Subgroups — C₅×#79080 #14413110

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₃×M₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₅×ΓL(1,𝔽₂₅)	C₂	1	1	yes	maximal, characteristic
3	C₅×D₃×#117	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#424	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5119	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5102	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4999	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4839	C₂	1	4	yes	maximal, complemented
9	C₅×#4837	C₂	1	4	yes	maximal, complemented
10	C₅×#2905	—	3	1	no	maximal, Hall
11	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₅×C₈	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×#208	C₂²	1	1	yes	characteristic
17	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
18	C₅×D₃×M₁₆	—	2	4	no	—
19	C₂×C₅×ΓL(1,𝔽₂₅)	—	2	4	no	—
20	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	—
21	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	—
22	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	—
23	C₂×C₅×D₃×C₈	C₂²	1	2	yes	—
24	C₅×#892	C₄	1	2	yes	—
25	C₅×D₃×C₄⋊C₄	C₄	1	2	yes	—
26	C₅×D₃×C₂²⋊C₄	C₄	1	2	yes	—
27	C₅×#877	C₄	1	2	yes	—
28	C₅×#872	C₂²	1	2	yes	—
29	C₄²×C₅×D₃	C₂²	1	2	yes	—
30	C₃×C₅×C₄⋊C₈	C₂²	1	4	yes	complemented
31	C₅×Dic₃⋊C₈	C₂²	1	4	yes	complemented
32	C₅×Dic₃⋊C₈	C₂²	1	4	yes	complemented
33	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	4	yes	complemented
34	#79080	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
35	C₂²×C₅×M₁₆	—	3	1	no	—
36	C₂²×C₅×M₁₆	—	3	1	no	—
37	C₂×C₅×#117	—	3	1	no	—
38	C₅×#424	—	3	4	no	—
39	C₅×#424	—	3	1	no	—
40	C₅×#424	—	3	1	no	—
41	C₅×#424	—	3	1	no	—
42	C₅×#424	D₃	1	1	yes	characteristic, complemented
43	C₅×#423	—	3	4	no	—
44	C₂³×C₅×D₃	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
46	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄×C₅×D₃	C₂×C₄	1	4	yes	—
48	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄×C₅×D₃	D₄	1	4	yes	—
51	C₂×C₄×C₅×D₃	Q₈	1	4	yes	—
52	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
53	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
54	C₃×C₅×M₁₆	—	2	2	no	—
55	C₂×C₃×C₅×C₈	—	2	2	no	—
56	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
57	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
58	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
59	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
60	C₃×C₄²×C₅	C₂³	1	2	yes	—
61	C₅×#217	C₂×C₄	1	2	yes	—
62	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	4	yes	—
63	C₅×C₄⋊Dic₃	C₂×C₄	1	2	yes	—
64	C₅×Dic₃⋊C₄	C₂×C₄	1	4	yes	—
65	C₄×C₅×Dic₃	C₂×C₄	1	4	yes	—
66	C₄×C₅×Dic₃	C₂³	1	2	yes	—
67	C₅×#208	—	2	2	no	—
68	C₂×C₅×C₃⋊C₈	—	2	2	no	—
