Subgroups — C₅×#79371 #14413993

Order 1920.

784 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₃×#117	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#433	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5000	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4840	C₂	1	2	yes	maximal, complemented
5	C₅×#4837	C₂	1	2	yes	maximal, complemented
6	C₅×#4726	C₂	1	2	yes	maximal
7	C₅×#4720	C₂	1	2	yes	maximal, complemented
8	C₅×#4709	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#4707	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4690	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₅×ΓL(1,𝔽₂₅)	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#2921	—	3	1	no	maximal, Hall
13	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
14	C₃×C₅×#117	C₂²	1	1	yes	characteristic
15	C₅×#926	C₂²	1	1	yes	characteristic
16	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	—
17	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	—
18	C₅×#892	C₄	1	2	yes	—
19	C₅×D₃×C₄⋊C₄	C₄	1	2	yes	—
20	C₅×D₃×C₂²⋊C₄	C₄	1	2	yes	—
21	C₅×#877	C₄	1	2	yes	—
22	C₅×#872	C₂²	1	1	yes	characteristic
23	C₅×#872	C₂²	1	1	yes	characteristic
24	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
25	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
26	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	complemented
27	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
28	C₃×C₅×#97	C₂²	1	1	yes	characteristic, complemented
29	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
30	C₅×#830	C₂²	1	2	yes	—
31	C₅×(C₂×D₃)⋊C₈	C₂²	1	2	yes	—
32	C₅×(C₂×D₃)⋊C₈	C₂²	1	2	yes	—
33	C₅×#815	C₂²	1	2	yes	complemented
34	C₅×Dic₃⋊C₈	C₂²	1	2	yes	complemented
35	C₅×Dic₃⋊C₈	C₂²	1	2	yes	complemented
36	C₅×C₈×Dic₃	C₂²	1	2	yes	complemented
37	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	2	yes	complemented
38	C₅×#803	C₂²	1	1	yes	characteristic, complemented
39	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
40	#79371	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
41	C₂×C₅×#117	—	3	1	no	—
42	C₅×#433	—	3	2	no	—
43	C₅×#433	—	3	2	no	—
44	C₅×#433	—	3	1	no	—
45	C₅×#433	—	3	1	no	—
46	C₅×#433	—	3	1	no	—
47	C₅×#433	D₃	1	1	yes	characteristic, complemented
48	C₅×#423	—	3	2	no	—
49	C₅×#407	—	3	2	no	—
50	C₄×C₅×M₁₆	—	3	1	no	—
51	C₄×C₅×M₁₆	—	3	1	no	—
52	C₂³×C₅×D₃	C₂×C₄	1	1	yes	characteristic
53	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
54	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄×C₅×D₃	—	2	4	no	—
56	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
59	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
60	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
61	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
62	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
63	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
64	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
65	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
66	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
67	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
