Subgroups — C₅×#79012 #14413161

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#901	C₂	1	2	yes	maximal
2	C₄×C₅×#235	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5102	C₂	1	2	yes	maximal, complemented
5	C₅×#4924	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4839	C₂	1	4	yes	maximal, complemented
7	C₅×#4837	C₂	1	2	yes	maximal, complemented
8	C₅×D₃×C₄⋊C₈	C₂	1	2	yes	maximal, complemented
9	C₅×#2906	—	3	1	no	maximal, Hall
10	C₂×C₅×#235	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
12	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
13	C₄×C₅×#67	C₄	1	2	yes	—
14	C₄×C₅×#67	C₄	1	2	yes	—
15	C₅×#926	C₂²	1	1	yes	characteristic
16	C₂×C₅×#208	C₂²	1	2	yes	—
17	C₅×#901	—	2	8	no	—
18	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	4	yes	—
19	C₂×C₅×D₃×C₈	C₂²	1	4	yes	—
20	C₄×C₅×D₁₂	C₄	1	1	yes	characteristic
21	C₄×C₅×D₁₂	C₄	1	1	yes	characteristic
22	C₅×#872	C₂²	1	2	yes	—
23	C₄²×C₅×D₃	C₂²	1	2	yes	—
24	C₄×C₅×Dic₆	C₄	1	1	yes	characteristic
25	C₄×C₅×Dic₆	C₄	1	1	yes	characteristic
26	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	—
29	C₅×Dic₃⋊C₈	C₂²	1	4	yes	—
30	C₅×Dic₃⋊C₈	C₂²	1	4	yes	—
31	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	2	yes	—
32	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	2	yes	—
33	#79012	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
34	C₂×C₅×#131	—	3	2	no	—
35	C₄×C₅×#41	—	3	1	no	—
36	C₅×#424	—	3	4	no	—
37	C₅×#424	—	3	2	no	—
38	C₅×#423	—	3	2	no	—
39	C₅×#423	—	3	1	no	—
40	C₂×C₅×C₄⋊C₈	—	3	2	no	—
41	C₂×C₅×C₄⋊C₈	D₃	1	1	yes	characteristic, complemented
42	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
43	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
45	C₂×C₅×#67	C₂×C₄	1	2	yes	—
46	C₅×#235	D₄	1	4	yes	—
47	C₅×#235	Q₈	1	4	yes	—
48	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
50	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
51	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
52	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
53	C₂×C₃×C₅×C₈	—	2	4	no	—
54	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
55	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
56	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
57	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
58	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
59	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
60	C₅×#217	C₂×C₄	1	2	yes	—
61	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
62	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
63	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
64	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
65	C₅×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
66	C₅×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
67	C₄×C₅×Dic₃	C₂×C₄	1	2	yes	—
68	C₄×C₅×Dic₃	C₂×C₄	1	2	yes	—
69	C₄×C₅×Dic₃	C₂³	1	2	yes	—
70	C₅×#208	—	2	4	no	—
71	C₂×C₅×C₃⋊C₈	C₂³	1	4	yes	—
72	C₅×ΓL(1,𝔽₂₅)	—	2	8	no	—
73	C₅×D₃×C₈	—	2	8	no	—
74	C₂×#901	C₂×C₅	1	2	yes	—
75	C₄×#235	C₂×C₅	1	1	yes	characteristic
76	C₂×C₃×C₄⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
77	#5102	C₂×C₅	1	2	yes	complemented
78	#4924	C₂×C₅	1	1	yes	characteristic, complemented
79	#4839	C₂×C₅	1	4	yes	complemented
80	#4837	C₂×C₅	1	2	yes	complemented
81	D₃×C₄⋊C₈	C₂×C₅	1	2	yes	complemented
82	C₂×C₅×#41	—	3	1	no	—
83	C₅×#131	—	6	8	no	—
84	C₂×C₅×M₁₆	—	3	2	no	—
85	C₂×C₅×M₁₆	—	3	4	no	—