69	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
70	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
71	C₅×ΓL(1,𝔽₂₅)	—	2	4	no	—
72	C₅×ΓL(1,𝔽₂₅)	—	2	4	no	—
73	C₅×ΓL(1,𝔽₂₅)	—	2	4	no	—
74	C₅×D₃×C₈	—	2	4	no	—
75	C₂×D₃×M₁₆	C₂×C₅	1	1	yes	characteristic
76	C₂²×ΓL(1,𝔽₂₅)	C₂×C₅	1	1	yes	characteristic
77	D₃×#117	C₂×C₅	1	1	yes	characteristic
78	C₃×#424	C₂×C₅	1	1	yes	characteristic, complemented
79	#5119	C₂×C₅	1	1	yes	characteristic, complemented
80	#5102	C₂×C₅	1	1	yes	characteristic, complemented
81	#4999	C₂×C₅	1	1	yes	characteristic, complemented
82	#4839	C₂×C₅	1	4	yes	complemented
83	#4837	C₂×C₅	1	4	yes	complemented
84	C₂³×C₄×C₅	—	3	1	no	—
85	C₂×C₅×M₁₆	—	3	1	no	—
86	C₂×C₅×M₁₆	—	3	2	no	—
87	C₂×C₅×M₁₆	—	3	2	no	—
88	C₂×C₅×M₁₆	—	3	2	no	—
89	C₂×C₅×M₁₆	—	6	4	no	—
90	C₂×C₅×M₁₆	—	6	4	no	—
91	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
92	C₂²×C₅×C₈	—	3	1	no	—
93	C₂²×C₅×C₈	—	3	2	no	—
94	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
95	C₅×#117	—	3	1	no	—
96	C₅×#117	—	3	2	no	—
97	C₅×#117	—	3	2	no	—
98	C₅×#117	—	3	2	no	—
99	C₅×#117	C₂×D₃	1	1	yes	characteristic
100	C₂×C₅×C₄⋊C₄	—	3	2	no	—
101	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
102	C₂×C₄²×C₅	—	3	2	no	—
103	C₅×C₄⋊C₈	—	3	4	no	—
104	C₅×C₄⋊C₈	—	3	4	no	—
105	C₅×C₄⋊C₈	—	3	4	no	—
106	C₅×C₄⋊C₈	C₂×D₃	1	4	yes	complemented
107	#2905	—	3	1	no	Sylow
108	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₅×D₃	—	4	2	no	—
110	C₂²×C₅×D₃	C₄⋊C₄	1	4	yes	—
111	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
114	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
116	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
117	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
118	C₂×C₅×Dic₃	C₄⋊C₄	1	4	yes	—
119	C₂×C₅×Dic₃	C₂²×C₄	1	4	yes	—
120	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
122	C₄×C₅×D₃	—	4	4	no	—
123	C₄×C₅×D₃	C₄⋊C₄	1	4	yes	—
124	C₄×C₅×D₃	C₄⋊C₄	1	4	yes	—
125	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
126	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
127	C₄×C₅×D₃	C₂×Q₈	1	2	yes	—
128	C₄×C₅×D₃	C₂×Q₈	1	2	yes	—
129	C₃×C₅×C₈	—	2	2	no	—
130	C₃×C₅×C₈	—	2	2	no	—
131	C₅×C₃⋊C₈	—	2	2	no	—
132	C₅×C₃⋊C₈	—	2	2	no	—
133	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
134	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
135	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
136	C₃×#117	C₂²×C₅	1	1	yes	characteristic
137	#926	C₂²×C₅	1	1	yes	characteristic
138	C₂×#208	C₂²×C₅	1	1	yes	characteristic
139	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
140	D₃×M₁₆	—	2	4	no	—
141	C₂×ΓL(1,𝔽₂₅)	—	2	4	no	—
142	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	2	yes	—
143	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	2	yes	—