68	C₅×#217	C₂×C₄	1	2	yes	—
69	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
70	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
71	C₅×C₄⋊Dic₃	C₂×C₄	1	2	yes	—
72	C₅×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
73	C₅×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
74	C₄×C₅×Dic₃	C₂×C₄	1	2	yes	—
75	C₄×C₅×Dic₃	C₂×C₄	1	2	yes	—
76	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
77	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
78	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
79	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
80	C₅×ΓL(1,𝔽₂₅)	—	2	4	no	—
81	C₅×ΓL(1,𝔽₂₅)	—	2	4	no	—
82	D₃×#117	C₂×C₅	1	1	yes	characteristic
83	C₃×#433	C₂×C₅	1	1	yes	characteristic, complemented
84	#5000	C₂×C₅	1	1	yes	characteristic, complemented
85	#4840	C₂×C₅	1	2	yes	complemented
86	#4837	C₂×C₅	1	2	yes	complemented
87	#4726	C₂×C₅	1	2	yes	—
88	#4720	C₂×C₅	1	2	yes	complemented
89	#4709	C₂×C₅	1	1	yes	characteristic, complemented
90	#4707	C₂×C₅	1	1	yes	characteristic, complemented
91	#4690	C₂×C₅	1	1	yes	characteristic, complemented
92	C₄×ΓL(1,𝔽₂₅)	C₂×C₅	1	1	yes	characteristic, complemented
93	C₂³×C₄×C₅	—	3	1	no	—
94	C₂×C₅×M₁₆	—	3	2	no	—
95	C₂×C₅×M₁₆	—	3	2	no	—
96	C₅×#117	—	3	1	no	—
97	C₅×#117	—	3	2	no	—
98	C₅×#117	—	3	2	no	—
99	C₅×#117	—	3	1	no	—
100	C₅×#117	—	3	1	no	—
101	C₅×#117	C₂×D₃	1	1	yes	characteristic
102	C₂×C₅×C₄⋊C₄	—	3	2	no	—
103	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
104	C₂×C₄²×C₅	—	3	1	no	—
105	C₂×C₄²×C₅	—	3	1	no	—
106	C₅×C₄⋊C₈	—	3	2	no	—
107	C₅×C₄⋊C₈	—	3	2	no	—
108	C₅×C₄⋊C₈	—	3	2	no	—
109	C₅×C₄⋊C₈	C₂×D₃	1	2	yes	complemented
110	C₅×C₂²⋊C₈	—	3	2	no	—
111	C₅×C₂²⋊C₈	—	3	2	no	—
112	C₅×C₂²⋊C₈	—	3	2	no	—
113	C₅×C₂²⋊C₈	C₂×D₃	1	2	yes	—
114	C₅×#97	—	3	2	no	—
115	C₅×#97	—	3	1	no	—
116	C₅×#97	C₂×D₃	1	1	yes	characteristic, complemented
117	C₄×C₅×C₈	—	3	2	no	—
118	C₄×C₅×C₈	—	3	1	no	—
119	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic, complemented
120	#2921	—	3	1	no	Sylow
121	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₅×D₃	—	2	2	no	—
123	C₂²×C₅×D₃	—	4	2	no	—
124	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₃×C₄×C₅	—	2	2	no	—
127	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
128	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
129	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
131	C₂×C₅×Dic₃	—	2	2	no	—
132	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
133	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
134	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
136	C₄×C₅×D₃	—	2	2	no	—
137	C₄×C₅×D₃	—	2	2	no	—
138	C₄×C₅×D₃	—	2	2	no	—
139	C₄×C₅×D₃	—	4	2	no	—
140	C₄×C₅×D₃	—	4	2	no	—
141	C₄×C₅×D₃	#41	1	4	yes	—
142	C₃×C₅×C₈	—	2	2	no	—
143	C₃×C₅×C₈	—	2	2	no	—
144	C₅×C₃⋊C₈	—	2	2	no	—
145	C₅×C₃⋊C₈	—	2	2	no	—
146	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
147	C₃×#117	C₂²×C₅	1	1	yes	characteristic
148	#926	C₂²×C₅	1	1	yes	characteristic
149	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	2	yes	—
