Subgroups — C₅×#78657 #14415220

Order 1920.

1000 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×#5832	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#948	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#907	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#408	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5118	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5110	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×C₈×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4729	C₂	1	4	yes	maximal, complemented
9	C₅×#67⋊C₈	C₂	1	4	yes	maximal, complemented
10	C₅×#2931	—	3	1	no	maximal, Hall
11	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
12	C₂×C₅×#235	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
15	C₅×#948	—	2	4	no	—
16	C₅×#947	C₄	1	1	yes	characteristic
17	C₅×#944	C₄	1	1	yes	characteristic
18	C₅×#940	C₄	1	1	yes	characteristic
19	C₅×#939	C₄	1	4	yes	—
20	C₅×#936	C₄	1	1	yes	characteristic
21	C₄×C₅×#67	C₂²	1	4	yes	—
22	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
23	C₂×C₅×#208	C₂²	1	2	yes	—
24	C₂×C₅×#208	C₂²	1	1	yes	characteristic
25	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	—
26	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
27	C₅×#907	—	2	4	no	—
28	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	—
29	C₂×C₅×D₃×C₈	C₂²	1	2	yes	—
30	C₃×C₅×C₂²⋊C₈	C₂²	1	4	yes	—
31	C₅×(C₂×D₃)⋊C₈	C₂²	1	4	yes	—
32	C₅×Dic₃⋊C₈	C₂²	1	4	yes	—
33	C₅×C₈×Dic₃	C₂²	1	2	yes	—
34	C₅×C₈×Dic₃	C₂²	1	2	yes	—
35	#78657	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
36	C₂×C₅×#131	—	3	1	no	—
37	C₂×C₅×#131	—	3	1	no	—
38	C₅×#532	—	3	1	no	—
39	C₅×#436	—	3	4	no	—
40	C₅×C₈×D₄	—	3	4	no	—
41	C₅×#423	—	3	1	no	—
42	C₅×#408	—	3	1	no	—
43	C₅×#408	D₃	1	1	yes	characteristic, complemented
44	C₂×C₄×C₅×C₈	—	3	1	no	—
45	C₃×C₅×#41	—	2	2	no	—
46	C₃×C₅×#41	—	2	2	no	—
47	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
48	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
49	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
50	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
51	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
52	C₂×C₅×#67	C₂×C₄	1	4	yes	—
53	C₂×C₅×#67	C₂×C₄	1	2	yes	—
54	C₂²×C₅×Dic₃	C₂×C₄	1	2	yes	—
55	C₅×#235	—	2	2	no	—
56	C₅×#235	—	2	2	no	—
57	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
59	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
60	C₃×C₅×M₁₆	—	2	2	no	—
61	C₂×C₃×C₅×C₈	—	2	2	no	—
62	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
63	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
64	C₅×#217	C₂×C₄	1	4	yes	—
65	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	4	yes	—
66	C₅×Dic₃⋊C₄	C₂×C₄	1	4	yes	—
67	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
68	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