144	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	2	yes	—
145	C₂×D₃×C₈	C₂²×C₅	1	2	yes	—
146	#892	C₄×C₅	1	2	yes	—
147	D₃×C₄⋊C₄	C₄×C₅	1	2	yes	—
148	D₃×C₂²⋊C₄	C₄×C₅	1	2	yes	—
149	#877	C₄×C₅	1	2	yes	—
150	#872	C₂²×C₅	1	2	yes	—
151	C₄²×D₃	C₂²×C₅	1	2	yes	—
152	C₃×C₄⋊C₈	C₂²×C₅	1	4	yes	complemented
153	Dic₃⋊C₈	C₂²×C₅	1	4	yes	complemented
154	Dic₃⋊C₈	C₂²×C₅	1	4	yes	complemented
155	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	4	yes	complemented
156	C₂⁴×C₅	—	3	1	no	—
157	C₂²×C₄×C₅	—	3	1	no	—
158	C₂²×C₄×C₅	—	3	1	no	—
159	C₂²×C₄×C₅	—	3	1	no	—
160	C₂²×C₄×C₅	—	3	4	no	—
161	C₂²×C₄×C₅	—	3	4	no	—
162	C₂²×C₄×C₅	—	3	1	no	—
163	C₂²×C₄×C₅	—	3	1	no	—
164	C₂²×C₄×C₅	—	3	4	no	—
165	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
166	C₅×M₁₆	—	2	2	no	—
167	C₅×M₁₆	—	6	4	no	—
168	C₅×M₁₆	—	6	4	no	—
169	C₅×M₁₆	—	6	4	no	—
170	C₅×M₁₆	—	6	2	no	—
171	C₂×C₅×C₈	—	2	2	no	—
172	C₂×C₅×C₈	—	3	2	no	—
173	C₂×C₅×C₈	—	3	2	no	—
174	C₂×C₅×C₈	—	6	4	no	—
175	C₂×C₅×C₈	—	6	2	no	—
176	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
177	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
178	C₅×C₄⋊C₄	—	3	4	no	—
179	C₅×C₄⋊C₄	—	3	2	no	—
180	C₅×C₄⋊C₄	C₄×D₃	1	2	yes	—
181	C₅×C₂²⋊C₄	—	3	2	no	—
182	C₅×C₂²⋊C₄	—	3	4	no	—
183	C₅×C₂²⋊C₄	C₄×D₃	1	2	yes	—
184	C₄²×C₅	—	3	4	no	—
185	C₄²×C₅	—	3	2	no	—
186	C₄²×C₅	C₂²×D₃	1	2	yes	—
187	C₂²×M₁₆	—	3	1	no	—
188	C₂²×M₁₆	—	3	1	no	—
189	C₂×#117	—	3	1	no	—
190	#424	—	3	1	no	—
191	#424	—	3	1	no	—
192	#424	—	3	1	no	—
193	#424	—	3	4	no	—
194	#424	C₅×D₃	1	1	yes	characteristic, complemented
195	#423	—	3	4	no	—
196	C₂²×C₃×C₅	—	2	2	no	—
197	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	2	yes	—
198	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
199	C₂×C₅×D₃	—	2	2	no	—
200	C₂×C₅×D₃	—	2	2	no	—
201	C₂×C₅×D₃	—	4	4	no	—
202	C₂×C₅×D₃	C₂×C₄⋊C₄	1	2	yes	—
203	C₂×C₅×D₃	C₂×C₄⋊C₄	1	2	yes	—
204	C₃×C₄×C₅	—	2	4	no	—
205	C₃×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
206	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
207	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
208	C₅×Dic₃	—	2	4	no	—
209	C₅×Dic₃	C₂×C₄⋊C₄	1	2	yes	—
210	C₅×Dic₃	C₂×C₄⋊C₄	1	2	yes	—
211	C₂³×D₃	C₂×C₄×C₅	1	1	yes	characteristic
212	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
213	C₂²×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
214	C₂×C₄×D₃	C₂×C₄×C₅	1	4	yes	—
215	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
216	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
217	C₂×C₄×D₃	C₅×D₄	1	4	yes	—
218	C₂×C₄×D₃	C₅×Q₈	1	4	yes	—
219	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
220	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
221	C₃×M₁₆	—	2	2	no	—
222	C₂×C₃×C₈	—	2	2	no	—