150	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	2	yes	—
151	#892	C₄×C₅	1	2	yes	—
152	D₃×C₄⋊C₄	C₄×C₅	1	2	yes	—
153	D₃×C₂²⋊C₄	C₄×C₅	1	2	yes	—
154	#877	C₄×C₅	1	2	yes	—
155	#872	C₂²×C₅	1	1	yes	characteristic
156	#872	C₂²×C₅	1	1	yes	characteristic
157	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
158	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
159	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	complemented
160	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
161	C₃×#97	C₂²×C₅	1	1	yes	characteristic, complemented
162	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
163	#830	C₂²×C₅	1	2	yes	—
164	(C₂×D₃)⋊C₈	C₂²×C₅	1	2	yes	—
165	(C₂×D₃)⋊C₈	C₂²×C₅	1	2	yes	—
166	#815	C₂²×C₅	1	2	yes	complemented
167	Dic₃⋊C₈	C₂²×C₅	1	2	yes	complemented
168	Dic₃⋊C₈	C₂²×C₅	1	2	yes	complemented
169	C₈×Dic₃	C₂²×C₅	1	2	yes	complemented
170	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	2	yes	complemented
171	#803	C₂²×C₅	1	1	yes	characteristic, complemented
172	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
173	C₂⁴×C₅	—	3	1	no	—
174	C₂²×C₄×C₅	—	3	1	no	—
175	C₂²×C₄×C₅	—	3	1	no	—
176	C₂²×C₄×C₅	—	3	1	no	—
177	C₂²×C₄×C₅	—	3	1	no	—
178	C₂²×C₄×C₅	—	3	1	no	—
179	C₂²×C₄×C₅	—	3	2	no	—
180	C₂²×C₄×C₅	—	3	2	no	—
181	C₂²×C₄×C₅	—	6	4	no	—
182	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
183	C₅×M₁₆	—	6	4	no	—
184	C₅×M₁₆	—	6	4	no	—
185	C₂×C₅×C₈	—	3	2	no	—
186	C₂×C₅×C₈	—	3	2	no	—
187	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
188	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
189	C₅×C₄⋊C₄	—	3	2	no	—
190	C₅×C₄⋊C₄	—	3	2	no	—
191	C₅×C₄⋊C₄	—	3	2	no	—
192	C₅×C₄⋊C₄	C₄×D₃	1	2	yes	—
193	C₅×C₂²⋊C₄	—	3	2	no	—
194	C₅×C₂²⋊C₄	—	3	2	no	—
195	C₅×C₂²⋊C₄	—	3	2	no	—
196	C₅×C₂²⋊C₄	C₄×D₃	1	2	yes	—
197	C₄²×C₅	—	3	2	no	—
198	C₄²×C₅	—	3	2	no	—
199	C₄²×C₅	—	3	1	no	—
200	C₄²×C₅	—	3	1	no	—
201	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
202	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
203	C₂×#117	—	3	1	no	—
204	#433	—	3	1	no	—
205	#433	—	3	2	no	—
206	#433	—	3	2	no	—
207	#433	—	3	1	no	—
208	#433	—	3	1	no	—
209	#433	C₅×D₃	1	1	yes	characteristic, complemented
210	#423	—	3	2	no	—
211	#407	—	3	2	no	—
212	C₄×M₁₆	—	3	1	no	—
213	C₄×M₁₆	—	3	1	no	—
214	C₂²×C₃×C₅	—	2	1	no	—
215	C₂²×C₃×C₅	—	2	2	no	—
216	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
217	C₂×C₅×D₃	—	2	2	no	—
218	C₂×C₅×D₃	—	2	1	no	—
219	C₂×C₅×D₃	—	2	2	no	—
220	C₂×C₅×D₃	—	4	4	no	—
221	C₂×C₅×D₃	#117	1	2	yes	—
222	C₃×C₄×C₅	—	2	1	no	—
223	C₃×C₄×C₅	—	2	2	no	—
224	C₃×C₄×C₅	—	2	2	no	—
225	C₃×C₄×C₅	C₂×#41	1	2	yes	—
226	C₅×Dic₃	—	2	1	no	—
227	C₅×Dic₃	—	2	2	no	—
228	C₅×Dic₃	—	2	2	no	—
229	C₅×Dic₃	#117	1	2	yes	—
230	C₂³×D₃	C₂×C₄×C₅	1	1	yes	characteristic
231	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
232	C₂²×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
233	C₂×C₄×D₃	—	2	4	no	—
234	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
235	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
236	C₂×C₄×D₃	C₂×C₄×C₅	1	2	yes	—
237	C₂×C₄×D₃	C₂×C₄×C₅	1	2	yes	—
