Subgroups — C₅×#78879 #14438649

Order 1920.

784 conjugacy classes of subgroups.

The subgroup lattice has 588 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×#890	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#417	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5232	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5133	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×Dic₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4966	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4800	C₂	1	2	yes	maximal, complemented
9	C₅×#4797	C₂	1	2	yes	maximal, complemented
10	C₅×#4768	C₂	1	2	yes	maximal, complemented
11	C₅×#4764	C₂	1	2	yes	maximal, complemented
12	C₅×#3142	—	3	1	no	maximal, Hall
13	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
14	C₂×C₅×#235	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₅×#947	C₂²	1	1	yes	characteristic
18	C₅×#944	C₂²	1	1	yes	characteristic
19	C₅×#940	C₂²	1	1	yes	characteristic
20	C₅×#939	—	2	1	no	—
21	C₅×#939	—	2	1	no	—
22	C₅×#936	C₂²	1	1	yes	characteristic
23	C₄×C₅×#67	—	2	1	no	—
24	C₄×C₅×#67	—	2	1	no	—
25	C₂×C₅×C₄⋊Dic₃	—	2	1	no	—
26	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
27	C₂×C₅×Dic₃⋊C₄	—	2	1	no	—
28	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
29	C₂×C₅×#208	C₂²	1	1	yes	characteristic
30	C₅×#890	—	2	1	no	—
31	C₅×#890	—	2	1	no	—
32	C₅×#890	C₂²	1	2	yes	—
33	C₅×#890	C₂²	1	2	yes	—
34	C₃×C₅×#103	C₂²	1	2	yes	—
35	C₃×C₅×#102	C₂²	1	2	yes	—
36	C₅×#835	C₂²	1	2	yes	—
37	C₅×#832	C₂²	1	2	yes	—
38	C₅×#821	C₂²	1	2	yes	—
39	C₅×#816	C₂²	1	2	yes	—
40	C₅×#815	C₂²	1	2	yes	—
41	C₅×C₈×Dic₃	C₂²	1	2	yes	—
42	C₅×#810	C₂²	1	2	yes	—
43	C₅×#809	C₂²	1	2	yes	—
44	#78879	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
45	C₅×#532	—	3	1	no	—
46	C₂×C₅×#125	—	3	1	no	—
47	C₅×#491	—	3	2	no	—
48	C₅×#490	—	3	2	no	—
49	C₅×#488	—	3	2	no	—
50	C₅×#488	—	3	2	no	—
51	C₅×#417	—	3	1	no	—
52	C₅×#417	—	3	1	no	—
53	C₅×#417	—	3	1	no	—
54	C₅×#417	D₃	1	1	yes	characteristic, complemented
55	C₄×C₅×M₁₆	—	3	1	no	—
56	C₃×C₅×#41	—	2	2	no	—
57	C₃×C₅×#41	—	2	2	no	—
58	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
59	C₂×C₃×C₅×D₄	—	2	1	no	—
60	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
61	C₂²×C₃×C₄×C₅	—	2	1	no	—
62	C₂²×C₃×C₄×C₅	—	2	1	no	—
63	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
64	C₂×C₅×#67	—	2	1	no	—
65	C₂×C₅×#67	—	2	1	no	—
66	C₂×C₅×#67	—	2	1	no	—
67	C₂²×C₅×Dic₃	—	2	1	no	—
68	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
69	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
70	C₅×#235	—	2	2	no	—
71	C₅×#235	—	2	2	no	—
72	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
73	C₂×C₄×C₅×D₃	—	2	1	no	—
74	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