223	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
224	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
225	C₃×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
226	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
227	C₃×C₄²	C₂³×C₅	1	2	yes	—
228	#217	C₂×C₄×C₅	1	2	yes	—
229	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	4	yes	—
230	C₄⋊Dic₃	C₂×C₄×C₅	1	2	yes	—
231	Dic₃⋊C₄	C₂×C₄×C₅	1	4	yes	—
232	C₄×Dic₃	C₂×C₄×C₅	1	4	yes	—
233	C₄×Dic₃	C₂³×C₅	1	2	yes	—
234	#208	—	2	2	no	—
235	C₂×C₃⋊C₈	—	2	2	no	—
236	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
237	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
238	ΓL(1,𝔽₂₅)	—	2	4	no	—
239	ΓL(1,𝔽₂₅)	—	2	4	no	—
240	ΓL(1,𝔽₂₅)	—	2	4	no	—
241	D₃×C₈	—	2	4	no	—
242	C₂³×C₅	—	3	1	no	—
243	C₂³×C₅	—	3	1	no	—
244	C₂³×C₅	—	3	4	no	—
245	C₂³×C₅	—	12	2	no	—
246	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
247	C₂×C₄×C₅	—	3	4	no	—
248	C₂×C₄×C₅	—	3	1	no	—
249	C₂×C₄×C₅	—	3	1	no	—
250	C₂×C₄×C₅	—	3	4	no	—
251	C₂×C₄×C₅	—	3	4	no	—
252	C₂×C₄×C₅	—	3	2	no	—
253	C₂×C₄×C₅	—	3	2	no	—
254	C₂×C₄×C₅	—	3	2	no	—
255	C₂×C₄×C₅	—	3	2	no	—
256	C₂×C₄×C₅	—	3	4	no	—
257	C₂×C₄×C₅	—	12	4	no	—
258	C₂×C₄×C₅	C₂×C₄×D₃	1	4	yes	—
259	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
260	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
261	C₂×C₄×C₅	D₃×Q₈	1	2	yes	—
262	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
263	C₅×C₈	—	2	2	no	—
264	C₅×C₈	—	2	2	no	—
265	C₅×C₈	—	6	2	no	—
266	C₅×C₈	—	6	2	no	—
267	C₂³×C₄	—	3	1	no	—
268	C₂×M₁₆	—	3	1	no	—
269	C₂×M₁₆	—	3	2	no	—
270	C₂×M₁₆	—	3	2	no	—
271	C₂×M₁₆	—	3	2	no	—
272	C₂×M₁₆	—	6	4	no	—
273	C₂×M₁₆	—	6	4	no	—
274	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
275	C₂²×C₈	—	3	1	no	—
276	C₂²×C₈	—	3	2	no	—
277	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
278	#117	—	3	1	no	—
279	#117	—	3	2	no	—
280	#117	—	3	2	no	—
281	#117	—	3	2	no	—
282	#117	C₂×C₅×D₃	1	1	yes	characteristic
283	C₂×C₄⋊C₄	—	3	2	no	—
284	C₂×C₂²⋊C₄	—	3	2	no	—
285	C₂×C₄²	—	3	2	no	—
286	C₄⋊C₈	—	3	4	no	—
287	C₄⋊C₈	—	3	4	no	—
288	C₄⋊C₈	—	3	4	no	—
289	C₄⋊C₈	C₂×C₅×D₃	1	4	yes	complemented
290	C₂×C₃×C₅	—	2	2	no	—
291	C₂×C₃×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
292	C₂×C₃×C₅	#568	1	2	yes	—
293	C₅×D₃	—	2	2	no	—
294	C₅×D₃	—	2	2	no	—
295	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
296	C₂²×D₃	—	4	2	no	—
297	C₂²×D₃	C₅×C₄⋊C₄	1	4	yes	—
298	C₂²×D₃	C₂²×C₄×C₅	1	1	yes	characteristic
299	C₂²×D₃	C₂²×C₄×C₅	1	1	yes	characteristic
300	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
301	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
302	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
303	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