238	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
239	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
240	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
241	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
242	C₃×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
243	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
244	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
245	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
246	#217	C₂×C₄×C₅	1	2	yes	—
247	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	2	yes	—
248	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	2	yes	—
249	C₄⋊Dic₃	C₂×C₄×C₅	1	2	yes	—
250	Dic₃⋊C₄	C₂×C₄×C₅	1	2	yes	—
251	Dic₃⋊C₄	C₂×C₄×C₅	1	2	yes	—
252	C₄×Dic₃	C₂×C₄×C₅	1	2	yes	—
253	C₄×Dic₃	C₂×C₄×C₅	1	2	yes	—
254	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
255	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
256	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
257	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
258	ΓL(1,𝔽₂₅)	—	2	4	no	—
259	ΓL(1,𝔽₂₅)	—	2	4	no	—
260	C₂³×C₅	—	3	1	no	—
261	C₂³×C₅	—	3	1	no	—
262	C₂³×C₅	—	6	2	no	—
263	C₂³×C₅	—	12	2	no	—
264	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
265	C₂×C₄×C₅	—	2	2	no	—
266	C₂×C₄×C₅	—	3	1	no	—
267	C₂×C₄×C₅	—	3	4	no	—
268	C₂×C₄×C₅	—	3	2	no	—
269	C₂×C₄×C₅	—	3	2	no	—
270	C₂×C₄×C₅	—	3	1	no	—
271	C₂×C₄×C₅	—	6	2	no	—
272	C₂×C₄×C₅	—	6	2	no	—
273	C₂×C₄×C₅	—	6	2	no	—
274	C₂×C₄×C₅	—	6	2	no	—
275	C₂×C₄×C₅	—	12	2	no	—
276	C₂×C₄×C₅	—	12	2	no	—
277	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
278	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
279	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
280	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
281	C₅×C₈	—	2	2	no	—
282	C₅×C₈	—	2	2	no	—
283	C₅×C₈	—	6	2	no	—
284	C₅×C₈	—	6	2	no	—
285	C₂³×C₄	—	3	1	no	—
286	C₂×M₁₆	—	3	2	no	—
287	C₂×M₁₆	—	3	2	no	—
288	#117	—	3	1	no	—
289	#117	—	3	2	no	—
290	#117	—	3	2	no	—
291	#117	—	3	1	no	—
292	#117	—	3	1	no	—
293	#117	C₂×C₅×D₃	1	1	yes	characteristic
294	C₂×C₄⋊C₄	—	3	2	no	—
295	C₂×C₂²⋊C₄	—	3	2	no	—
296	C₂×C₄²	—	3	1	no	—
297	C₂×C₄²	—	3	1	no	—
298	C₄⋊C₈	—	3	2	no	—
299	C₄⋊C₈	—	3	2	no	—
300	C₄⋊C₈	—	3	2	no	—
301	C₄⋊C₈	C₂×C₅×D₃	1	2	yes	complemented
302	C₂²⋊C₈	—	3	2	no	—
303	C₂²⋊C₈	—	3	2	no	—
304	C₂²⋊C₈	—	3	2	no	—
305	C₂²⋊C₈	C₂×C₅×D₃	1	2	yes	—
306	#97	—	3	2	no	—
307	#97	—	3	1	no	—
308	#97	C₂×C₅×D₃	1	1	yes	characteristic, complemented
309	C₄×C₈	—	3	2	no	—
310	C₄×C₈	—	3	1	no	—
311	C₄×C₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
312	C₂×C₃×C₅	—	4	1	no	—
313	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
314	C₂×C₃×C₅	#568	1	2	yes	—
315	C₅×D₃	—	2	2	no	—
316	C₅×D₃	—	4	1	no	—
317	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
318	C₂²×D₃	—	2	2	no	—
319	C₂²×D₃	—	4	2	no	—
320	C₂²×D₃	C₂²×C₄×C₅	1	1	yes	characteristic
321	C₂²×D₃	C₂²×C₄×C₅	1	1	yes	characteristic
322	C₂×C₃×C₄	—	2	2	no	—
323	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
324	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
