no	—
333	C₅×Dic₃	—	2	1	no	—
334	C₅×Dic₃	—	2	1	no	—
335	C₅×Dic₃	—	2	1	no	—
336	C₅×Dic₃	C₄×Q₈	1	2	yes	—
337	C₂×C₃×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
338	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
339	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
340	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
341	C₂×Dic₆	C₂×C₄×C₅	1	1	yes	characteristic
342	C₂×Dic₆	C₂×C₄×C₅	1	1	yes	characteristic
343	C₂×Dic₆	C₂×C₄×C₅	1	1	yes	characteristic
344	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
345	C₂×C₃×C₈	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	C₂×C₄×C₅	1	1	yes	characteristic
349	C₃×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
350	C₃×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
351	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
352	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
353	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
354	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
355	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
356	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
357	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
358	C₄⋊Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
359	C₄⋊Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
360	C₄⋊Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
361	Dic₃⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
362	Dic₃⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
363	Dic₃⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
364	Dic₃⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
365	Dic₃⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
366	Dic₃⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
367	Dic₃⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
368	Dic₃⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
369	Dic₃⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
370	Dic₃⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
371	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
372	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
373	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
374	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
375	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
376	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
377	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
378	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
379	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
380	ΓL(1,𝔽₂₅)	—	2	2	no	—
381	ΓL(1,𝔽₂₅)	—	2	2	no	—
382	D₃×C₈	—	2	2	no	—
383	D₃×C₈	C₅×Q₈	1	4	yes	complemented
384	C₂³×C₅	—	3	1	no	—
385	C₅×Q₈	—	4	1	no	—
386	C₅×Q₈	—	12	1	no	—
387	C₅×Q₈	—	12	1	no	—
388	C₅×Q₈	—	12	1	no	—
389	C₂×C₄×C₅	—	3	1	no	—
390	C₂×C₄×C₅	—	3	2	no	—
391	C₂×C₄×C₅	—	3	2	no	—
392	C₂×C₄×C₅	—	3	1	no	—
393	C₂×C₄×C₅	—	3	1	no	—
394	C₂×C₄×C₅	—	3	1	no	—
395	C₂×C₄×C₅	—	3	1	no	—
396	C₂×C₄×C₅	—	3	1	no	—
397	C₂×C₄×C₅	—	3	1	no	—
398	C₂×C₄×C₅	—	12	1	no	—
399	C₂×C₄×C₅	—	12	1	no	—
400	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
401	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
402	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
403	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
404	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
405	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
406	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
407	C₅×C₈	—	2	1	no	—
408	C₅×C₈	—	2	1	no	—
409	C₅×C₈	—	2	1	no	—
410	C₅×C₈	—	3	2	no	—
411	C₅×C₈	—	6	1	no	—
412	C₅×C₈	—	6	1	no	—
413	C₅×C₈	—	6	1	no	—
414	C₅×C₈	D₃×Q₈	1	2	yes	—
415	C₂×M₁₆	—	3	1	no	—
416	C₂×M₁₆	—	3	1	no	—
417	C₂²×C₈	—	3	1	no	—
418	C₂²×C₈	—	3	1	no	—
419	C₄⋊Q₈	—	3	1	no	—
420	C₄⋊Q₈	—	3	1	no	—
421	#125	—	3	1	no	—