69	C₄×C₅×Dic₃	C₂³	1	2	yes	—
70	C₅×#208	—	2	2	no	—
71	C₅×#208	—	2	4	no	—
72	C₂×C₅×C₃⋊C₈	—	2	4	no	—
73	C₂×C₅×C₃⋊C₈	D₄	1	4	yes	complemented
74	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
75	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
76	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
77	C₅×ΓL(1,𝔽₂₅)	—	2	4	no	—
78	C₅×D₃×C₈	—	2	4	no	—
79	#5832	C₂×C₅	1	1	yes	characteristic
80	C₂×#948	C₂×C₅	1	1	yes	characteristic, complemented
81	C₂×#907	C₂×C₅	1	1	yes	characteristic, complemented
82	C₃×#408	C₂×C₅	1	1	yes	characteristic, complemented
83	#5118	C₂×C₅	1	1	yes	characteristic, complemented
84	#5110	C₂×C₅	1	1	yes	characteristic, complemented
85	C₂×C₈×Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
86	#4729	C₂×C₅	1	4	yes	complemented
87	#67⋊C₈	C₂×C₅	1	4	yes	complemented
88	C₂×C₅×#41	—	3	1	no	—
89	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
90	C₅×#131	—	6	4	no	—
91	C₅×#131	—	6	4	no	—
92	C₂×C₅×M₁₆	—	3	1	no	—
93	C₂×C₅×M₁₆	—	3	2	no	—
94	C₂×C₅×M₁₆	—	3	2	no	—
95	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
96	C₂²×C₅×C₈	—	3	1	no	—
97	C₂²×C₅×C₈	—	3	2	no	—
98	C₂²×C₅×C₈	—	3	2	no	—
99	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
100	C₅×C₄⋊Q₈	—	3	1	no	—
101	C₅×#127	—	3	1	no	—
102	C₅×#124	—	3	1	no	—
103	C₅×#124	—	3	1	no	—
104	C₅×#121	—	3	4	no	—
105	C₄×C₅×D₄	—	3	4	no	—
106	C₂×C₄²×C₅	—	3	1	no	—
107	C₅×C₄⋊C₈	—	3	4	no	—
108	C₅×C₂²⋊C₈	—	3	4	no	—
109	C₅×C₂²⋊C₈	C₂×D₃	1	4	yes	—
110	C₄×C₅×C₈	—	3	2	no	—
111	C₄×C₅×C₈	—	3	2	no	—
112	#2931	—	3	1	no	Sylow
113	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
114	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
116	C₃×C₅×Q₈	—	2	2	no	—
117	C₃×C₅×D₄	—	2	4	no	—
118	C₃×C₅×D₄	—	2	2	no	—
119	C₂×C₃×C₄×C₅	—	2	2	no	—
120	C₂×C₃×C₄×C₅	—	2	2	no	—
121	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
122	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
124	C₂×C₃×C₄×C₅	#41	1	2	yes	—
125	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
126	C₅×#67	—	2	4	no	—
127	C₅×#67	—	2	8	no	—
128	C₂×C₅×Dic₃	—	2	4	no	—
129	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
130	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
131	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
132	C₅×D₁₂	—	2	2	no	—
133	C₄×C₅×D₃	—	2	2	no	—
134	C₄×C₅×D₃	—	2	2	no	—
135	C₅×Dic₆	—	2	2	no	—
136	C₃×C₅×C₈	—	2	2	no	—
137	C₃×C₅×C₈	—	2	2	no	—
138	C₅×C₃⋊C₈	—	2	2	no	—
139	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	—
140	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	—
141	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
142	C₂×#235	C₂²×C₅	1	1	yes	characteristic
143	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
144	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
145	#948	—	2	4	no	—
146	#947	C₄×C₅	1	1	yes	characteristic
147	#944	C₄×C₅	1	1	yes	characteristic