86	C₂²×C₅×C₈	—	3	4	no	—
87	C₂²×C₅×C₈	C₂×D₃	1	2	yes	—
88	C₄×C₅×Q₈	—	3	1	no	—
89	C₄×C₅×Q₈	—	3	1	no	—
90	C₄×C₅×D₄	—	3	2	no	—
91	C₄×C₅×D₄	—	3	2	no	—
92	C₄×C₅×D₄	—	3	1	no	—
93	C₄×C₅×D₄	—	3	1	no	—
94	C₅×#117	—	3	1	no	—
95	C₅×#117	—	3	2	no	—
96	C₂×C₄²×C₅	—	3	2	no	—
97	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
98	C₅×C₄⋊C₈	—	3	4	no	—
99	C₅×C₄⋊C₈	—	3	4	no	—
100	C₅×C₄⋊C₈	—	3	2	no	—
101	C₅×C₄⋊C₈	—	3	2	no	—
102	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
103	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
104	C₅×C₄⋊C₈	C₂×D₃	1	2	yes	—
105	#2906	—	3	1	no	Sylow
106	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
108	C₂×C₃×C₄×C₅	—	2	2	no	—
109	C₂×C₃×C₄×C₅	—	4	1	no	—
110	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
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	C₅×#67	C₄⋊C₄	1	8	yes	—
119	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
120	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
121	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
122	C₅×D₁₂	C₄⋊C₄	1	4	yes	—
123	C₄×C₅×D₃	—	2	4	no	—
124	C₄×C₅×D₃	—	4	2	no	—
125	C₄×C₅×D₃	C₂×D₄	1	4	yes	—
126	C₄×C₅×D₃	C₂×Q₈	1	4	yes	—
127	C₅×Dic₆	C₄⋊C₄	1	4	yes	—
128	C₃×C₅×C₈	—	2	2	no	—
129	C₃×C₅×C₈	—	2	2	no	—
130	C₅×C₃⋊C₈	—	2	4	no	—
131	C₂×#235	C₂²×C₅	1	1	yes	characteristic
132	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
133	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
134	C₄×#67	C₄×C₅	1	2	yes	—
135	C₄×#67	C₄×C₅	1	2	yes	—
136	#926	C₂²×C₅	1	1	yes	characteristic
137	C₂×#208	C₂²×C₅	1	2	yes	—
138	#901	—	2	8	no	—
139	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	4	yes	—
140	C₂×D₃×C₈	C₂²×C₅	1	4	yes	—
141	C₄×D₁₂	C₄×C₅	1	1	yes	characteristic
142	C₄×D₁₂	C₄×C₅	1	1	yes	characteristic
143	#872	C₂²×C₅	1	2	yes	—
144	C₄²×D₃	C₂²×C₅	1	2	yes	—
145	C₄×Dic₆	C₄×C₅	1	1	yes	characteristic
146	C₄×Dic₆	C₄×C₅	1	1	yes	characteristic
147	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
148	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
149	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	—
150	Dic₃⋊C₈	C₂²×C₅	1	4	yes	—
151	Dic₃⋊C₈	C₂²×C₅	1	4	yes	—
152	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	2	yes	—
153	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	2	yes	—
154	C₅×#41	—	3	4	no	—
155	C₅×#41	—	3	4	no	—
156	C₂×C₅×Q₈	—	3	1	no	—
157	C₂×C₅×D₄	—	3	2	no	—
158	C₂×C₅×D₄	—	3	1	no	—
159	C₂²×C₄×C₅	—	3	2	no	—
160	C₂²×C₄×C₅	—	3	2	no	—
161	C₂²×C₄×C₅	—	3	2	no	—
162	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
163	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
164	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
165	C₅×M₁₆	—	6	8	no	—
166	C₅×M₁₆	—	6	4	no	—
167	C₂×C₅×C₈	—	2	4	no	—
168	C₂×C₅×C₈	—	3	4	no	—
169	C₂×C₅×C₈	—	6	8	no	—
170	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
171	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
172	C₅×C₄⋊C₄	—	3	2	no	—
173	C₅×C₄⋊C₄	—	3	2	no	—
174	C₅×C₄⋊C₄	—	3	1	no	—
175	C₅×C₄⋊C₄	—	3	1	no	—
176	C₅×C₂²⋊C₄	—	3	2	no	—
177	C₅×C₂²⋊C₄	—	3	2	no	—
178	C₅×C₂²⋊C₄	—	3	2	no	—
179	C₄²×C₅	—	3	2	no	—
180	C₄²×C₅	—	3	2	no	—
181	C₄²×C₅	—	3	2	no	—
182	C₄²×C₅	C₄×D₃	1	1	yes	characteristic
183	C₄²×C₅	C₄×D₃	1	1	yes	characteristic
184	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
185	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
186	C₂×#131	—	3	2	no	—
187	C₄×#41	—	3	1	no	—
188	#424	—	3	2	no	—
189	#424	—	3	4	no	—