75	C₃×C₅×M₁₆	—	2	2	no	—
76	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
77	C₃×C₅×C₄⋊C₄	—	2	1	no	—
78	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
79	C₅×#217	—	2	1	no	—
80	C₅×#217	—	2	1	no	—
81	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
82	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
83	C₅×C₄⋊Dic₃	—	2	1	no	—
84	C₅×C₄⋊Dic₃	—	2	2	no	—
85	C₅×C₄⋊Dic₃	—	2	2	no	—
86	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
87	C₅×Dic₃⋊C₄	—	2	2	no	—
88	C₅×Dic₃⋊C₄	—	2	2	no	—
89	C₅×Dic₃⋊C₄	—	2	1	no	—
90	C₅×Dic₃⋊C₄	—	2	1	no	—
91	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
92	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
93	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
94	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
95	C₅×#208	—	2	2	no	—
96	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
97	#5832	C₂×C₅	1	1	yes	characteristic
98	C₂×#890	C₂×C₅	1	1	yes	characteristic, complemented
99	C₃×#417	C₂×C₅	1	1	yes	characteristic, complemented
100	#5232	C₂×C₅	1	1	yes	characteristic, complemented
101	#5133	C₂×C₅	1	1	yes	characteristic, complemented
102	Dic₃×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
103	#4966	C₂×C₅	1	1	yes	characteristic, complemented
104	#4800	C₂×C₅	1	2	yes	complemented
105	#4797	C₂×C₅	1	2	yes	complemented
106	#4768	C₂×C₅	1	2	yes	complemented
107	#4764	C₂×C₅	1	2	yes	complemented
108	C₂×C₅×#41	—	3	1	no	—
109	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
110	C₂×C₅×M₁₆	—	3	1	no	—
111	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
112	C₅×C₄⋊Q₈	—	3	1	no	—
113	C₅×#127	—	3	1	no	—
114	C₅×#125	—	3	2	no	—
115	C₅×#125	—	3	2	no	—
116	C₅×#125	—	6	1	no	—
117	C₅×#125	—	6	1	no	—
118	C₅×#124	—	3	1	no	—
119	C₅×#124	—	3	1	no	—
120	C₅×#121	—	6	1	no	—
121	C₅×#121	—	6	1	no	—
122	C₄×C₅×D₄	—	6	1	no	—
123	C₄×C₅×D₄	—	6	1	no	—
124	C₂×C₅×C₄⋊C₄	—	3	1	no	—
125	C₂×C₅×C₄⋊C₄	—	6	1	no	—
126	C₂×C₅×C₄⋊C₄	—	6	1	no	—
127	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
128	C₂×C₄²×C₅	—	3	1	no	—
129	C₅×#103	—	3	2	no	—
130	C₅×#103	—	3	2	no	—
131	C₅×#103	—	3	2	no	—
132	C₅×#103	C₂×D₃	1	2	yes	—
133	C₅×#102	—	3	2	no	—
134	C₅×#102	—	3	2	no	—
135	C₅×#102	—	3	2	no	—
136	C₅×#102	C₂×D₃	1	2	yes	—
137	C₅×#97	—	3	2	no	—
138	C₄×C₅×C₈	—	3	2	no	—
139	#3142	—	3	1	no	Sylow
140	C₂³×C₃×C₅	—	2	1	no	—
141	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₅×D₃	—	2	1	no	—
143	C₃×C₅×Q₈	—	2	1	no	—
144	C₃×C₅×Q₈	—	2	1	no	—
145	C₃×C₅×D₄	—	2	1	no	—
146	C₃×C₅×D₄	—	2	1	no	—
147	C₃×C₅×D₄	—	4	2	no	—
148	C₂×C₃×C₄×C₅	—	2	2	no	—
149	C₂×C₃×C₄×C₅	—	2	1	no	—
150	C₂×C₃×C₄×C₅	—	4	2	no	—
151	C₂×C₃×C₄×C₅	—	4	2	no	—
152	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
153	C₂×C₃×C₄×C₅	#41	1	2	yes	—
154	C₂×C₃×C₄×C₅	#41	1	2	yes	—