325	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
326	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
327	C₂×Dic₃	—	2	2	no	—
328	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
329	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
330	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
331	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
332	C₄×D₃	—	2	2	no	—
333	C₄×D₃	—	2	2	no	—
334	C₄×D₃	—	2	2	no	—
335	C₄×D₃	—	4	2	no	—
336	C₄×D₃	—	4	2	no	—
337	C₄×D₃	C₅×#41	1	4	yes	—
338	C₃×C₈	—	2	2	no	—
339	C₃×C₈	—	2	2	no	—
340	C₃⋊C₈	—	2	2	no	—
341	C₃⋊C₈	—	2	2	no	—
342	C₂²×C₅	—	2	2	no	—
343	C₂²×C₅	—	2	1	no	—
344	C₂²×C₅	—	3	2	no	—
345	C₂²×C₅	—	6	2	no	—
346	C₂²×C₅	—	6	2	no	—
347	C₂²×C₅	—	6	1	no	—
348	C₂²×C₅	—	12	4	no	—
349	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
350	C₄×C₅	—	2	2	no	—
351	C₄×C₅	—	2	2	no	—
352	C₄×C₅	—	2	1	no	—
353	C₄×C₅	—	3	2	no	—
354	C₄×C₅	—	6	2	no	—
355	C₄×C₅	—	6	2	no	—
356	C₄×C₅	—	6	1	no	—
357	C₄×C₅	D₃×#41	1	2	yes	—
358	C₂⁴	—	3	1	no	—
359	C₂²×C₄	—	3	1	no	—
360	C₂²×C₄	—	3	1	no	—
361	C₂²×C₄	—	3	1	no	—
362	C₂²×C₄	—	3	1	no	—
363	C₂²×C₄	—	3	1	no	—
364	C₂²×C₄	—	3	2	no	—
365	C₂²×C₄	—	3	2	no	—
366	C₂²×C₄	—	6	4	no	—
367	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
368	M₁₆	—	6	4	no	—
369	M₁₆	—	6	4	no	—
370	C₂×C₈	—	3	2	no	—
371	C₂×C₈	—	3	2	no	—
372	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
373	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
374	C₄⋊C₄	—	3	2	no	—
375	C₄⋊C₄	—	3	2	no	—
376	C₄⋊C₄	—	3	2	no	—
377	C₄⋊C₄	C₄×C₅×D₃	1	2	yes	—
378	C₂²⋊C₄	—	3	2	no	—
379	C₂²⋊C₄	—	3	2	no	—
380	C₂²⋊C₄	—	3	2	no	—
381	C₂²⋊C₄	C₄×C₅×D₃	1	2	yes	—
382	C₄²	—	3	2	no	—
383	C₄²	—	3	2	no	—
384	C₄²	—	3	1	no	—
385	C₄²	—	3	1	no	—
386	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
387	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
388	C₃×C₅	#2921	1	1	yes	characteristic, complemented, Hall
389	C₂²×C₃	—	2	1	no	—
390	C₂²×C₃	—	2	2	no	—
391	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
392	C₂×D₃	—	2	2	no	—
393	C₂×D₃	—	2	1	no	—
394	C₂×D₃	—	2	2	no	—
395	C₂×D₃	—	4	4	no	—
396	C₂×D₃	C₅×#117	1	2	yes	—
397	C₃×C₄	—	2	1	no	—
398	C₃×C₄	—	2	2	no	—
399	C₃×C₄	—	2	2	no	—
400	C₃×C₄	C₂×C₅×#41	1	2	yes	—
401	Dic₃	—	2	1	no	—
402	Dic₃	—	2	2	no	—
403	Dic₃	—	2	2	no	—
404	Dic₃	C₅×#117	1	2	yes	—
405	C₂×C₅	—	4	1	no	—
406	C₂×C₅	—	6	2	no	—
407	C₂×C₅	—	12	1	no	—
408	C₂×C₅	D₃×#117	1	1	yes	characteristic
409	C₂×C₅	#5750	1	2	yes	—
410	C₂³	—	3	1	no	—
411	C₂³	—	3	1	no	—
412	C₂³	—	6	2	no	—
413	C₂³	—	12	2	no	—
414	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	3	1	no	—
417	C₂×C₄	—	3	4	no	—
418	C₂×C₄	—	3	2	no	—
419	C₂×C₄	—	3	2	no	—
420	C₂×C₄	—	3	1	no	—
421	C₂×C₄	—	6	2	no	—
422	C₂×C₄	—	6	2	no	—
423	C₂×C₄	—	6	2	no	—
424	C₂×C₄	—	6	2	no	—
425	C₂×C₄	—	12	2	no	—
426	C₂×C₄	—	12	2	no	—
427	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
428	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
429	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
430	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