190	#423	—	3	1	no	—
191	#423	—	3	2	no	—
192	C₂×C₄⋊C₈	—	3	2	no	—
193	C₂×C₄⋊C₈	C₅×D₃	1	1	yes	characteristic, complemented
194	C₂²×C₃×C₅	—	2	1	no	—
195	C₂²×C₃×C₅	—	2	1	no	—
196	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	2	yes	—
197	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
198	C₂×C₅×D₃	—	2	2	no	—
199	C₂×C₅×D₃	—	2	2	no	—
200	C₂×C₅×D₃	C₂×C₄⋊C₄	1	4	yes	—
201	C₃×C₄×C₅	—	2	1	no	—
202	C₃×C₄×C₅	—	2	1	no	—
203	C₃×C₄×C₅	—	2	1	no	—
204	C₃×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
205	C₃×C₄×C₅	#131	1	2	yes	complemented
206	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
207	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
208	C₅×Dic₃	—	2	2	no	—
209	C₅×Dic₃	—	2	2	no	—
210	C₅×Dic₃	C₂×C₄⋊C₄	1	4	yes	—
211	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
212	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
213	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
214	C₂×#67	C₂×C₄×C₅	1	2	yes	—
215	#235	C₅×D₄	1	4	yes	—
216	#235	C₅×Q₈	1	4	yes	—
217	C₂×D₁₂	C₂×C₄×C₅	1	1	yes	characteristic
218	C₂×C₄×D₃	C₂×C₄×C₅	1	2	yes	—
219	C₂×C₄×D₃	C₂×C₄×C₅	1	2	yes	—
220	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
221	C₂×Dic₆	C₂×C₄×C₅	1	1	yes	characteristic
222	C₂×C₃×C₈	—	2	4	no	—
223	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
224	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
225	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
226	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
227	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
228	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
229	#217	C₂×C₄×C₅	1	2	yes	—
230	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	2	yes	—
231	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	2	yes	—
232	C₄⋊Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
233	C₄⋊Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
234	Dic₃⋊C₄	C₂×C₄×C₅	1	2	yes	—
235	Dic₃⋊C₄	C₂×C₄×C₅	1	2	yes	—
236	C₄×Dic₃	C₂×C₄×C₅	1	2	yes	—
237	C₄×Dic₃	C₂×C₄×C₅	1	2	yes	—
238	C₄×Dic₃	C₂³×C₅	1	2	yes	—
239	#208	—	2	4	no	—
240	C₂×C₃⋊C₈	C₂³×C₅	1	4	yes	—
241	ΓL(1,𝔽₂₅)	—	2	8	no	—
242	D₃×C₈	—	2	8	no	—
243	C₂³×C₅	—	3	2	no	—
244	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
245	C₅×Q₈	—	3	4	no	—
246	C₅×D₄	—	3	8	no	—
247	C₅×D₄	—	3	4	no	—
248	C₂×C₄×C₅	—	2	2	no	—
249	C₂×C₄×C₅	—	3	2	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	—	4	1	no	—
255	C₂×C₄×C₅	—	6	4	no	—
256	C₂×C₄×C₅	—	12	2	no	—
257	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
258	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
259	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
260	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
261	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
262	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
263	C₂×C₄×C₅	D₃×Q₈	1	2	yes	—
264	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
265	C₅×C₈	—	2	2	no	—
266	C₅×C₈	—	2	2	no	—
267	C₅×C₈	—	6	4	no	—
268	C₂×#41	—	3	1	no	—
269	#131	—	6	8	no	—
270	C₂×M₁₆	—	3	2	no	—
271	C₂×M₁₆	—	3	4	no	—
272	C₂²×C₈	—	3	4	no	—
273	C₂²×C₈	C₂×C₅×D₃	1	2	yes	—
274	C₄×Q₈	—	3	1	no	—
275	C₄×Q₈	—	3	1	no	—
276	C₄×D₄	—	3	2	no	—
277	C₄×D₄	—	3	2	no	—
278	C₄×D₄	—	3	1	no	—
279	C₄×D₄	—	3	1	no	—
280	#117	—	3	1	no	—
281	#117	—	3	2	no	—
282	C₂×C₄²	—	3	2	no	—
283	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
284	C₄⋊C₈	—	3	4	no	—
285	C₄⋊C₈	—	3	4	no	—