155	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
156	C₅×#67	—	4	2	no	—
157	C₅×#67	—	4	2	no	—
158	C₅×#67	—	4	2	no	—
159	C₂×C₅×Dic₃	—	2	2	no	—
160	C₂×C₅×Dic₃	—	2	1	no	—
161	C₂×C₅×Dic₃	—	4	1	no	—
162	C₂×C₅×Dic₃	—	4	1	no	—
163	C₂×C₅×Dic₃	—	4	2	no	—
164	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
165	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
166	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
167	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
168	C₅×D₁₂	—	2	1	no	—
169	C₅×D₁₂	—	2	1	no	—
170	C₄×C₅×D₃	—	4	2	no	—
171	C₅×Dic₆	—	2	1	no	—
172	C₅×Dic₆	—	2	1	no	—
173	C₃×C₅×C₈	—	2	2	no	—
174	C₅×C₃⋊C₈	—	2	2	no	—
175	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
176	C₂×#235	C₂²×C₅	1	1	yes	characteristic
177	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
178	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
179	#947	C₂²×C₅	1	1	yes	characteristic
180	#944	C₂²×C₅	1	1	yes	characteristic
181	#940	C₂²×C₅	1	1	yes	characteristic
182	#939	—	2	1	no	—
183	#939	—	2	1	no	—
184	#936	C₂²×C₅	1	1	yes	characteristic
185	C₄×#67	—	2	1	no	—
186	C₄×#67	—	2	1	no	—
187	C₂×C₄⋊Dic₃	—	2	1	no	—
188	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
189	C₂×Dic₃⋊C₄	—	2	1	no	—
190	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
191	C₂×#208	C₂²×C₅	1	1	yes	characteristic
192	#890	—	2	1	no	—
193	#890	—	2	1	no	—
194	#890	C₂²×C₅	1	2	yes	—
195	#890	C₂²×C₅	1	2	yes	—
196	C₃×#103	C₂²×C₅	1	2	yes	—
197	C₃×#102	C₂²×C₅	1	2	yes	—
198	#835	C₂²×C₅	1	2	yes	—
199	#832	C₂²×C₅	1	2	yes	—
200	#821	C₂²×C₅	1	2	yes	—
201	#816	C₂²×C₅	1	2	yes	—
202	#815	C₂²×C₅	1	2	yes	—
203	C₈×Dic₃	C₂²×C₅	1	2	yes	—
204	#810	C₂²×C₅	1	2	yes	—
205	#809	C₂²×C₅	1	2	yes	—
206	C₅×#41	—	2	2	no	—
207	C₅×#41	—	2	2	no	—
208	C₅×#41	—	6	2	no	—
209	C₅×#41	—	6	2	no	—
210	C₂×C₅×Q₈	—	3	1	no	—
211	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
212	C₂×C₅×D₄	—	2	1	no	—
213	C₂×C₅×D₄	—	3	1	no	—
214	C₂×C₅×D₄	—	6	1	no	—
215	C₂×C₅×D₄	—	6	1	no	—
216	C₂×C₅×D₄	—	6	1	no	—
217	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
218	C₂²×C₄×C₅	—	2	1	no	—
219	C₂²×C₄×C₅	—	2	1	no	—
220	C₂²×C₄×C₅	—	3	1	no	—
221	C₂²×C₄×C₅	—	3	1	no	—
222	C₂²×C₄×C₅	—	6	1	no	—
223	C₂²×C₄×C₅	—	6	1	no	—
224	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
225	C₅×M₁₆	—	2	2	no	—
226	C₅×M₁₆	—	6	2	no	—
227	C₂×C₅×C₈	—	3	2	no	—
228	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
229	C₅×C₄⋊C₄	—	2	1	no	—
230	C₅×C₄⋊C₄	—	3	2	no	—
231	C₅×C₄⋊C₄	—	6	2	no	—
232	C₅×C₄⋊C₄	—	6	2	no	—
233	C₅×C₄⋊C₄	—	6	2	no	—
234	C₅×C₄⋊C₄	—	6	2	no	—
235	C₅×C₄⋊C₄	—	6	1	no	—
236	C₅×C₄⋊C₄	—	6	1	no	—
237	C₅×C₄⋊C₄	—	6	1	no	—
238	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
239	C₅×C₂²⋊C₄	—	6	1	no	—
240	C₅×C₂²⋊C₄	—	6	1	no	—