422	#125	—	3	1	no	—
423	C₂²⋊Q₈	—	3	1	no	—
424	C₂²⋊Q₈	—	3	1	no	—
425	C₂²⋊Q₈	—	3	1	no	—
426	C₂²⋊Q₈	—	3	1	no	—
427	C₄×Q₈	—	3	1	no	—
428	C₄×Q₈	—	3	1	no	—
429	C₄×Q₈	—	3	1	no	—
430	C₄×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
431	#117	—	3	1	no	—
432	#117	—	3	1	no	—
433	C₂×C₄²	—	3	1	no	—
434	C₄⋊C₈	—	3	1	no	—
435	C₄⋊C₈	—	3	1	no	—
436	C₄⋊C₈	—	3	1	no	—
437	C₄⋊C₈	—	3	1	no	—
438	C₄⋊C₈	—	3	1	no	—
439	C₄⋊C₈	—	3	1	no	—
440	C₄⋊C₈	—	3	1	no	—
441	C₄⋊C₈	—	3	1	no	—
442	C₄⋊C₈	—	3	1	no	—
443	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
444	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
445	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
446	#97	—	3	1	no	—
447	#97	—	3	1	no	—
448	#97	—	3	1	no	—
449	#97	—	3	1	no	—
450	#97	—	3	1	no	—
451	#97	—	3	1	no	—
452	#97	C₂×C₅×D₃	1	1	yes	characteristic
453	#97	C₂×C₅×D₃	1	1	yes	characteristic
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	C₂×C₃×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
459	C₂×C₃×C₅	#568	1	1	yes	characteristic
460	C₂×C₃×C₅	#568	1	1	yes	characteristic
461	C₅×D₃	—	2	2	no	—
462	C₂²×D₃	C₂²×C₄×C₅	1	1	yes	characteristic
463	C₃×Q₈	—	4	1	no	—
464	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
465	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
466	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
467	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
468	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
469	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
470	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
471	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
472	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
473	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
474	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
475	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
476	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
477	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
478	C₄×D₃	—	4	1	no	—
479	C₄×D₃	—	4	1	no	—
480	C₄×D₃	C₂×C₅×Q₈	1	2	yes	—
481	C₄×D₃	C₅×#41	1	2	yes	—
482	Dic₆	—	4	1	no	—
483	Dic₆	—	4	1	no	—
484	Dic₆	—	4	1	no	—
485	C₃×C₈	—	2	1	no	—
486	C₃×C₈	—	2	1	no	—
487	C₃×C₈	—	2	1	no	—
488	C₃×C₈	C₂×C₅×Q₈	1	2	yes	—
489	C₃⋊C₈	—	2	1	no	—
490	C₃⋊C₈	—	2	1	no	—
491	C₃⋊C₈	—	2	1	no	—
492	C₃⋊C₈	C₂×C₅×Q₈	1	2	yes	—
493	C₂²×C₅	—	3	2	no	—
494	C₂²×C₅	—	6	1	no	—
495	C₂²×C₅	—	6	1	no	—
496	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
497	C₄×C₅	—	2	1	no	—
498	C₄×C₅	—	2	1	no	—
499	C₄×C₅	—	2	1	no	—
500	C₄×C₅	—	2	1	no	—
501	C₄×C₅	—	2	1	no	—
502	C₄×C₅	—	2	1	no	—
503	C₄×C₅	—	3	2	no	—
504	C₄×C₅	—	6	1	no	—
505	C₄×C₅	—	6	1	no	—
506	C₄×C₅	—	6	1	no	—
507	C₄×C₅	—	6	1	no	—
508	C₄×C₅	—	6	1	no	—
509	C₄×C₅	—	6	1	no	—
510	C₄×C₅	C₂×D₃×Q₈	1	1	yes	characteristic
511	C₄×C₅	D₃×#41	1	1	yes	characteristic
512	C₂×Q₈	—	3	1	no	—
513	C₂×Q₈	—	3	1	no	—
514	C₂×Q₈	—	3	1	no	—
515	C₂×Q₈	C₄×C₅×D₃	1	1	yes	characteristic
516	C₂²×C₄	—	3	1	no	—
517	C₂²×C₄	—	3	1	no	—
518	C₂²×C₄	—	3	1	no	—
519	M₁₆	—	6	2	no	—
520	M₁₆	—	6	2	no	—
521	C₂×C₈	—	3	1	no	—
522	C₂×C₈	—	3	4	no	—
523	C₂×C₈	—	3	1	no	—
524	C₂×C₈	—	3	1	no	—
525	C₂×C₈	—	3	1	no	—
526	C₂×C₈	—	6	2	no	—
527	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
528	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
529	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
530	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
531	C₄⋊C₄	—	3	1	no	—
532	C₄⋊C₄	—	3	1	no	—
533	C₄⋊C₄	—	3	1	no	—
534	C₄⋊C₄	—	3	1	no	—
535	C₄⋊C₄	—	3	1	no	—
536	C₄⋊C₄	—	3	1	no	—
537	C₄⋊C₄	—	3	1	no	—
538	C₄⋊C₄	—	3	1	no	—
539	C₄⋊C₄	—	3	1	no	—
540	C₄⋊C₄	—	3	1	no	—
541	C₄⋊C₄	—	3	1	no	—
542	C₄⋊C₄	—	3	1	no	—
543	C₄⋊C₄	—	3	1	no	—
544	C₄⋊C₄	C₄×C₅×D₃	1	1	yes	characteristic
545	C₄⋊C₄	C₄×C₅×D₃	1	1	yes	characteristic
546	C₄⋊C₄	C₄×C₅×D₃	1	1	yes	characteristic