286	C₄⋊C₈	—	3	2	no	—
287	C₄⋊C₈	—	3	2	no	—
288	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
289	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
290	C₄⋊C₈	C₂×C₅×D₃	1	2	yes	—
291	C₂×C₃×C₅	—	2	2	no	—
292	C₂×C₃×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
293	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
294	C₂×C₃×C₅	#568	1	1	yes	characteristic
295	C₅×D₃	—	2	4	no	—
296	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
297	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
298	C₂×C₃×C₄	—	2	2	no	—
299	C₂×C₃×C₄	—	4	1	no	—
300	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
301	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
302	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
303	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
304	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
305	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
306	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
307	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
308	#67	C₅×C₄⋊C₄	1	8	yes	—
309	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
310	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
311	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
312	D₁₂	C₅×C₄⋊C₄	1	4	yes	—
313	C₄×D₃	—	2	4	no	—
314	C₄×D₃	—	4	2	no	—
315	C₄×D₃	C₂×C₅×D₄	1	4	yes	—
316	C₄×D₃	C₂×C₅×Q₈	1	4	yes	—
317	Dic₆	C₅×C₄⋊C₄	1	4	yes	—
318	C₃×C₈	—	2	2	no	—
319	C₃×C₈	—	2	2	no	—
320	C₃⋊C₈	—	2	4	no	—
321	C₂²×C₅	—	2	1	no	—
322	C₂²×C₅	—	2	1	no	—
323	C₂²×C₅	—	3	4	no	—
324	C₂²×C₅	—	6	2	no	—
325	C₂²×C₅	—	6	2	no	—
326	C₂²×C₅	D₃×C₄⋊C₄	1	2	yes	—
327	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
328	C₄×C₅	—	2	1	no	—
329	C₄×C₅	—	2	1	no	—
330	C₄×C₅	—	2	1	no	—
331	C₄×C₅	—	3	4	no	—
332	C₄×C₅	—	6	2	no	—
333	C₄×C₅	—	6	2	no	—
334	C₄×C₅	D₃×C₄⋊C₄	1	2	yes	—
335	C₄×C₅	#901	1	2	yes	complemented
336	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
337	C₄×C₅	C₂×D₃×Q₈	1	1	yes	characteristic
338	#41	—	3	4	no	—
339	#41	—	3	4	no	—
340	C₂×Q₈	—	3	1	no	—
341	C₂×D₄	—	3	2	no	—
342	C₂×D₄	—	3	1	no	—
343	C₂²×C₄	—	3	2	no	—
344	C₂²×C₄	—	3	2	no	—
345	C₂²×C₄	—	3	2	no	—
346	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
347	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
348	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
349	M₁₆	—	6	8	no	—
350	M₁₆	—	6	4	no	—
351	C₂×C₈	—	2	4	no	—
352	C₂×C₈	—	3	4	no	—
353	C₂×C₈	—	6	8	no	—
354	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
355	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
356	C₄⋊C₄	—	3	2	no	—
357	C₄⋊C₄	—	3	2	no	—
358	C₄⋊C₄	—	3	1	no	—
359	C₄⋊C₄	—	3	1	no	—
360	C₂²⋊C₄	—	3	2	no	—
361	C₂²⋊C₄	—	3	2	no	—
362	C₂²⋊C₄	—	3	2	no	—
363	C₄²	—	3	2	no	—
364	C₄²	—	3	2	no	—
365	C₄²	—	3	2	no	—
366	C₄²	C₄×C₅×D₃	1	1	yes	characteristic
367	C₄²	C₄×C₅×D₃	1	1	yes	characteristic
368	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
369	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
370	C₃×C₅	#2906	1	1	yes	characteristic, complemented, Hall
371	C₂²×C₃	—	2	1	no	—
372	C₂²×C₃	—	2	1	no	—
373	C₂²×C₃	C₂×C₅×C₄⋊C₄	1	2	yes	—
374	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
375	C₂×D₃	—	2	2	no	—
376	C₂×D₃	—	2	2	no	—
377	C₂×D₃	C₂×C₅×C₄⋊C₄	1	4	yes	—
378	C₃×C₄	—	2	1	no	—
379	C₃×C₄	—	2	1	no	—
380	C₃×C₄	—	2	1	no	—
381	C₃×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
382	C₃×C₄	C₅×#131	1	2	yes	complemented