431	C₈	—	2	2	no	—
432	C₈	—	2	2	no	—
433	C₈	—	6	2	no	—
434	C₈	—	6	2	no	—
435	C₂×C₃	—	4	1	no	—
436	C₂×C₃	C₂×C₅×#117	1	1	yes	characteristic
437	C₂×C₃	C₅×#568	1	2	yes	—
438	D₃	—	2	2	no	—
439	D₃	—	4	1	no	—
440	C₅	#79371	1	1	yes	characteristic, direct product factor, Sylow
441	C₂²	—	2	2	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	3	2	no	—
444	C₂²	—	6	2	no	—
445	C₂²	—	6	2	no	—
446	C₂²	—	6	1	no	—
447	C₂²	—	12	4	no	—
448	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
449	C₄	—	2	2	no	—
450	C₄	—	2	2	no	—
451	C₄	—	2	1	no	—
452	C₄	—	3	2	no	—
453	C₄	—	6	2	no	—
454	C₄	—	6	2	no	—
455	C₄	—	6	1	no	—
456	C₄	C₅×D₃×#41	1	2	yes	—
457	C₃	C₅×#2921	1	1	yes	characteristic, complemented, Sylow
458	C₂	—	4	1	no	—
459	C₂	—	6	2	no	—
460	C₂	—	12	1	no	—
461	C₂	C₅×D₃×#117	1	1	yes	characteristic
462	C₂	C₅×#5750	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₅	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#433	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂³×C₅×D₃	C₂×C₄
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₅×#433	D₃
hypocenter	C₃	C₅×#2921
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₅×#433

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#433	C₂	semidirect
3. C₅×#5000	C₂	semidirect
4. C₅×#4840	C₂	semidirect
5. C₅×#4837	C₂	semidirect
7. C₅×#4720	C₂	semidirect
8. C₅×#4709	C₂	semidirect
9. C₅×#4707	C₂	semidirect
10. C₅×#4690	C₂	semidirect
11. C₄×C₅×ΓL(1,𝔽₂₅)	C₂	semidirect
26. C₃×C₅×C₄⋊C₈	C₂²	semidirect
28. C₃×C₅×#97	C₂²	semidirect
29. C₃×C₄×C₅×C₈	C₂²	semidirect
33. C₅×#815	C₂²	semidirect
34. C₅×Dic₃⋊C₈	C₂²	semidirect
35. C₅×Dic₃⋊C₈	C₂²	semidirect
36. C₅×C₈×Dic₃	C₂²	semidirect
37. C₅×C₄⋊(C₃⋊C₈)	C₂²	semidirect
38. C₅×#803	C₂²	semidirect
39. C₄×C₅×C₃⋊C₈	C₂²	semidirect
40. #79371	C₅	direct (N × H)
47. C₅×#433	D₃	semidirect
83. C₃×#433	C₂×C₅	semidirect
84. #5000	C₂×C₅	semidirect
85. #4840	C₂×C₅	semidirect
86. #4837	C₂×C₅	semidirect
88. #4720	C₂×C₅	semidirect
89. #4709	C₂×C₅	semidirect
90. #4707	C₂×C₅	semidirect
91. #4690	C₂×C₅	semidirect
92. C₄×ΓL(1,𝔽₂₅)	C₂×C₅	semidirect
109. C₅×C₄⋊C₈	C₂×D₃	semidirect
116. C₅×#97	C₂×D₃	semidirect
119. C₄×C₅×C₈	C₂×D₃	semidirect
159. C₃×C₄⋊C₈	C₂²×C₅	semidirect
161. C₃×#97	C₂²×C₅	semidirect
162. C₃×C₄×C₈	C₂²×C₅	semidirect
166. #815	C₂²×C₅	semidirect
167. Dic₃⋊C₈	C₂²×C₅	semidirect
168. Dic₃⋊C₈	C₂²×C₅	semidirect
169. C₈×Dic₃	C₂²×C₅	semidirect
170. C₄⋊(C₃⋊C₈)	C₂²×C₅	semidirect
171. #803	C₂²×C₅	semidirect
172. C₄×C₃⋊C₈	C₂²×C₅	semidirect
209. #433	C₅×D₃	semidirect
301. C₄⋊C₈	C₂×C₅×D₃	semidirect
308. #97	C₂×C₅×D₃	semidirect
311. C₄×C₈	C₂×C₅×D₃	semidirect
388. C₃×C₅	#2921	semidirect
440. C₅	#79371	direct (N × H)
457. C₃	C₅×#2921	semidirect

Maximal subgroups

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

subgroup	index
C₅×D₃×#117	2
C₃×C₅×#433	2
C₅×#5000	2
C₅×#4840	2
C₅×#4837	2
C₅×#4726	2
C₅×#4720	2
C₅×#4709	2
C₅×#4707	2
C₅×#4690	2
C₄×C₅×ΓL(1,𝔽₂₅)	2
C₅×#2921	3
#79371	5

Subgroups — C5×#79371 #14413993

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#79371 #14413993