547	C₂²⋊C₄	—	3	1	no	—
548	C₂²⋊C₄	—	3	1	no	—
549	C₂²⋊C₄	—	3	1	no	—
550	C₂²⋊C₄	—	3	1	no	—
551	C₄²	—	3	1	no	—
552	C₄²	—	3	1	no	—
553	C₄²	—	3	1	no	—
554	C₄²	—	3	1	no	—
555	C₄²	—	3	1	no	—
556	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
557	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
558	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
559	C₃×C₅	#2961	1	1	yes	characteristic, complemented, Hall
560	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
561	C₂×D₃	—	2	1	no	—
562	C₂×D₃	—	2	1	no	—
563	C₂×D₃	C₄×C₅×Q₈	1	2	yes	—
564	C₃×C₄	—	2	1	no	—
565	C₃×C₄	—	2	1	no	—
566	C₃×C₄	—	2	1	no	—
567	C₃×C₄	—	2	1	no	—
568	C₃×C₄	—	2	1	no	—
569	C₃×C₄	—	2	1	no	—
570	C₃×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
571	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
572	Dic₃	—	2	1	no	—
573	Dic₃	—	2	1	no	—
574	Dic₃	—	2	1	no	—
575	Dic₃	—	2	1	no	—
576	Dic₃	—	2	1	no	—
577	Dic₃	—	2	1	no	—
578	Dic₃	C₄×C₅×Q₈	1	2	yes	—
579	C₂×C₅	—	6	2	no	—
580	C₂×C₅	C₄×D₃×Q₈	1	1	yes	characteristic
581	C₂×C₅	#5745	1	1	yes	characteristic
582	C₂×C₅	#5750	1	1	yes	characteristic
583	C₂³	—	3	1	no	—
584	Q₈	—	4	1	no	—
585	Q₈	—	12	1	no	—
586	Q₈	—	12	1	no	—
587	Q₈	—	12	1	no	—
588	C₂×C₄	—	3	1	no	—
589	C₂×C₄	—	3	2	no	—
590	C₂×C₄	—	3	2	no	—
591	C₂×C₄	—	3	1	no	—
592	C₂×C₄	—	3	1	no	—
593	C₂×C₄	—	3	1	no	—
594	C₂×C₄	—	3	1	no	—
595	C₂×C₄	—	3	1	no	—
596	C₂×C₄	—	3	1	no	—
597	C₂×C₄	—	12	1	no	—
598	C₂×C₄	—	12	1	no	—
599	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
600	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
601	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
602	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
603	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
604	C₂×C₄	C₂×C₄×C₅×D₃	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	—	2	1	no	—
609	C₈	—	3	2	no	—
610	C₈	—	6	1	no	—
611	C₈	—	6	1	no	—
612	C₈	—	6	1	no	—
613	C₈	C₅×D₃×Q₈	1	2	yes	—
614	C₂×C₃	C₂×C₄×C₅×Q₈	1	1	yes	characteristic
615	C₂×C₃	C₅×#568	1	1	yes	characteristic
616	C₂×C₃	C₅×#568	1	1	yes	characteristic
617	D₃	—	2	2	no	—
618	C₅	#79959	1	1	yes	characteristic, direct product factor, Sylow
619	C₂²	—	3	2	no	—
620	C₂²	—	6	1	no	—
621	C₂²	—	6	1	no	—
622	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
623	C₄	—	2	1	no	—
624	C₄	—	2	1	no	—
625	C₄	—	2	1	no	—
626	C₄	—	2	1	no	—
627	C₄	—	2	1	no	—
628	C₄	—	2	1	no	—
629	C₄	—	3	2	no	—
630	C₄	—	6	1	no	—
631	C₄	—	6	1	no	—
632	C₄	—	6	1	no	—
633	C₄	—	6	1	no	—
634	C₄	—	6	1	no	—
635	C₄	—	6	1	no	—
636	C₄	C₂×C₅×D₃×Q₈	1	1	yes	characteristic
637	C₄	C₅×D₃×#41	1	1	yes	characteristic
638	C₃	C₅×#2961	1	1	yes	characteristic, complemented, Sylow
639	C₂	—	6	2	no	—
640	C₂	C₄×C₅×D₃×Q₈	1	1	yes	characteristic
641	C₂	C₅×#5745	1	1	yes	characteristic
642	C₂	C₅×#5750	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×#2961
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
7. C₅×#4831	C₂	semidirect
8. C₅×#4828	C₂	semidirect
9. C₅×#4828	C₂	semidirect
12. C₅×#4701	C₂	semidirect
13. C₅×#4701	C₂	semidirect
15. C₅×#4679	C₂	semidirect
60. #79959	C₅	direct (N × H)
69. C₅×#446	D₃	semidirect
122. C₅×D₃×C₈	Q₈	semidirect
124. C₃×#446	C₂×C₅	semidirect
125. #5024	C₂×C₅	semidirect
129. #4831	C₂×C₅	semidirect
130. #4828	C₂×C₅	semidirect
131. #4828	C₂×C₅	semidirect
134. #4701	C₂×C₅	semidirect
135. #4701	C₂×C₅	semidirect
137. #4679	C₂×C₅	semidirect
311. #446	C₅×D₃	semidirect
383. D₃×C₈	C₅×Q₈	semidirect
559. C₃×C₅	#2961	semidirect
618. C₅	#79959	direct (N × H)
638. C₃	C₅×#2961	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×#5024	2
C₅×#4839	2
C₅×#4837	2
C₅×#4831	2
C₅×#4828	2
C₅×#4708	2
C₅×D₃×#97	2
C₅×#4701	2
C₅×#4689	2
C₅×#4679	2
C₅×#2961	3
#79959	5

Subgroups — C5×#79959 #14418565

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#79959 #14418565