241	C₅×C₂²⋊C₄	—	6	1	no	—
242	C₅×C₂²⋊C₄	—	6	1	no	—
243	C₄²×C₅	—	3	1	no	—
244	C₄²×C₅	—	3	1	no	—
245	C₄²×C₅	—	3	1	no	—
246	C₄²×C₅	—	3	1	no	—
247	#532	—	3	1	no	—
248	C₂×#125	—	3	1	no	—
249	#491	—	3	2	no	—
250	#490	—	3	2	no	—
251	#488	—	3	2	no	—
252	#488	—	3	2	no	—
253	#417	—	3	1	no	—
254	#417	—	3	1	no	—
255	#417	—	3	1	no	—
256	#417	C₅×D₃	1	1	yes	characteristic, complemented
257	C₄×M₁₆	—	3	1	no	—
258	C₂²×C₃×C₅	—	2	1	no	—
259	C₂²×C₃×C₅	—	2	1	no	—
260	C₂²×C₃×C₅	—	4	1	no	—
261	C₂²×C₃×C₅	—	4	1	no	—
262	C₂²×C₃×C₅	—	4	1	no	—
263	C₂²×C₃×C₅	#124	1	2	yes	—
264	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
265	C₂×C₅×D₃	—	4	1	no	—
266	C₂×C₅×D₃	—	4	1	no	—
267	C₂×C₅×D₃	—	4	1	no	—
268	C₃×C₄×C₅	—	4	1	no	—
269	C₃×C₄×C₅	—	4	2	no	—
270	C₃×C₄×C₅	#124	1	2	yes	—
271	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
272	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
273	C₅×Dic₃	—	2	1	no	—
274	C₅×Dic₃	—	2	1	no	—
275	C₅×Dic₃	—	2	1	no	—
276	C₅×Dic₃	—	2	1	no	—
277	C₅×Dic₃	—	4	1	no	—
278	C₅×Dic₃	—	4	2	no	—
279	C₃×#41	—	2	2	no	—
280	C₃×#41	—	2	2	no	—
281	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
282	C₂×C₃×D₄	—	2	1	no	—
283	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
284	C₂²×C₃×C₄	—	2	1	no	—
285	C₂²×C₃×C₄	—	2	1	no	—
286	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
287	C₂×#67	—	2	1	no	—
288	C₂×#67	—	2	1	no	—
289	C₂×#67	—	2	1	no	—
290	C₂²×Dic₃	—	2	1	no	—
291	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
292	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
293	#235	—	2	2	no	—
294	#235	—	2	2	no	—
295	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
296	C₂×C₄×D₃	—	2	1	no	—
297	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
298	C₃×M₁₆	—	2	2	no	—
299	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
300	C₃×C₄⋊C₄	—	2	1	no	—
301	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
302	#217	—	2	1	no	—
303	#217	—	2	1	no	—
304	(C₂×D₃)⋊C₄	—	2	1	no	—
305	(C₂×D₃)⋊C₄	—	2	1	no	—
306	C₄⋊Dic₃	—	2	1	no	—
307	C₄⋊Dic₃	—	2	2	no	—
308	C₄⋊Dic₃	—	2	2	no	—
309	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
310	Dic₃⋊C₄	—	2	2	no	—
311	Dic₃⋊C₄	—	2	2	no	—
312	Dic₃⋊C₄	—	2	1	no	—
313	Dic₃⋊C₄	—	2	1	no	—
314	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
315	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
316	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
317	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
318	#208	—	2	2	no	—
319	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
320	C₂³×C₅	—	2	1	no	—
321	C₂³×C₅	—	6	1	no	—
322	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
323	C₅×Q₈	—	2	1	no	—
324	C₅×Q₈	—	2	1	no	—
325	C₅×Q₈	—	6	1	no	—
326	C₅×Q₈	—	6	1	no	—
327	C₅×D₄	—	2	1	no	—
328	C₅×D₄	—	2	1	no	—