304	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
305	C₂×Dic₃	C₅×C₄⋊C₄	1	4	yes	—
306	C₂×Dic₃	C₂²×C₄×C₅	1	4	yes	—
307	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
308	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
309	C₄×D₃	—	4	4	no	—
310	C₄×D₃	C₅×C₄⋊C₄	1	4	yes	—
311	C₄×D₃	C₅×C₄⋊C₄	1	4	yes	—
312	C₄×D₃	C₂×C₅×D₄	1	2	yes	—
313	C₄×D₃	C₂×C₅×D₄	1	2	yes	—
314	C₄×D₃	C₂×C₅×Q₈	1	2	yes	—
315	C₄×D₃	C₂×C₅×Q₈	1	2	yes	—
316	C₃×C₈	—	2	2	no	—
317	C₃×C₈	—	2	2	no	—
318	C₃⋊C₈	—	2	2	no	—
319	C₃⋊C₈	—	2	2	no	—
320	C₂²×C₅	—	2	2	no	—
321	C₂²×C₅	—	3	2	no	—
322	C₂²×C₅	—	3	2	no	—
323	C₂²×C₅	—	6	2	no	—
324	C₂²×C₅	—	6	2	no	—
325	C₂²×C₅	—	12	4	no	—
326	C₂²×C₅	D₃×C₄⋊C₄	1	2	yes	—
327	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
328	C₄×C₅	—	2	4	no	—
329	C₄×C₅	—	3	2	no	—
330	C₄×C₅	—	3	2	no	—
331	C₄×C₅	—	6	4	no	—
332	C₄×C₅	D₃×C₄⋊C₄	1	2	yes	—
333	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
334	C₄×C₅	C₂×D₃×Q₈	1	1	yes	characteristic
335	C₂⁴	—	3	1	no	—
336	C₂²×C₄	—	3	1	no	—
337	C₂²×C₄	—	3	1	no	—
338	C₂²×C₄	—	3	1	no	—
339	C₂²×C₄	—	3	4	no	—
340	C₂²×C₄	—	3	4	no	—
341	C₂²×C₄	—	3	1	no	—
342	C₂²×C₄	—	3	1	no	—
343	C₂²×C₄	—	3	4	no	—
344	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
345	M₁₆	—	2	2	no	—
346	M₁₆	—	6	4	no	—
347	M₁₆	—	6	4	no	—
348	M₁₆	—	6	4	no	—
349	M₁₆	—	6	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	3	2	no	—
352	C₂×C₈	—	3	2	no	—
353	C₂×C₈	—	6	4	no	—
354	C₂×C₈	—	6	2	no	—
355	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
356	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
357	C₄⋊C₄	—	3	4	no	—
358	C₄⋊C₄	—	3	2	no	—
359	C₄⋊C₄	C₄×C₅×D₃	1	2	yes	—
360	C₂²⋊C₄	—	3	2	no	—
361	C₂²⋊C₄	—	3	4	no	—
362	C₂²⋊C₄	C₄×C₅×D₃	1	2	yes	—
363	C₄²	—	3	4	no	—
364	C₄²	—	3	2	no	—
365	C₄²	C₂²×C₅×D₃	1	2	yes	—
366	C₃×C₅	#2905	1	1	yes	characteristic, complemented, Hall
367	C₂²×C₃	—	2	2	no	—
368	C₂²×C₃	C₂×C₅×C₄⋊C₄	1	2	yes	—
369	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
370	C₂×D₃	—	2	2	no	—
371	C₂×D₃	—	2	2	no	—
372	C₂×D₃	—	4	4	no	—
373	C₂×D₃	C₂×C₅×C₄⋊C₄	1	2	yes	—
374	C₂×D₃	C₂×C₅×C₄⋊C₄	1	2	yes	—
375	C₃×C₄	—	2	4	no	—
376	C₃×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
377	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
378	C₃×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
379	Dic₃	—	2	4	no	—
380	Dic₃	C₂×C₅×C₄⋊C₄	1	2	yes	—
381	Dic₃	C₂×C₅×C₄⋊C₄	1	2	yes	—
382	C₂×C₅	—	2	2	no	—
383	C₂×C₅	—	6	2	no	—
384	C₂×C₅	—	6	2	no	—
385	C₂×C₅	C₂×D₃×C₄⋊C₄	1	1	yes	characteristic
386	C₂×C₅	#5750	1	2	yes	—
387	C₂³	—	3	1	no	—
388	C₂³	—	3	1	no	—
389	C₂³	—	3	4	no	—
390	C₂³	—	12	2	no	—
391	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
392	C₂×C₄	—	3	4	no	—
393	C₂×C₄	—	3	1	no	—
394	C₂×C₄	—	3	1	no	—
395	C₂×C₄	—	3	4	no	—