383	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
384	C₃×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
385	Dic₃	—	2	2	no	—
386	Dic₃	—	2	2	no	—
387	Dic₃	C₂×C₅×C₄⋊C₄	1	4	yes	—
388	C₂×C₅	—	2	2	no	—
389	C₂×C₅	—	6	4	no	—
390	C₂×C₅	C₂×D₃×C₄⋊C₄	1	1	yes	characteristic
391	C₂×C₅	C₂×#901	1	1	yes	characteristic
392	C₂×C₅	#5745	1	1	yes	characteristic
393	C₂³	—	3	2	no	—
394	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
395	Q₈	—	3	4	no	—
396	D₄	—	3	8	no	—
397	D₄	—	3	4	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	3	2	no	—
400	C₂×C₄	—	3	4	no	—
401	C₂×C₄	—	3	4	no	—
402	C₂×C₄	—	3	2	no	—
403	C₂×C₄	—	3	2	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	6	4	no	—
406	C₂×C₄	—	12	2	no	—
407	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
408	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
409	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
410	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
411	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
412	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
413	C₂×C₄	C₅×D₃×Q₈	1	2	yes	—
414	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
415	C₈	—	2	2	no	—
416	C₈	—	2	2	no	—
417	C₈	—	6	4	no	—
418	C₂×C₃	—	2	2	no	—
419	C₂×C₃	C₂²×C₅×C₄⋊C₄	1	1	yes	characteristic
420	C₂×C₃	C₂×C₅×#131	1	1	yes	characteristic
421	C₂×C₃	C₅×#568	1	1	yes	characteristic
422	D₃	—	2	4	no	—
423	C₅	#79012	1	1	yes	characteristic, direct product factor, Sylow
424	C₂²	—	2	1	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	3	4	no	—
427	C₂²	—	6	2	no	—
428	C₂²	—	6	2	no	—
429	C₂²	C₅×D₃×C₄⋊C₄	1	2	yes	—
430	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
431	C₄	—	2	1	no	—
432	C₄	—	2	1	no	—
433	C₄	—	2	1	no	—
434	C₄	—	3	4	no	—
435	C₄	—	6	2	no	—
436	C₄	—	6	2	no	—
437	C₄	C₅×D₃×C₄⋊C₄	1	2	yes	—
438	C₄	C₅×#901	1	2	yes	complemented
439	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
440	C₄	C₂×C₅×D₃×Q₈	1	1	yes	characteristic
441	C₃	C₅×#2906	1	1	yes	characteristic, complemented, Sylow
442	C₂	—	2	2	no	—
443	C₂	—	6	4	no	—
444	C₂	C₂×C₅×D₃×C₄⋊C₄	1	1	yes	characteristic
445	C₂	C₂×C₅×#901	1	1	yes	characteristic
446	C₂	C₅×#5745	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	C₂×C₃×C₅×C₄⋊C₈	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂×C₅×#235	C₂²
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₂×C₅×C₄⋊C₈	D₃
hypocenter	C₃	C₅×#2906
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₅×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
3. C₂×C₃×C₅×C₄⋊C₈	C₂	semidirect
4. C₅×#5102	C₂	semidirect
5. C₅×#4924	C₂	semidirect
6. C₅×#4839	C₂	semidirect
7. C₅×#4837	C₂	semidirect
8. C₅×D₃×C₄⋊C₈	C₂	semidirect
33. #79012	C₅	direct (N × H)
41. C₂×C₅×C₄⋊C₈	D₃	semidirect
76. C₂×C₃×C₄⋊C₈	C₂×C₅	semidirect
77. #5102	C₂×C₅	semidirect
78. #4924	C₂×C₅	semidirect
79. #4839	C₂×C₅	semidirect
80. #4837	C₂×C₅	semidirect
81. D₃×C₄⋊C₈	C₂×C₅	semidirect
193. C₂×C₄⋊C₈	C₅×D₃	semidirect
205. C₃×C₄×C₅	#131	semidirect
335. C₄×C₅	#901	semidirect
370. C₃×C₅	#2906	semidirect
382. C₃×C₄	C₅×#131	semidirect
423. C₅	#79012	direct (N × H)
438. C₄	C₅×#901	semidirect
441. C₃	C₅×#2906	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#901	2
C₄×C₅×#235	2
C₂×C₃×C₅×C₄⋊C₈	2
C₅×#5102	2
C₅×#4924	2
C₅×#4839	2
C₅×#4837	2
C₅×D₃×C₄⋊C₈	2
C₅×#2906	3
#79012	5

Subgroups — C5×#79012 #14413161

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#79012 #14413161