329	C₅×D₄	—	4	2	no	—
330	C₅×D₄	—	6	1	no	—
331	C₅×D₄	—	6	1	no	—
332	C₅×D₄	—	12	2	no	—
333	C₅×D₄	—	12	2	no	—
334	C₅×D₄	—	12	2	no	—
335	C₂×C₄×C₅	—	2	1	no	—
336	C₂×C₄×C₅	—	2	2	no	—
337	C₂×C₄×C₅	—	3	1	no	—
338	C₂×C₄×C₅	—	3	1	no	—
339	C₂×C₄×C₅	—	3	1	no	—
340	C₂×C₄×C₅	—	3	1	no	—
341	C₂×C₄×C₅	—	4	2	no	—
342	C₂×C₄×C₅	—	4	2	no	—
343	C₂×C₄×C₅	—	6	1	no	—
344	C₂×C₄×C₅	—	6	2	no	—
345	C₂×C₄×C₅	—	12	1	no	—
346	C₂×C₄×C₅	—	12	1	no	—
347	C₂×C₄×C₅	—	12	2	no	—
348	C₂×C₄×C₅	—	12	2	no	—
349	C₂×C₄×C₅	#235	1	2	yes	—
350	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
351	C₂×C₄×C₅	#237	1	2	yes	—
352	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
353	C₅×C₈	—	2	2	no	—
354	C₅×C₈	—	6	2	no	—
355	C₂×#41	—	3	1	no	—
356	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
357	C₂×M₁₆	—	3	1	no	—
358	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
359	C₄⋊Q₈	—	3	1	no	—
360	#127	—	3	1	no	—
361	#125	—	3	2	no	—
362	#125	—	3	2	no	—
363	#125	—	6	1	no	—
364	#125	—	6	1	no	—
365	#124	—	3	1	no	—
366	#124	—	3	1	no	—
367	#121	—	6	1	no	—
368	#121	—	6	1	no	—
369	C₄×D₄	—	6	1	no	—
370	C₄×D₄	—	6	1	no	—
371	C₂×C₄⋊C₄	—	3	1	no	—
372	C₂×C₄⋊C₄	—	6	1	no	—
373	C₂×C₄⋊C₄	—	6	1	no	—
374	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
375	C₂×C₄²	—	3	1	no	—
376	#103	—	3	2	no	—
377	#103	—	3	2	no	—
378	#103	—	3	2	no	—
379	#103	C₂×C₅×D₃	1	2	yes	—
380	#102	—	3	2	no	—
381	#102	—	3	2	no	—
382	#102	—	3	2	no	—
383	#102	C₂×C₅×D₃	1	2	yes	—
384	#97	—	3	2	no	—
385	C₄×C₈	—	3	2	no	—
386	C₂×C₃×C₅	—	2	2	no	—
387	C₂×C₃×C₅	—	8	1	no	—
388	C₂×C₃×C₅	C₂×#124	1	1	yes	characteristic
389	C₂×C₃×C₅	#575	1	1	yes	characteristic
390	C₂×C₃×C₅	#575	1	1	yes	characteristic
391	C₅×D₃	—	8	1	no	—
392	C₂³×C₃	—	2	1	no	—
393	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
394	C₂²×D₃	—	2	1	no	—
395	C₃×Q₈	—	2	1	no	—
396	C₃×Q₈	—	2	1	no	—
397	C₃×D₄	—	2	1	no	—
398	C₃×D₄	—	2	1	no	—
399	C₃×D₄	—	4	2	no	—
400	C₂×C₃×C₄	—	2	2	no	—
401	C₂×C₃×C₄	—	2	1	no	—
402	C₂×C₃×C₄	—	4	2	no	—
403	C₂×C₃×C₄	—	4	2	no	—
404	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
405	C₂×C₃×C₄	C₅×#41	1	2	yes	—
406	C₂×C₃×C₄	C₅×#41	1	2	yes	—
407	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
408	#67	—	4	2	no	—
409	#67	—	4	2	no	—
410	#67	—	4	2	no	—
411	C₂×Dic₃	—	2	2	no	—
412	C₂×Dic₃	—	2	1	no	—
413	C₂×Dic₃	—	4	1	no	—
414	C₂×Dic₃	—	4	1	no	—
415	C₂×Dic₃	—	4	2	no	—
416	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
417	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
418	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
419	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
420	D₁₂	—	2	1	no	—
421	D₁₂	—	2	1	no	—
422	C₄×D₃	—	4	2	no	—
423	Dic₆	—	2	1	no	—
424	Dic₆	—	2	1	no	—
425	C₃×C₈	—	2	2	no	—
426	C₃⋊C₈	—	2	2	no	—
427	C₂²×C₅	—	2	1	no	—