148	#940	C₄×C₅	1	1	yes	characteristic
149	#939	C₄×C₅	1	4	yes	—
150	#936	C₄×C₅	1	1	yes	characteristic
151	C₄×#67	C₂²×C₅	1	4	yes	—
152	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
153	C₂×#208	C₂²×C₅	1	2	yes	—
154	C₂×#208	C₂²×C₅	1	1	yes	characteristic
155	C₂²×C₃⋊C₈	C₂²×C₅	1	2	yes	—
156	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
157	#907	—	2	4	no	—
158	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	2	yes	—
159	C₂×D₃×C₈	C₂²×C₅	1	2	yes	—
160	C₃×C₂²⋊C₈	C₂²×C₅	1	4	yes	—
161	(C₂×D₃)⋊C₈	C₂²×C₅	1	4	yes	—
162	Dic₃⋊C₈	C₂²×C₅	1	4	yes	—
163	C₈×Dic₃	C₂²×C₅	1	2	yes	—
164	C₈×Dic₃	C₂²×C₅	1	2	yes	—
165	C₅×#41	—	2	2	no	—
166	C₅×#41	—	2	2	no	—
167	C₅×#41	—	6	2	no	—
168	C₅×#41	—	6	2	no	—
169	C₂×C₅×Q₈	—	3	1	no	—
170	C₂×C₅×Q₈	C₄×D₃	1	1	yes	characteristic
171	C₂×C₅×D₄	—	3	4	no	—
172	C₂×C₅×D₄	—	3	2	no	—
173	C₂×C₅×D₄	—	3	1	no	—
174	C₂×C₅×D₄	C₄×D₃	1	2	yes	—
175	C₂×C₅×D₄	C₄×D₃	1	1	yes	characteristic
176	C₂²×C₄×C₅	—	3	2	no	—
177	C₂²×C₄×C₅	—	3	2	no	—
178	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
179	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
180	C₅×M₁₆	—	2	2	no	—
181	C₅×M₁₆	—	6	4	no	—
182	C₅×M₁₆	—	6	4	no	—
183	C₅×M₁₆	—	6	2	no	—
184	C₂×C₅×C₈	—	2	2	no	—
185	C₂×C₅×C₈	—	3	4	no	—
186	C₂×C₅×C₈	—	3	1	no	—
187	C₂×C₅×C₈	—	3	1	no	—
188	C₂×C₅×C₈	—	3	2	no	—
189	C₂×C₅×C₈	—	6	4	no	—
190	C₂×C₅×C₈	—	6	4	no	—
191	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
192	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
193	C₅×C₄⋊C₄	—	3	4	no	—
194	C₅×C₂²⋊C₄	—	3	4	no	—
195	C₅×C₂²⋊C₄	—	3	4	no	—
196	C₄²×C₅	—	3	1	no	—
197	C₄²×C₅	—	3	1	no	—
198	C₄²×C₅	—	3	2	no	—
199	C₂×#131	—	3	1	no	—
200	C₂×#131	—	3	1	no	—
201	#532	—	3	1	no	—
202	#436	—	3	4	no	—
203	C₈×D₄	—	3	4	no	—
204	#423	—	3	1	no	—
205	#408	—	3	1	no	—
206	#408	C₅×D₃	1	1	yes	characteristic, complemented
207	C₂×C₄×C₈	—	3	1	no	—
208	C₂²×C₃×C₅	—	2	2	no	—
209	C₂²×C₃×C₅	—	2	2	no	—
210	C₂²×C₃×C₅	—	2	4	no	—
211	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
212	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
213	C₂×C₅×D₃	—	2	2	no	—
214	C₂×C₅×D₃	—	2	4	no	—
215	C₃×C₄×C₅	—	2	2	no	—
216	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
217	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
218	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
219	C₅×Dic₃	—	2	2	no	—
220	C₅×Dic₃	—	2	2	no	—
221	C₅×Dic₃	#131	1	4	yes	complemented
222	C₃×#41	—	2	2	no	—
223	C₃×#41	—	2	2	no	—
224	C₂×C₃×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
225	C₂×C₃×D₄	C₂×C₄×C₅	1	1	yes	characteristic
226	C₂×C₃×D₄	C₂×C₄×C₅	1	2	yes	—
227	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
228	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
229	C₂×#67	C₂×C₄×C₅	1	4	yes	—
230	C₂×#67	C₂×C₄×C₅	1	2	yes	—
231	C₂²×Dic₃	C₂×C₄×C₅	1	2	yes	—
232	#235	—	2	2	no	—