396	C₂×C₄	—	3	4	no	—
397	C₂×C₄	—	3	2	no	—
398	C₂×C₄	—	3	2	no	—
399	C₂×C₄	—	3	2	no	—
400	C₂×C₄	—	3	2	no	—
401	C₂×C₄	—	3	4	no	—
402	C₂×C₄	—	12	4	no	—
403	C₂×C₄	C₂×C₄×C₅×D₃	1	4	yes	—
404	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
405	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
406	C₂×C₄	C₅×D₃×Q₈	1	2	yes	—
407	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
408	C₈	—	2	2	no	—
409	C₈	—	2	2	no	—
410	C₈	—	6	2	no	—
411	C₈	—	6	2	no	—
412	C₂×C₃	—	2	2	no	—
413	C₂×C₃	C₂²×C₅×C₄⋊C₄	1	1	yes	characteristic
414	C₂×C₃	C₅×#568	1	2	yes	—
415	D₃	—	2	2	no	—
416	D₃	—	2	2	no	—
417	C₅	#79080	1	1	yes	characteristic, direct product factor, Sylow
418	C₂²	—	2	2	no	—
419	C₂²	—	3	2	no	—
420	C₂²	—	3	2	no	—
421	C₂²	—	6	2	no	—
422	C₂²	—	6	2	no	—
423	C₂²	—	12	4	no	—
424	C₂²	C₅×D₃×C₄⋊C₄	1	2	yes	—
425	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
426	C₄	—	2	4	no	—
427	C₄	—	3	2	no	—
428	C₄	—	3	2	no	—
429	C₄	—	6	4	no	—
430	C₄	C₅×D₃×C₄⋊C₄	1	2	yes	—
431	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
432	C₄	C₂×C₅×D₃×Q₈	1	1	yes	characteristic
433	C₃	C₅×#2905	1	1	yes	characteristic, complemented, Sylow
434	C₂	—	2	2	no	—
435	C₂	—	6	2	no	—
436	C₂	—	6	2	no	—
437	C₂	C₂×C₅×D₃×C₄⋊C₄	1	1	yes	characteristic
438	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×#424	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂³×C₅×D₃	C₂×C₄
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₅×#424	D₃
hypocenter	C₃	C₅×#2905
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₅×#424

Complements

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

N	H ≅ G/N	type
4. C₃×C₅×#424	C₂	semidirect
5. C₅×#5119	C₂	semidirect
6. C₅×#5102	C₂	semidirect
7. C₅×#4999	C₂	semidirect
8. C₅×#4839	C₂	semidirect
9. C₅×#4837	C₂	semidirect
30. C₃×C₅×C₄⋊C₈	C₂²	semidirect
31. C₅×Dic₃⋊C₈	C₂²	semidirect
32. C₅×Dic₃⋊C₈	C₂²	semidirect
33. C₅×C₄⋊(C₃⋊C₈)	C₂²	semidirect
34. #79080	C₅	direct (N × H)
42. C₅×#424	D₃	semidirect
78. C₃×#424	C₂×C₅	semidirect
79. #5119	C₂×C₅	semidirect
80. #5102	C₂×C₅	semidirect
81. #4999	C₂×C₅	semidirect
82. #4839	C₂×C₅	semidirect
83. #4837	C₂×C₅	semidirect
106. C₅×C₄⋊C₈	C₂×D₃	semidirect
152. C₃×C₄⋊C₈	C₂²×C₅	semidirect
153. Dic₃⋊C₈	C₂²×C₅	semidirect
154. Dic₃⋊C₈	C₂²×C₅	semidirect
155. C₄⋊(C₃⋊C₈)	C₂²×C₅	semidirect
194. #424	C₅×D₃	semidirect
289. C₄⋊C₈	C₂×C₅×D₃	semidirect
366. C₃×C₅	#2905	semidirect
417. C₅	#79080	direct (N × H)
433. C₃	C₅×#2905	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×D₃×M₁₆	2
C₂²×C₅×ΓL(1,𝔽₂₅)	2
C₅×D₃×#117	2
C₃×C₅×#424	2
C₅×#5119	2
C₅×#5102	2
C₅×#4999	2
C₅×#4839	2
C₅×#4837	2
C₅×#2905	3
#79080	5

Subgroups — C5×#79080 #14413110

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#79080 #14413110