428	C₂²×C₅	—	2	1	no	—
429	C₂²×C₅	—	4	1	no	—
430	C₂²×C₅	—	4	1	no	—
431	C₂²×C₅	—	4	1	no	—
432	C₂²×C₅	—	12	1	no	—
433	C₂²×C₅	—	12	1	no	—
434	C₂²×C₅	—	12	1	no	—
435	C₂²×C₅	#885	1	2	yes	—
436	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
437	C₄×C₅	—	4	1	no	—
438	C₄×C₅	—	4	2	no	—
439	C₄×C₅	—	6	1	no	—
440	C₄×C₅	—	6	1	no	—
441	C₄×C₅	—	6	1	no	—
442	C₄×C₅	—	6	1	no	—
443	C₄×C₅	—	12	1	no	—
444	C₄×C₅	—	12	2	no	—
445	C₄×C₅	#885	1	2	yes	—
446	C₄×C₅	C₂×#235	1	1	yes	characteristic
447	C₄×C₅	C₂×#237	1	1	yes	characteristic
448	#41	—	2	2	no	—
449	#41	—	2	2	no	—
450	#41	—	6	2	no	—
451	#41	—	6	2	no	—
452	C₂×Q₈	—	3	1	no	—
453	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
454	C₂×D₄	—	2	1	no	—
455	C₂×D₄	—	3	1	no	—
456	C₂×D₄	—	6	1	no	—
457	C₂×D₄	—	6	1	no	—
458	C₂×D₄	—	6	1	no	—
459	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	3	1	no	—
463	C₂²×C₄	—	3	1	no	—
464	C₂²×C₄	—	6	1	no	—
465	C₂²×C₄	—	6	1	no	—
466	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
467	M₁₆	—	2	2	no	—
468	M₁₆	—	6	2	no	—
469	C₂×C₈	—	3	2	no	—
470	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	—	3	2	no	—
473	C₄⋊C₄	—	6	2	no	—
474	C₄⋊C₄	—	6	2	no	—
475	C₄⋊C₄	—	6	2	no	—
476	C₄⋊C₄	—	6	2	no	—
477	C₄⋊C₄	—	6	1	no	—
478	C₄⋊C₄	—	6	1	no	—
479	C₄⋊C₄	—	6	1	no	—
480	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
481	C₂²⋊C₄	—	6	1	no	—
482	C₂²⋊C₄	—	6	1	no	—
483	C₂²⋊C₄	—	6	1	no	—
484	C₂²⋊C₄	—	6	1	no	—
485	C₄²	—	3	1	no	—
486	C₄²	—	3	1	no	—
487	C₄²	—	3	1	no	—
488	C₄²	—	3	1	no	—
489	C₃×C₅	#3142	1	1	yes	characteristic, complemented, Hall
490	C₂²×C₃	—	2	1	no	—
491	C₂²×C₃	—	2	1	no	—
492	C₂²×C₃	—	4	1	no	—
493	C₂²×C₃	—	4	1	no	—
494	C₂²×C₃	—	4	1	no	—
495	C₂²×C₃	C₅×#124	1	2	yes	—
496	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
497	C₂×D₃	—	4	1	no	—
498	C₂×D₃	—	4	1	no	—
499	C₂×D₃	—	4	1	no	—
500	C₃×C₄	—	4	1	no	—
501	C₃×C₄	—	4	2	no	—
502	C₃×C₄	C₅×#124	1	2	yes	—
503	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
504	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
505	Dic₃	—	2	1	no	—
506	Dic₃	—	2	1	no	—
507	Dic₃	—	2	1	no	—
508	Dic₃	—	2	1	no	—
509	Dic₃	—	4	1	no	—
510	Dic₃	—	4	2	no	—
511	C₂×C₅	—	2	2	no	—
512	C₂×C₅	—	8	1	no	—
513	C₂×C₅	—	24	1	no	—
514	C₂×C₅	C₂×#885	1	1	yes	characteristic
515	C₂×C₅	#5773	1	1	yes	characteristic
516	C₂×C₅	#5777	1	1	yes	characteristic
517	C₂³	—	2	1	no	—
518	C₂³	—	6	1	no	—
519	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
520	Q₈	—	2	1	no	—
521	Q₈	—	2	1	no	—
522	Q₈	—	6	1	no	—
523	Q₈	—	6	1	no	—
524	D₄	—	2	1	no	—
525	D₄	—	2	1	no	—
526	D₄	—	4	2	no	—
527	D₄	—	6	1	no	—
528	D₄	—	6	1	no	—
529	D₄	—	12	2	no	—
530	D₄	—	12	2	no	—
531	D₄	—	12	2	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	3	1	no	—
535	C₂×C₄	—	3	1	no	—
536	C₂×C₄	—	3	1	no	—