233	#235	—	2	2	no	—
234	C₂×D₁₂	C₂×C₄×C₅	1	1	yes	characteristic
235	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
236	C₂×Dic₆	C₂×C₄×C₅	1	1	yes	characteristic
237	C₃×M₁₆	—	2	2	no	—
238	C₂×C₃×C₈	—	2	2	no	—
239	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
240	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
241	#217	C₂×C₄×C₅	1	4	yes	—
242	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	4	yes	—
243	Dic₃⋊C₄	C₂×C₄×C₅	1	4	yes	—
244	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
245	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
246	C₄×Dic₃	C₂³×C₅	1	2	yes	—
247	#208	—	2	2	no	—
248	#208	—	2	4	no	—
249	C₂×C₃⋊C₈	—	2	4	no	—
250	C₂×C₃⋊C₈	C₅×D₄	1	4	yes	complemented
251	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
252	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
253	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
254	ΓL(1,𝔽₂₅)	—	2	4	no	—
255	D₃×C₈	—	2	4	no	—
256	C₂³×C₅	—	3	2	no	—
257	C₂³×C₅	C₂×C₄×D₃	1	2	yes	—
258	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
259	C₅×Q₈	—	2	2	no	—
260	C₅×Q₈	—	6	2	no	—
261	C₅×D₄	—	2	4	no	—
262	C₅×D₄	—	2	2	no	—
263	C₅×D₄	—	6	8	no	—
264	C₅×D₄	—	6	4	no	—
265	C₅×D₄	—	6	2	no	—
266	C₂×C₄×C₅	—	2	2	no	—
267	C₂×C₄×C₅	—	2	2	no	—
268	C₂×C₄×C₅	—	3	2	no	—
269	C₂×C₄×C₅	—	3	2	no	—
270	C₂×C₄×C₅	—	3	2	no	—
271	C₂×C₄×C₅	—	6	4	no	—
272	C₂×C₄×C₅	—	6	2	no	—
273	C₂×C₄×C₅	—	6	2	no	—
274	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
275	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
276	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
277	C₂×C₄×C₅	#237	1	2	yes	—
278	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
279	C₅×C₈	—	2	2	no	—
280	C₅×C₈	—	2	2	no	—
281	C₅×C₈	—	3	2	no	—
282	C₅×C₈	—	3	2	no	—
283	C₅×C₈	—	6	2	no	—
284	C₂×#41	—	3	1	no	—
285	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
286	#131	—	6	4	no	—
287	#131	—	6	4	no	—
288	C₂×M₁₆	—	3	1	no	—
289	C₂×M₁₆	—	3	2	no	—
290	C₂×M₁₆	—	3	2	no	—
291	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
292	C₂²×C₈	—	3	1	no	—
293	C₂²×C₈	—	3	2	no	—
294	C₂²×C₈	—	3	2	no	—
295	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
296	C₄⋊Q₈	—	3	1	no	—
297	#127	—	3	1	no	—
298	#124	—	3	1	no	—
299	#124	—	3	1	no	—
300	#121	—	3	4	no	—
301	C₄×D₄	—	3	4	no	—
302	C₂×C₄²	—	3	1	no	—
303	C₄⋊C₈	—	3	4	no	—
304	C₂²⋊C₈	—	3	4	no	—
305	C₂²⋊C₈	C₂×C₅×D₃	1	4	yes	—
306	C₄×C₈	—	3	2	no	—
307	C₄×C₈	—	3	2	no	—
308	C₂×C₃×C₅	—	2	2	no	—
309	C₂×C₃×C₅	—	4	2	no	—
310	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
311	C₂×C₃×C₅	C₂×#131	1	2	yes	—
312	C₅×D₃	—	4	2	no	—
313	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
314	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
315	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
316	C₃×Q₈	—	2	2	no	—
317	C₃×D₄	—	2	4	no	—
318	C₃×D₄	—	2	2	no	—