537	C₂×C₄	—	3	1	no	—
538	C₂×C₄	—	4	2	no	—
539	C₂×C₄	—	4	2	no	—
540	C₂×C₄	—	6	1	no	—
541	C₂×C₄	—	6	2	no	—
542	C₂×C₄	—	12	1	no	—
543	C₂×C₄	—	12	1	no	—
544	C₂×C₄	—	12	2	no	—
545	C₂×C₄	—	12	2	no	—
546	C₂×C₄	C₅×#235	1	2	yes	—
547	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
548	C₂×C₄	C₅×#237	1	2	yes	—
549	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
550	C₈	—	2	2	no	—
551	C₈	—	6	2	no	—
552	C₂×C₃	—	2	2	no	—
553	C₂×C₃	—	8	1	no	—
554	C₂×C₃	C₂×C₅×#124	1	1	yes	characteristic
555	C₂×C₃	C₅×#575	1	1	yes	characteristic
556	C₂×C₃	C₅×#575	1	1	yes	characteristic
557	D₃	—	8	1	no	—
558	C₅	#78879	1	1	yes	characteristic, direct product factor, Sylow
559	C₂²	—	2	1	no	—
560	C₂²	—	2	1	no	—
561	C₂²	—	4	1	no	—
562	C₂²	—	4	1	no	—
563	C₂²	—	4	1	no	—
564	C₂²	—	12	1	no	—
565	C₂²	—	12	1	no	—
566	C₂²	—	12	1	no	—
567	C₂²	C₅×#885	1	2	yes	—
568	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
569	C₄	—	4	1	no	—
570	C₄	—	4	2	no	—
571	C₄	—	6	1	no	—
572	C₄	—	6	1	no	—
573	C₄	—	6	1	no	—
574	C₄	—	6	1	no	—
575	C₄	—	12	1	no	—
576	C₄	—	12	2	no	—
577	C₄	C₅×#885	1	2	yes	—
578	C₄	C₂×C₅×#235	1	1	yes	characteristic
579	C₄	C₂×C₅×#237	1	1	yes	characteristic
580	C₃	C₅×#3142	1	1	yes	characteristic, complemented, Sylow
581	C₂	—	2	2	no	—
582	C₂	—	8	1	no	—
583	C₂	—	24	1	no	—
584	C₂	C₂×C₅×#885	1	1	yes	characteristic
585	C₂	C₅×#5773	1	1	yes	characteristic
586	C₂	C₅×#5777	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂×D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#417	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₅×#5832	C₂
hypercenter	C₅×#417	D₃
hypocenter	C₃	C₅×#3142
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#417

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#890	C₂	semidirect
3. C₃×C₅×#417	C₂	semidirect
4. C₅×#5232	C₂	semidirect
5. C₅×#5133	C₂	semidirect
6. C₅×Dic₃×M₁₆	C₂	semidirect
7. C₅×#4966	C₂	semidirect
8. C₅×#4800	C₂	semidirect
9. C₅×#4797	C₂	semidirect
10. C₅×#4768	C₂	semidirect
11. C₅×#4764	C₂	semidirect
44. #78879	C₅	direct (N × H)
54. C₅×#417	D₃	semidirect
98. C₂×#890	C₂×C₅	semidirect
99. C₃×#417	C₂×C₅	semidirect
100. #5232	C₂×C₅	semidirect
101. #5133	C₂×C₅	semidirect
102. Dic₃×M₁₆	C₂×C₅	semidirect
103. #4966	C₂×C₅	semidirect
104. #4800	C₂×C₅	semidirect
105. #4797	C₂×C₅	semidirect
106. #4768	C₂×C₅	semidirect
107. #4764	C₂×C₅	semidirect
256. #417	C₅×D₃	semidirect
489. C₃×C₅	#3142	semidirect
558. C₅	#78879	direct (N × H)
580. C₃	C₅×#3142	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×#890	2
C₃×C₅×#417	2
C₅×#5232	2
C₅×#5133	2
C₅×Dic₃×M₁₆	2
C₅×#4966	2
C₅×#4800	2
C₅×#4797	2
C₅×#4768	2
C₅×#4764	2
C₅×#3142	3
#78879	5

Subgroups — C5×#78879 #14438649

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#78879 #14438649