319	C₂×C₃×C₄	—	2	2	no	—
320	C₂×C₃×C₄	—	2	2	no	—
321	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
322	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
323	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
324	C₂×C₃×C₄	C₅×#41	1	2	yes	—
325	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
326	#67	—	2	4	no	—
327	#67	—	2	8	no	—
328	C₂×Dic₃	—	2	4	no	—
329	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
330	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
331	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
332	D₁₂	—	2	2	no	—
333	C₄×D₃	—	2	2	no	—
334	C₄×D₃	—	2	2	no	—
335	Dic₆	—	2	2	no	—
336	C₃×C₈	—	2	2	no	—
337	C₃×C₈	—	2	2	no	—
338	C₃⋊C₈	—	2	2	no	—
339	C₃⋊C₈	C₂×C₅×D₄	1	2	yes	—
340	C₃⋊C₈	C₂×C₅×D₄	1	2	yes	—
341	C₂²×C₅	—	2	2	no	—
342	C₂²×C₅	—	2	2	no	—
343	C₂²×C₅	—	2	4	no	—
344	C₂²×C₅	—	6	2	no	—
345	C₂²×C₅	—	6	4	no	—
346	C₂²×C₅	#67⋊C₄	1	2	yes	—
347	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
348	C₄×C₅	—	2	2	no	—
349	C₄×C₅	—	3	4	no	—
350	C₄×C₅	—	6	2	no	—
351	C₄×C₅	—	6	2	no	—
352	C₄×C₅	#67⋊C₄	1	2	yes	—
353	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
354	C₄×C₅	C₂×#237	1	1	yes	characteristic
355	#41	—	2	2	no	—
356	#41	—	2	2	no	—
357	#41	—	6	2	no	—
358	#41	—	6	2	no	—
359	C₂×Q₈	—	3	1	no	—
360	C₂×Q₈	C₄×C₅×D₃	1	1	yes	characteristic
361	C₂×D₄	—	3	4	no	—
362	C₂×D₄	—	3	2	no	—
363	C₂×D₄	—	3	1	no	—
364	C₂×D₄	C₄×C₅×D₃	1	2	yes	—
365	C₂×D₄	C₄×C₅×D₃	1	1	yes	characteristic
366	C₂²×C₄	—	3	2	no	—
367	C₂²×C₄	—	3	2	no	—
368	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
369	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
370	M₁₆	—	2	2	no	—
371	M₁₆	—	6	4	no	—
372	M₁₆	—	6	4	no	—
373	M₁₆	—	6	2	no	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	3	4	no	—
376	C₂×C₈	—	3	1	no	—
377	C₂×C₈	—	3	1	no	—
378	C₂×C₈	—	3	2	no	—
379	C₂×C₈	—	6	4	no	—
380	C₂×C₈	—	6	4	no	—
381	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
382	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
383	C₄⋊C₄	—	3	4	no	—
384	C₂²⋊C₄	—	3	4	no	—
385	C₂²⋊C₄	—	3	4	no	—
386	C₄²	—	3	1	no	—
387	C₄²	—	3	1	no	—
388	C₄²	—	3	2	no	—
389	C₃×C₅	#2931	1	1	yes	characteristic, complemented, Hall
390	C₂²×C₃	—	2	2	no	—
391	C₂²×C₃	—	2	2	no	—
392	C₂²×C₃	—	2	4	no	—
393	C₂²×C₃	C₄×C₅×D₄	1	2	yes	—
394	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
395	C₂×D₃	—	2	2	no	—
396	C₂×D₃	—	2	4	no	—
397	C₃×C₄	—	2	2	no	—
398	C₃×C₄	C₄×C₅×D₄	1	2	yes	—
399	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
400	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
401	Dic₃	—	2	2	no	—
402	Dic₃	—	2	2	no	—
403	Dic₃	C₅×#131	1	4	yes	complemented
404	C₂×C₅	—	2	2	no	—
405	C₂×C₅	—	4	2	no	—
406	C₂×C₅	—	12	2	no	—
407	C₂×C₅	C₂×#67⋊C₄	1	1	yes	characteristic
408	C₂×C₅	D₃×#131	1	2	yes	—
409	C₂³	—	3	2	no	—
410	C₂³	C₂×C₄×C₅×D₃	1	2	yes	—
411	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
412	Q₈	—	2	2	no	—
413	Q₈	—	6	2	no	—
414	D₄	—	2	4	no	—
415	D₄	—	2	2	no	—
416	D₄	—	6	8	no	—
417	D₄	—	6	4	no	—
418	D₄	—	6	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	3	2	no	—
422	C₂×C₄	—	3	2	no	—
423	C₂×C₄	—	3	2	no	—
424	C₂×C₄	—	6	4	no	—
425	C₂×C₄	—	6	2	no	—
426	C₂×C₄	—	6	2	no	—
427	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
428	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
429	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
430	C₂×C₄	C₅×#237	1	2	yes	—
431	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
432	C₈	—	2	2	no	—
433	C₈	—	2	2	no	—
434	C₈	—	3	2	no	—
435	C₈	—	3	2	no	—
436	C₈	—	6	2	no	—
437	C₂×C₃	—	2	2	no	—
438	C₂×C₃	—	4	2	no	—
439	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
440	C₂×C₃	C₂×C₅×#131	1	2	yes	—
441	D₃	—	4	2	no	—
442	C₅	#78657	1	1	yes	characteristic, direct product factor, Sylow
443	C₂²	—	2	2	no	—
444	C₂²	—	2	2	no	—
445	C₂²	—	2	4	no	—
446	C₂²	—	6	2	no	—
447	C₂²	—	6	4	no	—
448	C₂²	C₅×#67⋊C₄	1	2	yes	—
449	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
450	C₄	—	2	2	no	—
451	C₄	—	3	4	no	—
452	C₄	—	6	2	no	—
453	C₄	—	6	2	no	—
454	C₄	C₅×#67⋊C₄	1	2	yes	—
455	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
456	C₄	C₂×C₅×#237	1	1	yes	characteristic
457	C₃	C₅×#2931	1	1	yes	characteristic, complemented, Sylow
458	C₂	—	2	2	no	—
459	C₂	—	4	2	no	—
460	C₂	—	12	2	no	—
461	C₂	C₂×C₅×#67⋊C₄	1	1	yes	characteristic
462	C₂	C₅×D₃×#131	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×#408	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₅×#5832	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₅×#408	D₃
hypocenter	C₃	C₅×#2931
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₅×#408

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#948	C₂	semidirect
3. C₂×C₅×#907	C₂	semidirect
4. C₃×C₅×#408	C₂	semidirect
5. C₅×#5118	C₂	semidirect
6. C₅×#5110	C₂	semidirect
7. C₂×C₅×C₈×Dic₃	C₂	semidirect
8. C₅×#4729	C₂	semidirect
9. C₅×#67⋊C₈	C₂	semidirect
35. #78657	C₅	direct (N × H)
43. C₅×#408	D₃	semidirect
73. C₂×C₅×C₃⋊C₈	D₄	semidirect
80. C₂×#948	C₂×C₅	semidirect
81. C₂×#907	C₂×C₅	semidirect
82. C₃×#408	C₂×C₅	semidirect
83. #5118	C₂×C₅	semidirect
84. #5110	C₂×C₅	semidirect
85. C₂×C₈×Dic₃	C₂×C₅	semidirect
86. #4729	C₂×C₅	semidirect
87. #67⋊C₈	C₂×C₅	semidirect
206. #408	C₅×D₃	semidirect
221. C₅×Dic₃	#131	semidirect
250. C₂×C₃⋊C₈	C₅×D₄	semidirect
389. C₃×C₅	#2931	semidirect
403. Dic₃	C₅×#131	semidirect
442. C₅	#78657	direct (N × H)
457. C₃	C₅×#2931	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5832	2
C₂×C₅×#948	2
C₂×C₅×#907	2
C₃×C₅×#408	2
C₅×#5118	2
C₅×#5110	2
C₂×C₅×C₈×Dic₃	2
C₅×#4729	2
C₅×#67⋊C₈	2
C₅×#2931	3
#78657	5

Subgroups — C5×#78657 #14415220

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#78657 #14415220